text:
1. Home
2. Crushing Plant
3. combination 5c3

# combination 5c3

Giant pandas are black and white and loved all over. The giant panda is a national treasure in China and is therefore protected by law in its bamboo forest home. This unique bear has long been revered by the Chinese and can be found in Chinese art dating back thousands of years. The Chinese call their beloved pandas large bear-cats

Send Email:[email protected]

### giant pandafacts and pictures -animals

Giant Panda High in dense bamboo forests in the misty, rainy mountains of southwestern China lives one of the world's rarest mammals: the giant panda, also called the panda. Only about 1,500 of

### giant panda- facts, diet, habitat & pictures on animalia.bio

The Giant panda is a bear of medium to large size with a large head, small eyes, long muzzle, large nose and short tail. It has a very good sense of smell. It has large jaws with strong muscles, and together with its flat molars, is able to crush bamboo leaves and stems

### giant panda| facts, habitat, population, & diet | britannica

Giant panda, (Ailuropoda melanoleuca), also called panda bear, bearlike mammal inhabiting bamboo forests in the mountains of central China. Its striking coat of black and white, combined with a bulky body and round face, gives it a captivating appearance that has endeared it to people worldwide

### giant panda| species | wwf - world wildlife fund

A newborn panda is about the size of a stick of butter—about 1/900th the size of its mother—but females can grow up to about 200 pounds, while males can grow up to about 300 pounds as adults. These bears are excellent tree climbers despite their bulk

### giant pandas— all the things you want to know

Giant pandas love climbing trees, particularly the playful cubs. Giant pandas spend as long as 14 hours eating per day as the bamboo provides a low amount of calories so they get hungry very quickly. When they are full, they will sleep for 2 to 4 hours. When they wake up again, they will look for more food

### 50giant panda factsthat you never knew about

There may be two subspecies of giant pandas. These panda subspecies are determined by their distinct color patterns, cranial sizes, and population genetics. Although they share close similarities with giant pandas, their minor differences set them apart. For one, the A. m. melanoleuca refers to the native pandas in Sichuan

### giant panda-wikipedia

The giant panda (Ailuropoda melanoleuca; Chinese: 大熊猫; pinyin: dàxióngmāo), also known as the panda bear or simply the panda, is a bear native to South Central China. It is characterised by large, black patches around its eyes, over the ears, and across its round body. The name "giant panda" is sometimes used to distinguish it from the red panda, a neighboring musteloid

### giant panda|smithsonian's national zoo

A giant panda's digestive system is more similar to that of a carnivore than an herbivore, and so much of what is eaten is passed as waste. To make up for the inefficient digestion, a panda needs to consume a comparatively large amount of food—from 20 to 40 pounds of bamboo each day—to get all its nutrients. To obtain this much food means

### giant panda| national geographic

Giant pandas are solitary. They have a highly developed sense of smell that males use to avoid each other and to find females for mating in the spring. After a five-month pregnancy, females give

### giant panda| species | wwf - world wildlife fund

A newborn panda is about the size of a stick of butter—about 1/900th the size of its mother—but females can grow up to about 200 pounds, while males can grow up to about 300 pounds as adults. These bears are excellent tree climbers despite their bulk

### giant panda| facts, habitat, population, & diet | britannica

Giant panda, (Ailuropoda melanoleuca), also called panda bear, bearlike mammal inhabiting bamboo forests in the mountains of central China. Its striking coat of black and white, combined with a bulky body and round face, gives it a captivating appearance that has endeared it to people worldwide

### giant pandafacts and pictures -animals

Giant Panda High in dense bamboo forests in the misty, rainy mountains of southwestern China lives one of the world's rarest mammals: the giant panda, also called the panda. Only about 1,500 of

### giant panda|san diego zooanimals & plants

Giant pandas are black and white and loved all over. The giant panda is a national treasure in China and is therefore protected by law in its bamboo forest home. This unique bear has long been revered by the Chinese and can be found in Chinese art dating back thousands of years. The Chinese call their beloved pandas large bear-cats

### giant panda- facts, diet, habitat & pictures on animalia.bio

The Giant panda is a bear of medium to large size with a large head, small eyes, long muzzle, large nose and short tail. It has a very good sense of smell. It has large jaws with strong muscles, and together with its flat molars, is able to crush bamboo leaves and stems

### giant pandas— all the things you want to know

Giant pandas love climbing trees, particularly the playful cubs. Giant pandas spend as long as 14 hours eating per day as the bamboo provides a low amount of calories so they get hungry very quickly. When they are full, they will sleep for 2 to 4 hours. When they wake up again, they will look for more food

### 50giant panda factsthat you never knew about

There may be two subspecies of giant pandas. These panda subspecies are determined by their distinct color patterns, cranial sizes, and population genetics. Although they share close similarities with giant pandas, their minor differences set them apart. For one, the A. m. melanoleuca refers to the native pandas in Sichuan

### giant panda-wikipedia

The giant panda (Ailuropoda melanoleuca; Chinese: 大熊猫; pinyin: dàxióngmāo), also known as the panda bear or simply the panda, is a bear native to South Central China. It is characterised by large, black patches around its eyes, over the ears, and across its round body. The name "giant panda" is sometimes used to distinguish it from the red panda, a neighboring musteloid

### giant panda|smithsonian's national zoo

A giant panda's digestive system is more similar to that of a carnivore than an herbivore, and so much of what is eaten is passed as waste. To make up for the inefficient digestion, a panda needs to consume a comparatively large amount of food—from 20 to 40 pounds of bamboo each day—to get all its nutrients. To obtain this much food means

### giant panda| national geographic

Giant pandas are solitary. They have a highly developed sense of smell that males use to avoid each other and to find females for mating in the spring. After a five-month pregnancy, females give

### giant panda| species | wwf - world wildlife fund

A newborn panda is about the size of a stick of butter—about 1/900th the size of its mother—but females can grow up to about 200 pounds, while males can grow up to about 300 pounds as adults. These bears are excellent tree climbers despite their bulk

### giant panda| facts, habitat, population, & diet | britannica

Giant panda, (Ailuropoda melanoleuca), also called panda bear, bearlike mammal inhabiting bamboo forests in the mountains of central China. Its striking coat of black and white, combined with a bulky body and round face, gives it a captivating appearance that has endeared it to people worldwide

### 6 choose 3 or 6c3 work with steps - getcalc.com

6 CHOOSE 3 = 20 possible combinations. 20 is the total number of all possible combinations for choosing 3 elements at a time from 6 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 6 CHOOSE 3 can also be written as 6C 3 in the format of nCr or nCk

### c program to find the value of ncr(combination) using

To find combination we use the concept of finding factorial of a number and use the standard formula for nCr=n!/r!* (n-r)!. Dry Run of the Program Take input n=5 and r=3 ncr=fact (n)/fact (r)*fact (n-r) i.e. npr=fact (5)/fact (3)*fact (5-3) i.e. npr=fact (5)/fact (3)*fact (2)

### 5c3 - step-by-step calculator - symbolab

Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step

### 5.4: combinations - mathematics libretexts

A combination of a set of elements is an arrangement where each element is used once, and order is not important. The Number of Combinations of n Objects Taken r at a Time \[\mathrm{nCr}=\frac{\mathrm{n} !}{(\mathrm{n}-\mathrm{r}) ! \mathrm{r} !} ... ( 4C2 ) ( 5C3 ) Since our next task is to make word sequences out of these letters, we multiply

### 5 combinations of 3 - math celebrity

A combination is a way to order or arrange a set or number of things (uniquely) The formula for a combination of choosing r unique ways from n possibilities is: n C r = n! r!(n - r)! where n is the number of items and r is the unique arrangements. Plugging in our numbers of n = 5 and r = 3, we get:

### combinations formula with solved example questions

The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set. It shows how many different possible subsets can be made from the larger set. It should be noted that the formula for permutation and combination are interrelated and are mentioned below

### permutation and combination(definition, formulas & examples)

Permutation and combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called combination

### permutation and combinationpractice questions

Here we need the number of possible combinations of 3 out of 5 freshmen,5C3, and the number of possible combinations of 3 out of the 15 sophomores and juniors, 15C3. Note that we want 3 freshmen and 3 students from the other classes. Therefore, we multiply the number of possible groups of 3 of the 5 freshmen times the number of possible groups

### permutations and combinations and theti-84 plus -dummies

You can work permutations and combinations on the TI-84 Plus calculator. A permutation, denoted by nPr, answers the question: “From a set of n different items, how many ways can you select and order (arrange) r of these items?” One thing to keep in mind is that order is important when working with permutations. Permutation […]

### nominal wall thickness stainless pipe - sch40 steel pipes

nominal wall thickness stainless pipe. Description: Pipes - Nominal Wall Thickness - Engineering ToolBox; Stainless Steel Pipes - Dimensions and Weights ANSI/ASME 36.19 - Dimensions, wall thickness and weights of stainless steel pipes according to ASME B36.19 - Stainless Steel Pipe; Steel Pipe Dimensions - ANSI Schedule 40 - Internal and external diameters, areas, weights, volumes an

### 5.4:combinations- mathematics libretexts

A combination of a set of elements is an arrangement where each element is used once, and order is not important. The Number of Combinations of n Objects Taken r at a Time \[\mathrm{nCr}=\frac{\mathrm{n} !}{(\mathrm{n}-\mathrm{r}) ! \mathrm{r} !} ... ( 4C2 ) ( 5C3 ) Since our next task is to make word sequences out of these letters, we multiply

### theimportance of permutations and combinations in modern

Therefore 5C3 would also equal ten. The number of combinations is always smaller than the number of permutations for the same problem. Another example of a combination is the lottery. In the California Lotto, it is not required that you pick the numbers in the order that they appear

### iterate through allcombinationsof features by selection

Thanks for your reply. I will try it. And I have one more question. These sample code is combination for 5C2. I want to create all combiantions 5C3 , 5C4 , 5C5. Please let me know your advice and comments. – user26117 Jan 23 '14 at 11:55

### combinatorics -permutations - combinations- mathematics

The solution is quite clear: 3600 = 3C2 * 5C3 * 5!. But, why I do not get the same result, if the method of permutations is used instead: 5*4*3*3*2 = 360 (I choose 3 out of five consonants and 2 out of three vowels)? If I operate with numbers, I can get the same result using either methods (permutationa, combinations) - for exemple, how many

### 4c3+5c3+6c3+7c3+8c3+9c3 will behere ncr = n!/[r!*(n-r

28 Nov 2012 combination 4C3+5C3+6C3+7C3+8C3+9C3 will be here nCr = n!/[r!*(n-r)!] and ! is factorial for example 6! = 6*5*4*3*2*1 and 5! = 5*4*3**2*1 OPtion 1) 134 2) 209 3) 311 4) 349 5) 396 6) 456 7) 549 8) 679 9) 999 10) none of these Solution. it is important to notice that nCr+nC(r-1)=(n+1)Cr

### permutation and combination calculator

Permutation (nPr) and Combination (nCr) calculator uses total number of objects n and sample size r, r\leq n, and calculates permutations or combinations of a number of objects r, are taken from a given set n. It is an online math tool which determines the number of combinations and permutations that result when we choose r objects

### combinations- selecting a subset regardless to order

The elements of a subset are not ordered. When thinking of combinations, do not think about order! Combination A combination containing k objects is a subset containing k objects.. We want to develop a formula for computing the number of combinations of n objects taken k at a time without actually listing the combinations or subsets

### 5.3exercise 3 – permutations and combinations| finite math

24) Out of 30 applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female graduates, 2 are bilingual women, 6 are bilingual graduates and 2 are bilingual female graduates

### binomial expansion, what is thevalue of 5c2 (ncr

May 01, 2010 · 5C0 5C1 5C2 5C3 5C4 5C5 1 5 10 10 5 1. 4 0. How do you think about the answers? You can sign in to vote the answer. Sign in. Minh. 1 decade ago. 5C2 means how many ways there are to choose 2 terms in 5 different terms, PAscal's triangle just an name or amazing discovery that guide you to work out the answer, you should understand the meaning of


text:
Article Contents
Article Contents

# Correlation priors

• We propose a new class of Gaussian priors, correlation priors. In contrast to some well-known smoothness priors, they have stationary covariances. The correlation priors are given in a parametric form with two parameters: correlation power and correlation length. The first parameter is connected with our prior information on the variance of the unknown. The second parameter is our prior belief on how fast the correlation of the unknown approaches zero. Roughly speaking, the correlation length is the distance beyond which two points of the unknown may be considered independent.
The prior distribution is constructed to be essentially independent of the discretization so that the a posteriori distribution will be essentially independent of the discretization grid. The covariance of a discrete correlation prior may be formed by combining the Fisher information of a discrete white noise and different-order difference priors. This is interpreted as a combination of virtual measurements of the unknown. Closed-form expressions for the continuous limits are calculated. Also, boundary correction terms for correlation priors on finite intervals are given.
A numerical example, deconvolution with a Gaussian kernel and a correlation prior, is computed.
Mathematics Subject Classification: Primary: 65Q10, 60G10; Secondary: 42A38.

 Citation:

•  [1] D. Calvetti and E. Somersalo, "Introduction to Bayesian Scientific Computing - Ten Lectures on Subjective Computing," Springer, 2007. [2] I. I. Gikhman and A. V. Skorokhod, "The Theory of Stochastic Processes I," Springer, 1974. [3] I. S. Gradshteyn and I. M. Ryzhik, "Table of Integrals, Series and Products," Academic Press, 1965. [4] J. Kaipio and E. Somersalo, "Statistical and Computational Inverse Problems," Springer, 2005. [5] J. P. Kaipio, V. Kolehmainen, M. Vauhkonen and E. Somersalo, Inverse problems with structural prior information, Inverse Problems, 15 (1999), 713-729.doi: 10.1088/0266-5611/15/3/306. [6] S. Lasanen and L. Roininen, "Statistical Inversion with Green's Priors," 5th Int. Conf. Inv. Prob. Eng. Proc., Cambridge, 2005. [7] M. Orispää and M. Lehtinen, Fortran linear inverse problem solver, Inverse Problems and Imaging, 4 (2010), 482-503. [8] A. Tarantola, "Inverse Problem Theory. Methods for Data Fitting and Model Parameter Estimation," Elsevier, 1987. [9] A. Tarantola and B. Valette, Inverse Problems = Quest for Information, Journal of Geophysics, 50 (1982), 159-170. [10] R. L. Wolpert and M. S. Taqqu, Fractional Ornstein-Uhlenbeck Lévy processes and the Telecom process: Upstairs and downstairs, Signal Processing, 85 (2005), 1523-1545.doi: 10.1016/j.sigpro.2004.09.016.

format: plain


text:
# Rooks on a 15x15 chessboard

On a 15x15 chessboard there are 15 rooks that do not attack each other (via ordinary rook moves). Then each of the rooks makes one move like that of a knight.

Is it possible that after all this is done, the 15 rooks still do not attack each other (via ordinary rook moves)?

• essentially, create a path of fifteen moves for a knight ending on the starting square on a 15x15 chessboard such that no position is in the same column or row as a different position – Slepz Feb 23 '16 at 20:15
• Possibly relevant: I think this is possible for any $N\times N$ board with $N$ a multiple of 4. – dpwilson Feb 23 '16 at 20:44
• @dpwilson There's an easy way to do that - four knights on a diagonal in a 4x4 can move to the other diagonal. Have all the knights of the $N\times N$ board be on a diagonal. Treat each group of four knights as if they were on a 4x4. – Rob Watts Feb 23 '16 at 20:54
• @RobWatts: Yes, that is why I proposed that it is possible. – dpwilson Feb 23 '16 at 21:06
• @dpwilson: $6 \times 6$ is also possible. Start with a diagonal, then move $a1 \to b3$, $b2 \to d1$, $c3 \to a2$, and similarly with the next three ($d4 \to f5$, $e5 \to c6$, $f6 \to e4$). This means any even number is achievable (except $2 \times 2$ of course). – Tyler Seacrest Feb 23 '16 at 23:36

No

Since there is (initially and finally) a rook in each row and column, we can say the sum of all rooks' X and Y positions must be equal to 2 $\times$ (15 + 14 + ... + 1) = 120.

A knight's move will increment the rook's (X + Y) by +3, +1, -1, or -3, all of which are odd numbers.

The sum of 15 odd numbers (15 knight moves) is an odd number.

Since we are performing 15 moves, we are adding an odd number to the sum of the rooks' X and Y positions.

The final sum of the rooks' X and Y positions cannot be equal to the initial sum since performing 15 knight moves adds a non-zero number to that sum.

Since the initial sum is 120, the final sum cannot be 120 and therefore can't be a legal (non-attacking) position.

This proof can be extended to any $N\times N$ board where $N$ is odd.

• An alternative but similar approach would be to say that if there are an odd number of knight moves, either an odd number must have a single-space vertical move, or an odd number must have a single-space horizontal move. If the number of short vertical moves is odd, the number of rooks moving from even to odd rows won't match the number moving from odd to even. Likewise for horizontal moves and even/odd columns. – supercat Feb 24 '16 at 16:26

Yes, in at least three cases that I can think of:

1. The board wraps itself - i.e. from the top row, move 1 up, and you are now on the bottom row. In that case, all of the rooks make an identical move, and they are still safe.

2. You said all the rooks make one move. You didn't say, that they make ONLY one move. So, the rooks simple move out, then back to their original position.

3. The rooks move like knights. Presumably they also take like knights. In that case, I think the solution is obvious ;).


text:
Motivated by the puzzle Secret Santa 🎅, whose solution is quite well known, I propose a far harder puzzle (I think):

A group of $N$ people place their names into a hat. Each person draws a name at random to decide who they will give a gift to. What is the probability that at least one pair of people end up picking each other? What is the expected number of such pairs?

So for example, if $N = 2$, then there is a $\frac{1}{2}$ chance of such a pair occurring, as either each person picks themselves or they pick each other and create a pair. Therefore the expected number is also $\frac{1}{2}$.

If $N = 3$ it is possible to check that the probability is $\frac{1}{3}$, and the expected number of such pairs is $1$. (I am not sure of this, someone check it please)

In general, one might ask this for an arbitrary cycle, i.e. what is the probability and expected number of $k$ cycles of gifting occurring among $N$ people.


text:
# Different axiomatizations of set equality

I've seen two definitions (or axioms?) of set equality:

1. $a=b \Leftrightarrow (\forall x : x \in a \Leftrightarrow x \in b)$
2. $a=b \Leftrightarrow (\forall x : a \in x \Leftrightarrow b \in x)$

That is, two sets are considered equal, if

1. They contain the same sets
2. They are contained in the same sets

ZFC seems to include the first version.

My question is: what is the connection between these? Does one follow from another?

I suspect the first version to be an axiom of (any) set theory, while the second is a consequence of first-order axioms for equality, like $a=b \Leftrightarrow [\phi(a) \leftrightarrow \phi(b)]$. In this case, why we need a special axiom in set theory? Doesn't it follow from equality axioms?

• Where have you seen (2) as an axiom? Not a theorem, an axiom. – David C. Ullrich Feb 7 '16 at 18:19
• @DavidC.Ullrich I've seen that far more rarely than the first version, but wikipedia mensions it as an axiom: en.wikipedia.org/wiki/… – lisyarus Feb 7 '16 at 18:22
• If I'm reading that article correctly, under "FOL with equality" it's said to be a "Logic axiom", by which they mean it follows from standard FOL with equality, as it should, not that it's an axiom of set theory. I see it listed as a "set theory axiom" under FOL without equality. If for whatever reason we want to talk aobut equality of sets in FOL wihtout equality then yes of course we need to add it as an axiom to our set theory. – David C. Ullrich Feb 7 '16 at 18:38
• The second axiom is the Leibnizian principle of Identity of indiscernibles. – Pedro Sánchez Terraf Feb 7 '16 at 19:46
• You may want to take a look at page 29 of Schechter’s Handbook of Analysis and its Foundations. He discusses more in depth the two approaches from the Wikipedia page: (a) starting from a first-order theory with equality and requiring that this equality coincides with (one of) the equality induced by $\in$; (b) starting from a first-order theory without equality, defining the equality to be the one induced by $\in$ and requiring that it behaves like a proper equality. – Vej Kse Feb 14 '16 at 15:25

## 2 Answers

The situation is rather simple at a higher level of abstraction. We are interested here in a collection of objects U, equipped with some binary relation $\prec$, from which we can define two equivalence relations on U:

• $b_0\simeq b_1$ iff $\forall a, a \prec b_0 \iff a \prec b_1$;
• $a_0\backsimeq a_1$ iff $\forall b, a_0 \prec b \iff a_1 \prec b$.

An equality on U must be an equivalence relation $=$ for which all formulae all stable under substitution of equals by equals. In general, we would require that all operations preserve the equality and all relations are invariant under it. Here, we just need $\prec$ to be invariant under $=$, i.e.:

1. $b_0 = b_1 \Longrightarrow b_0 \simeq b_1$;
2. $a_0 = a_1 \Longrightarrow a_0 \backsimeq a_1$.

These are the left-to-right directions of your conditions 1 and 2.

Now, it’s obvious that doing the following is equivalent:

• Start from $U$, $\prec$ and an equality $=$ (satisfying 1 and 2), and require that $=$ coincides with $\simeq$ (i.e. the reverse of 1 holds).
• Start from $U$, $\prec$, define $=$ to be $\simeq$ (so that 1 and its reverse hold) and, to ensure that it is a proper equality, require condition 2.

Most often, people do the first and call the reverse of 1 (or the equivalence) the Axiom of Extensionality; some (like Takeuti and Zaring in Introduction to Axiomatic Set Theory, pp. 7-8 or Schechter in Handbook of Analysis and its Foundations, p. 29) do the second and call 2 the Axiom of Extensionality.

As Eric Wofsey mentions, the reverse of 2 holds if singletons exist, i.e. if for any $a$, there is a $b$ such that $x \prec b$ iff $x = a$: we apply the definition of $a_0 \backsimeq a_1$ to that singleton $b$ obtained from $a_0$ (or $a_1$). If we add everywhere the assumption of the existence of singletons, the two approaches above are thus also equivalent to

• Start from $U$, $\prec$, define $=$ to be $\backsimeq$ (so that 2 and its reverse hold), and require 1 and its reverse.

The equality axioms of first-order logic are $a=b \Rightarrow [\phi(a) \Leftrightarrow \phi(b)]$, not $a=b \Leftrightarrow [\phi(a) \Leftrightarrow \phi(b)]$. So only the $\Rightarrow$ direction of (1) and (2) follows from general first order-logic, whereas the $\Leftarrow$ direction has real content specific to set theory. I've never seen (2) actually stated as an axiom of set theory. However, it follows from the usual axioms of set theory. For instance, Pairing says that for any $a$, there exists a set $x$ such that for all $c$, $c\in x \Leftrightarrow (c=a\vee c=a)$. If $a\in x\Leftrightarrow b\in x$, plugging in the $x$ obtained from Pairing above gives that $b\in x$ and hence $b=a$. This gives the $\Leftarrow$ direction of (2); as mentioned before, the $\Rightarrow$ direction is just part of first-order logic and has nothing to do with set theory in particular.

Note, however, that (2) does not imply (1), even in the presence of all the other axioms of set theory (and thus by symmetry, (1) does not imply (2) without assuming any additional axioms). Indeed, (2) follows from Pairing and no other axioms, so any model of all the axioms of set theory except (1) will still satisfy (2).


text:
User gerard - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T08:40:50Z http://mathoverflow.net/feeds/user/26503 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/129580/what-is-known-about-the-area-of-the-symmetric-pythagorean-tree What is known about the area of the symmetric Pythagorean tree? Gerard 2013-05-03T20:52:57Z 2013-05-10T10:13:27Z
What is known about the area of the symmetric Pythagorean tree? (Closed unit square as base, area of enclosed triangles not included.) The problem in calculating the area is that squares start to overlap from the sixth iteration onwards.

Without much effort it can be computed that height is 4 and breadth is 6, so an upper bound for the area is 24. Wikipedia reports that lower and upper bounds can with some effort be tightened to 5 and 18, respectively. The accompanying Wikipedia talk page reports on numerical approximations (pixel counts) that end somewhere near 14. Other than that, no trace of a hint of an exact answer in the literature.

Seems like a simple high-school problem. On closer inspection I believe it is not, due to the problem of overlapping squares.
 http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values A function that is defined everywhere but has unknown values Gerard 2012-09-14T11:13:54Z 2012-09-15T20:00:10Z
For pedagogical purposes I am looking for a function $\mathbb{N}\to\mathbb{N}$ that is defined everywhere but has most of its values unknown. Although such a function cannot be simple by definition, I nevertheless hope that there is such a function that is simple to explain.

I have listed a few examples myself which I am not very satisfied with for various reasons:

The halting function. This function is one of the uncomputable functions (probably the only uncomputable function) that is most easy to explain.

My problem with this one is that it involves computability theory, and I do not want to draw in computability if that is not necessary.

The busy beaver function. Also an uncomputable function. Which is a bit harder to explain.

The function that is $1$ everywhere if Goldbach's conjecture is true, and $0$ everywhere if Goldbach's conjecture is false.

Problem: this is a constant function.

The function that is $1$ if $n$ is even and every even number is the sum of $n$ primes, or $n$ is odd and every odd number is the sum of $n$ primes. (And $0$ in all other cases.) For $n=2$ I believe this is the Goldbach conjecture, and for $n=3$ I believe this is the weak Goldbach conjecture. So this function is already a headeache for $n=2,3$, let alone for $n>3$.

Personally, this would be my favourite if it wasn't so baroque and over the top.

The Collatz characteristic function. $1$ if the Collatz sequence converges, $0$ if it does not.

Problem: too easy to verify on individual arguments. And it has little illustrative value because the Collatz characteristic function seems to be $1$ everywhere. (Emphasis on "seems".)

The function $\mathbb{N}\to\mathbb{N}_0:n\mapsto \mbox{number of living people aged}(n)$.

Problem: depends on the real world. Not really a pure Platonic math function. (And function values change constantly throughout time.)

BTW: My question rules out computable functions. Values of computable functions on their domain of definition are known due to, e.g., dovetailing. (So strictly speaking, the 3rd item should be ruled out for this reason since constant functions are computable.)

Thank you.
 http://mathoverflow.net/questions/129580/what-is-known-about-the-area-of-the-symmetric-pythagorean-tree Comment by Gerard Gerard 2013-05-09T09:14:11Z 2013-05-09T09:14:11Z Why I do care? Because it is a challenging problem I am thinking about for a long while, got no further, and decided to share. Simple. http://mathoverflow.net/questions/129580/what-is-known-about-the-area-of-the-symmetric-pythagorean-tree Comment by Gerard Gerard 2013-05-03T23:10:14Z 2013-05-03T23:10:14Z Okay, incorporated link. http://mathoverflow.net/questions/129580/what-is-known-about-the-area-of-the-symmetric-pythagorean-tree Comment by Gerard Gerard 2013-05-03T22:26:24Z 2013-05-03T22:26:24Z "My guess". Wrong guess, do to neglect of overlap. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107172#107172 Comment by Gerard Gerard 2012-09-17T09:18:35Z 2012-09-17T09:18:35Z Thanks for slimming down the example. I took note. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107284#107284 Comment by Gerard Gerard 2012-09-17T07:27:30Z 2012-09-17T07:27:30Z Fair enough. I agree we (I) began to move to shaky grounds, which led to all kinds of suggestions. Nevertheless, I spotted an answer I think can use, so am more than satisfied. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values Comment by Gerard Gerard 2012-09-16T09:27:17Z 2012-09-16T09:27:17Z Fair enough. I agree we (I) began to move to shaky grounds, which led to all kinds of suggestions. Nevertheless, I spotted an answer I can use, so am more than satisfied. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107233#107233 Comment by Gerard Gerard 2012-09-15T16:07:04Z 2012-09-15T16:07:04Z Thanks. Example 1 is a real-word example, like my own Example 6. Point 2 is indeed treated later on in the course. http://mathoverflow.net/questions/9754/magic-trick-based-on-deep-mathematics Comment by Gerard Gerard 2012-09-15T14:37:08Z 2012-09-15T14:37:08Z Well, how you've put your question is certainly a nice trick to generate much page views. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107204#107204 Comment by Gerard Gerard 2012-09-15T14:34:04Z 2012-09-15T14:34:04Z With Polignac's conjecture I think I have found my example. My nr. 2 (with attractive demonstrative features) is Yoav Kallus' suggestion on Conway's Game of Life "halting problem". Joel David Hamkins'solution on true but principally unprovable statements seems for what I can see the most accurate but less suitable for classroom discussion. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107218#107218 Comment by Gerard Gerard 2012-09-14T23:44:42Z 2012-09-14T23:44:42Z Might be a solution but too involved for freshman computer science. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107178#107178 Comment by Gerard Gerard 2012-09-14T23:34:26Z 2012-09-14T23:34:26Z Still, this solution, notwithstanding that it excels for classroom use, still involves an argument that is linked to computability, which is something I'd rather like to avoid. (It is OK if you call me picky.) http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107167#107167 Comment by Gerard Gerard 2012-09-14T23:23:18Z 2012-09-14T23:23:18Z I don't understand why this answer on diagonal Ramsey numbers is upvoted so many times. Although function values are difficult to compute, the function itself is computable (cf. Remark Jason Rute). http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values Comment by Gerard Gerard 2012-09-14T23:17:40Z 2012-09-14T23:17:40Z You're right. Every constant function is computable. So my own example (3) does not qualify. I already complained that I am not satisfied with (3) because it is a constant function. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107209#107209 Comment by Gerard Gerard 2012-09-14T23:12:44Z 2012-09-14T23:12:44Z Same considerations as with Barry's solution: I want to know for sure that for enough $n$ it is common knowledge that $f(n)$ is a proposition that until now lacks proof or disproof. http://mathoverflow.net/questions/107163/a-function-that-is-defined-everywhere-but-has-unknown-values/107204#107204 Comment by Gerard Gerard 2012-09-14T23:10:52Z 2012-09-14T23:10:52Z Very close in spirit. But then I want to know for sure that for enough $n$, the proposition $f(n)=1$ is unknown. I.e., I want to know for sure that for enough $n$ it is common knowledge that $f(n)$ is a proposition that lacks proof or disproof until now. (Like is the case with, e.g., Goldbach's conjecture.) How do I know?


text:
## Stream: new members

### Topic: Mac installation

#### David Michael Roberts (Oct 08 2018 at 08:51):

I notice @Scott Morrison put up a nice short video on getting required dependencies, VS Code and Lean installed on Mac, here: https://www.youtube.com/watch?v=k8U6YOK7c0M

#### Kevin Buzzard (Oct 08 2018 at 08:56):

I also rewrote my cheap Windows installation page: https://xenaproject.wordpress.com/a-cheap-hack-to-get-lean-and-mathlib-running-on-a-windows-10-machine/ . I intend over the next day or two to make a link at the top of my blog pointing to various installation pages / posts, which are now randomly scattered online.

#### Scott Morrison (Oct 08 2018 at 09:49):

I'm still going to make the corresponding video for installation on Windows!

#### Kevin Buzzard (Oct 08 2018 at 10:11):

Be sure to ping me when you do. I am expecting this question to come up a fair bit at Imperial over the next few weeks

#### Scott Morrison (Oct 09 2018 at 03:35):

Okay, the video for installing on Windows 10 is now up! https://www.youtube.com/watch?v=2f_9Zetekd8&feature=youtu.be

#### Mario Carneiro (Oct 09 2018 at 05:16):

@Kevin Buzzard Would it be possible for you to write a page for mathlib that links to the various tutorials and videos for installing lean and/or mathlib?

#### Kevin Buzzard (Oct 09 2018 at 06:09):

I will try to find the time today. On this thread we have Scott's two videos, there are my cheap and less cheap blog posts, there is some elan link somewhere... Is that it?

#### Kevin Buzzard (Oct 09 2018 at 06:09):

There's the official instructions of course!

#### Mario Carneiro (Oct 09 2018 at 06:32):

It would also be good to have follow on instructions for people who followed Scott's instructions and want mathlib

#### Scott Morrison (Oct 09 2018 at 06:58):

Yes, I was thinking that's a separate video, that applies equally on Windows and macos, because it happens entirely within VS Code.

#### Scott Morrison (Oct 09 2018 at 06:59):

(That's part of the reason for setting up a usable terminal on Windows, so afterwards everything can be done from VS Code.)

#### Scott Morrison (Oct 09 2018 at 06:59):

(Although it occurs to me the Windows video should have included that one extra step, to hook up git bash as the default terminal instead of powershell.)

#### Johan Commelin (Oct 09 2018 at 08:08):

@Neil Strickland This thread contains two videos with installation instructions. Kevin is also updating his instructions. Would you mind adding links to these videos etc on your MO post? I think you pointed out a very good issue (that installation was horribly difficult). I also hope that we are addressing them now. What do you think?

#### David Michael Roberts (Oct 09 2018 at 10:49):

Maybe the windows video should go in its own topic, for ease of finding?

#### Scott Morrison (Oct 09 2018 at 11:06):

Hopefully there will be permanent links to these soon from more prominent places...

#### Kevin Buzzard (Oct 09 2018 at 12:27):

I am just going to have an "installing lean" link at the top of my blog with multiple options

#### David Michael Roberts (Oct 10 2018 at 04:51):

OK, so I have actually installed Lean and VS code as per @Scott Morrison 's video, and now want to do some mathlibbing. But I am told by @Kevin Buzzard 's post https://xenaproject.wordpress.com/2017/12/02/how-to-install-mathlib-and-keep-it-up-to-date/ that I probably am better off with the nightly build of lean, so that mathlib will have the latest and greatest stuff. After following the instructions at that post:

leanpkg new my_project
cd my_project
leanpkg build

I get

davidroberts\$ leanpkg build
configuring my_project 0.1
mathlib: trying to update _target/deps/mathlib to revision 905345a2ceaa5d0c7bc2f6310026961416b2cae4
> git checkout --detach 905345a2ceaa5d0c7bc2f6310026961416b2cae4    # in directory _target/deps/mathlib
HEAD is now at 905345a fix(data/array/lemmas,...): fix build
> lean --make src

and this was much much quicker than I thought it would be. Is it working or no?

#### Scott Morrison (Oct 10 2018 at 04:51):

It could well be.

#### Scott Morrison (Oct 10 2018 at 04:51):

leanpkg build, and lean --make src don't compile all of mathlib

#### Scott Morrison (Oct 10 2018 at 04:51):

They only compile those parts of it which are imported by some file in src/.

#### Scott Morrison (Oct 10 2018 at 04:51):

This might mean nothing at all at the moment.

#### Scott Morrison (Oct 10 2018 at 04:52):

Add a file under src/ that imports, e.g. data.nat.prime.

#### Scott Morrison (Oct 10 2018 at 04:53):

However, what you did _still_ doesn't get you the latest and greatest version of mathlib.

:-(

#### Scott Morrison (Oct 10 2018 at 04:54):

If you look up that git commit hash you'll see it's from June 21.

#### Scott Morrison (Oct 10 2018 at 04:54):

This is because leanpkg is taking you to the latest commit on the lean-3.4.1 branch, which for some reason (@Mario Carneiro ?) never gets updated?

#### Scott Morrison (Oct 10 2018 at 04:55):

(We _really_ need to fix this issue.)

#### Mario Carneiro (Oct 10 2018 at 04:55):

Don't blame me, Kevin wanted it to stay still

#### Scott Morrison (Oct 10 2018 at 04:55):

To get the actual latest version, you should edit your leanpkg.toml file.

#### Mario Carneiro (Oct 10 2018 at 04:55):

I guess it points to something like the earliest commit compatible with 3.4.1?

#### Scott Morrison (Oct 10 2018 at 04:56):

And replace the line lean_version = ... with lean_version = "nightly-2018-08-23".

#### Scott Morrison (Oct 10 2018 at 04:57):

(I better make another video. :-)

#### David Michael Roberts (Oct 10 2018 at 04:57):

Aha, doing leanpkg build after adding a file to src/containing import data.nat.prime (plus an #eval 2+2) makes it do a lot more

#### David Michael Roberts (Oct 10 2018 at 04:57):

And replace the line lean_version = ... with lean_version = "nightly-2018-08-23".

ah, ok! I'll do that once the current build has finished

#### Scott Morrison (Oct 10 2018 at 04:58):

I wonder if @Kevin Buzzard cares about where lean-3.4.1 points, anymore.

#### Scott Morrison (Oct 10 2018 at 04:58):

If he doesn't, do you think we can keep it closer to master, @Mario Carneiro ?

#### Mario Carneiro (Oct 10 2018 at 04:58):

I guess, but how close?

#### Scott Morrison (Oct 10 2018 at 04:59):

As often as you can be bothered pushing it?

#### Scott Morrison (Oct 10 2018 at 04:59):

Have a script that keeps it right up to master??

#### David Michael Roberts (Oct 10 2018 at 05:01):

Well, that's doing something.

#### David Michael Roberts (Oct 10 2018 at 05:01):

Question: why the nightly from the 21st of June?

Oh ...

#### David Michael Roberts (Oct 10 2018 at 05:02):

Is that the 'latest and greatest' version of mathlib?

No.

#### Scott Morrison (Oct 10 2018 at 05:03):

These nightlies are versions of Lean, not of mathlib.

#### Scott Morrison (Oct 10 2018 at 05:03):

mathlib changes most days!

#### Scott Morrison (Oct 10 2018 at 05:03):

I've just edited my instruction above. You should use nightly-2018-08-23.

#### Scott Morrison (Oct 10 2018 at 05:03):

(And maybe even edit your message above where you quoted me, so we can completely rewrite history. :-)

Done!

#### David Michael Roberts (Oct 10 2018 at 05:08):

I now have nightly-2018-08-23, thanks!

#### Kevin Buzzard (Oct 10 2018 at 06:23):

The "you're better off with the nightly build" comment was from when Lean 3.4 was changing a lot, and mathlib would change to keep up with Lean. This is all much less of an issue nowadays.

#### Kevin Buzzard (Oct 10 2018 at 06:25):

Don't blame me, Kevin wanted it to stay still

I wanted it to stay still between June and September. Thank you very much Mario for making it stay still over my summer project. I now really really don't want it to stay still any more for the simple reason that it is causing constant confusion amongst users.

#### Kevin Buzzard (Oct 10 2018 at 06:27):

Can we just delete the branch @Mario Carneiro or will this cause a new kind of confusion amongst users?

#### Mario Carneiro (Oct 10 2018 at 06:27):

No, it ties in to the way leanpkg works

#### Mario Carneiro (Oct 10 2018 at 06:27):

I think leanpkg gets even more confused if it's not there at all

#### Kevin Buzzard (Oct 10 2018 at 06:28):

I was fearing this. Can we get it to track master somehow?

#### Mario Carneiro (Oct 10 2018 at 06:28):

Does someone want to write a git hook so that when I commit to master lean-3.4.1 moves too?

Last updated: May 10 2021 at 00:31 UTC


text:
# Distance from Subset of Real Numbers to Element/Proof 1

## Theorem

Let $S$ be a subset of the set of real numbers $\R$.

Let $x \in \R$ be a real number.

Let $\map d {x, S}$ be the distance between $x$ and $S$.

Then:

$x \in S \implies \map d {x, S} = 0$

## Proof

From the definition of distance:

$\forall x, y \in \R: \map d {x, y} = \size {x - y}$

Thus:

$\displaystyle \map d {x, S} = \map {\inf_{y \mathop \in S} } {\size {x - y} }$

Consider the set $T = \set {\size {x - y}: y \in S}$.

This has $0$ as a lower bound as Absolute Value is Bounded Below by Zero.

So:

$\displaystyle \map d {x, S} = \map {\inf_{y \mathop \in S} } {\size {x - y} } \ge 0$

If $x \in S$ then:

$\size {x - x} = 0 \in T$

and so:

$\displaystyle 0 \le \map {\inf_{y \mathop \in S} } {\map d {x, y} }$

Thus:

$\displaystyle \map d {x, S} = \map {\inf_{y \mathop \in S} } {\map d {x, y} } = 0$

$\blacksquare$


text:
## If x is a subset of Y then, is inverse of x also a subset of Y?

Let $f : X \rightarrow Y$ be a function. If B is subset of y then its inverse image $f^-B$ is the subset of x define by $f^-B = {x : f(x) \in B}$ Now prove the following. $i. B_1 \subset B_2 \Rightarrow f^-B_1 \subset f^- B_1$ […]

## If x belongs to the domain then does f(x) belong to the range?

Let $F : x \Rightarrow y$ be a function. Then prove that $i. A_1 \subset A_2 \Rightarrow F(A_1) \subset F(A_2)$ $ii. F(\cup_i A_i) = \cup_i F(A_i)$ $iii.F(\cap_i A_i) \subset \cap_i f(A_i)$ Solution $Let \ f: x \rightarrow y$ be a function. i. $Let\ y \in f(A_1)$ \$Then\ \exists x \in […]

Scroll to top


text:
Haemophilia A is a hereditary bleeding disorder caused by the partial or complete deficiency of coagulation factor VIII (FVIII), which affects 1 in 5000 males1. Patients with haemophilia A are categorized into mild (0.05–0.4 IU/mL FVIII), moderate (0.01–0.05 IU/mL FVIII) or severe (< 0.01 IU/mL FVIII) cases according to their plasma FVIII level. The bleeding phenotype of these patients ranges from mild (prolonged bleeding after tooth extraction, trauma or surgery) to severe (spontaneous joint and muscle bleeding), although this does not always correspond with the FVIII plasma level2.

The thrombin generation (TG) test is a global coagulation assay, which measures the overall function of the coagulation system. In general, a high TG test result is associated with thrombosis3,4,5, whereas low TG is related to bleeding problems6,7,8. The TG test has previously been used to evaluate the haemostatic potential in haemophilia A patients and proved to be especially helpful for treatment management in these patients9. Typically, the TG test result is reduced in haemophilia A patients, but not fully absent10, and can be attributed to an imbalance in the pro- and anticoagulants in haemophilia A patients. Activated FVIII is the essential cofactor of FIXa, which converts FX into FXa. FXa together with FVa subsequently activates prothrombin into thrombin, allowing the formation of a fibrin clot. The production of thrombin is impeded in haemophilia A due to low levels of FVIII, which plays an important role in the acceleration of thrombin production. This causes the haemostatic balance to shift towards an over-anticoagulated system, which is associated with bleeding, because thrombin inactivation mechanisms remain unchanged in haemophilia A.

Thrombin dynamics analysis quantifies the processes of prothrombin conversion and thrombin inactivation that determine the balance between hypo- and hypercoagulability11. It can be used to accurately pinpoint a specific mechanistic target in the coagulation cascade and thus study underlying mechanisms of the coagulation system. In haemophilia A, the reduction of TG caused by low FVIII activity attenuates the conversion of prothrombin into thrombin. Prothrombin conversion is usually not routinely determined in haemophilia A. Nevertheless, the quantification of prothrombin conversion can give insight in both the effect of lower FVIII levels and the role of the remainder of the coagulation system, which is known to vary a lot between individuals, and its interplay with the low FVIII levels.

Currently, FVIII concentrates are used to treat bleeding in severe haemophilia prophylactically or therapeutically. Despite the success of FVIII replacement therapy, the treatment is invasive and stressful for the patients, because intravenous infusion is needed two to three times a week. Therefore, new treatment strategies for haemophilia A have been designed. A novel treatment approach is the restoration of the balance between pro- and anticoagulants, which is distorted in haemophilia A due to the lack of FVIII. Haemophilia A patients that suffer from co-inherited deficiencies in natural anticoagulants, such as antithrombin (AT) or protein C and S have a favourable bleeding phenotype compared to haemophilia patients without co-inherited deficiencies12,13,14,15,16. Additionally, a murine model showed that TG was increased upon AT reduction17. Fitusiran is a novel RNAi therapeutic that mimics this protective trait by reducing the production of the natural anticoagulant AT in haemophilia A patients18,19,20. This approach aims to restore to restore the balance between pro- and anticoagulant pathways that determine the TG process, by lowering thrombin inactivation as a response to reduced prothrombin conversion due to the lack of FVIII.

In this study, we investigated the balance of prothrombin conversion and thrombin inactivation in mild, moderate and severe haemophilia A patients and healthy controls and studied the inter-individual variability. In addition, we used in silico modelling to investigate the effect of AT reduction on the TG curves and the haemostatic balance in haemophilia A patients.

## Results

### Thrombin generation

TG was measured in 26 haemophilia A patients and 27 age- and sex-matched controls (Table 1). The mean age for both groups was 49 years and the average FVIII level was 0.083 IU/mL and 1.41 IU/mL, in patients and controls respectively. In the haemophilia A group, based on the FVIII levels, 11 patients were classified as mild haemophilia A patients, 10 patients as moderate and 5 patients as severe. The TG test was triggered with 1 pM TF (Fig. 1) and 5 pM tissue factor (TF) (Fig. 2). The average TG curve of the haemophilia A patients is distinctly lower than the average TG curve of the control group for both TF concentrations. Time-to-peak was prolonged by 1.8-fold (p < 0.001) in haemophilia A patients. Peak height (-80%), velocity index (− 92%) and ETP (− 51%) were significantly lower in patients (p < 0.001) at 1 pM TF. Similarly, at 5 pM TF, peak height and velocity index were significantly lower in patients (− 44% and − 73%, p < 0.001), whereas, the ETP did not differ between patients and controls (1344 nM*min vs. 1498 nM*min). The lag time did also not differ between the two groups, irrespectively of the trigger concentration. TG results showed a trend towards lower peak height according to the severity of haemophilia A, but this was not statistically significant.

### Thrombin dynamics

TG is a balance between pro- and anticoagulant processes, and when this balance is disturbed, it will result in bleeding or thrombosis. The pro- and anticoagulant processes underlying TG can be studied computationally by thrombin dynamics analysis11. In this approach, prothrombin conversion is quantified by the total amount of prothrombin converted (PCtot) and the maximum prothrombin conversion rate (PCmax). Prothrombin conversion was calculated from the TG curves measured at 1 and 5 pM TF (Figs. 3 and 4). The average prothrombin conversion curve was lower in haemophilia A patients than in controls. The quantification of each individual curve showed that both PCtot and PCmax are significantly lower in the haemophilia group (p < 0.001), independently of the TF concentration. In patients and controls, PCmax was significantly correlated with the plasma FVIII level: R = 0.85 with p < 0.001 at 1 pM TF and R = 0.75 with p < 0.001. Interestingly, at 1 pM TF, the FVIII level was positively correlated with PCtot (R = 0.48, p < 0.001), whereas the correlation was negative at 5 pM TF (R = − 0.69, p < 0.001). Thrombin inactivation during the TG test was quantified as the formation of thrombin-antithrombin (T-AT) and thrombin-α2Macroglobulin (T-α2M) complexes. T-AT and T-α2M were reduced by 50% and 33%, respectively in haemophilia patients compared to healthy controls (p < 0.0001) at 1 pM TF (Fig. 3D, E). Alike PCtot, T-AT and T-α2M complex formation was weakly positively associated with the FVIII level at low TF (R = 0.52 and R = 0.32, p < 0.05), but negatively associated at a higher TF concentration (R = − 0.68 and R = − 0.65, p < 0.001). Additionally we found a positive correlation between FVII and the thrombin decay capacity (R = 0.45, p < 0.001), indicating a higher thrombin inactivation capacity in subjects with higher FVIII levels.

### In silico experiments

Lower TG in haemophilia A patients is caused by lower prothrombin conversion as a result of the (partial) deficiency in FVIII activity, while thrombin inactivation is unchanged. Targeting thrombin inactivation, more specifically thrombin inactivation by AT, has been proposed as a novel treatment strategy in haemophilia A20. We used in silico experimentation to simulate the reduction of AT in haemophilia A patients. We investigated whether targeting of antithrombin could restore the TG potential by lowering AT levels to 90%, 80%, 70%, 60%, 50%, 40%, 30%, 25%, 20%, 15%, 10%, 5% and 2.5% of the original plasma level (Fig. 5). The lowering of AT partially normalized the TG curve dose-dependently in all patients. Peak height and velocity index increased dose-dependently, ETP and lag time lag time were unchanged and time-to-peak decreased with decreasing AT level. The average peak height was 41 nM ± 24 nM in haemophilia patients at 100% AT. A reduction of 50% of the original AT level could restore the TG profile in haemophilia A patients up to an average peak height of 69 nM ± 37 nM. A further reduction of AT to 5% increased the peak height to 93 ± 48 nM. For some patients, the peak height was restored to be within the normal range if AT levels were below 15%.

Moreover, the mean velocity index of 4.6 nM/min ± 3.3 nM/min at 100% AT in haemophilia A patients was restored to 13.5 nM/min ± 9.4 nM/min at 50% antithrombin. The reduction of AT to 5% increased the velocity index to 24.5 ± 15.9 nM/min and thereby reached the normal range in some patients.

Figure 5 shows that the effect of AT lowering varies between the patients, irrespectively of their FVIII plasma level. If AT was reduced to 50%, this resulted in an average increase of the peak height by 56% in mild haemophilia A patients, 75% in moderate patients and 82% in severe patients. A further reduction to 5% AT, as is typically achieved with current therapeutic strategies increased the peak height by 109%, 136%, and 148%, respectively in mild, moderate and severe haemophilia A patients.

## Discussion

TG is known to be reduced in haemophilia A because low FVIII levels attenuate the activation pathway of prothrombin. In the present study, we quantified prothrombin conversion and thrombin inactivation in haemophilia A using thrombin dynamics analysis11 and investigated inter-patient variation. Additionally, we studied the effect of novel AT targeting treatment strategies on TG using in silico experimentation21.

TG parameters ETP and peak height were significantly decreased in haemophilia A patients, especially when triggered with a low TF concentration. The effect on the ETP was less pronounced when TG was triggered with higher TF concentration, probably because then the assay becomes less sensitive to the factors of the intrinsic coagulation cascade22. Nevertheless, thrombin was formed at a slower pace, which was reflected in a longer time-to-peak and a lower peak height and velocity index. Thrombin dynamics analysis revealed that prothrombin conversion is decreased in haemophilia A patients. PCtot was significantly lower in haemophilia A patients and also this effect is more pronounced at low TF concentrations. PCmax was significantly lower in patients for both triggers, indicating that the TG profile is not only lower because less thrombin is formed but also because it is formed at a slower rate. As a consequence, T-AT and T-α2M complex formation, which depends on the amount of thrombin formed, are lower in haemophilia A.

Our results can be explained by the (partial) FVIII deficiency in haemophilia A, resulting in decreased prothrombin conversion downstream the coagulation cascade when a low TF trigger is used as previously reported23. FVIII is an important cofactor in the coagulation cascade that, once activated, can enhance the velocity of FXa formation by FIXa in vitro, up to 103–106-fold (depending of the experimental conditions used)24. Moreover, irrespectively of the trigger concentration used, no differences in lag time were observed between patients and controls. This is mainly due to the initiation of the TG test with TF, which together with FVIIa can activate FX and subsequently form the first traces of thrombin independently of FVIII (a)25.

We show that the balance between pro- and anticoagulant shifts towards bleeding in haemophilia A. It has been proposed in the past that the balance between prothrombin conversion and thrombin inactivation can be restored by decreasing the inactivation of the formed thrombin, e.g. by inhibiting APC, AT or TFPI26,27. The inhibition of AT in silico increases TG test parameters ETP, peak height and velocity index significantly, suggesting that targeting AT could be successful in haemophiliacs in an attempt to restore the balance between prothrombin conversion and thrombin inactivation. Pasi et al. recently showed in a phase I study that targeting AT with RNAi therapeutical fitusiran increased TG in both haemophilia A and B patients in a dose-dependent manner20. Our results suggest that a large reduction of AT is necessary to reach the thrombin generation capacity of a normal subject. Indeed, the phase I study on fitusiran indicated that a therapeutical reduction of antithrombin levels by 75% in hemophilia A patients brings the thrombin generation capacity into the lower normal range20. The phase II study on fitusiran showed that an AT reduction of 78–88% was achieved when a fixed dose of 50 mg was administered28. Indeed our in silico analysis shows a reduction of AT by more than 85% bring TG in the normal range in a part of the patients, but not all.

Besides the variation in AT lowering after administration of a fixed dose of an antithrombin level reducing drug, our study indicates that inter-individual variation in response to AT reduction is large. The remainder of the coagulation system does not respond identically in each patient at a certain AT level and we show that the effect of AT reduction is irrespective of the baseline FVIII plasma level. Additionally, previous reports suggest that haemophilia treatment should become more individualized27,29. It would be interesting to investigate further how the TG test and thrombin dynamics analysis could be utilized to optimize the individual treatment of each patient. We now show for the first time that in silico thrombin dynamics experimentation could be used for example to estimate the dose of an AT-targeting drug in each individual patient. In a broader sense, the TG test and thrombin dynamics analysis might be used as a strategy to estimate the optimal dosing of other therapeutics such as FVIII or bypassing agents in the future.

There were some limitations in the current study, such as the low number of patients. Analysis of a higher number hemophilia A patients could render significant differences between mild, moderate and severe patient as well, in addition to the differences found between patients and controls. Additionally, the same methodology as used in the current study could be used to investigate the dynamics of thrombin generation in hemophilia B patients. Nevertheless, for this initial manuscript, we focused on hemophilia A because of its higher prevalence.

To conclude, we found a disturbed balance between prothrombin conversion and thrombin inactivation in patients with haemophilia A. Especially the rate of prothrombin conversion is lower in haemophilia patients causing low TG. Although PCtot ranged from low to normal in patients compared to healthy subjects, thrombin formation in haemophilia A is a slower process due to the (partial) lack of FVIII. In silico experimentation shows that the therapeutic reduction of AT levels leads to an increased TG. AT reduction is a novel and successful treatment to prevent bleeding for haemophilia A patients. This study shows that thrombin generation and thrombin dynamics analysis are an opportunity to individualize patient care in the future bytailoring the dosing of AT level reducing drugs to the coagulation system of individual patients.

## Methods

### Participants and sample handling

26 haemophilia A patients and 27 age- and sex-matched control subjects were enrolled in this study (Table 1). Haemophilia A severity was determined based on the patients FVIII level: patients with FVIII levels below 0.40 IU/mL were classified as mild, below 0.05 IU/mL as moderate and below 0.01 IU/mL as severe haemophilia patients. Healthy subjects did not report any known coagulation defects and had FVIII levels above 0.85 IU/mL. The study protocol was approved by the medical ethics committees of the Erasmus Medical Center (Rotterdam) and the Maastricht University Medical Center (Maastricht). Written informed consent was obtained in concordance with the declaration of Helsinki. Whole blood was collected on 3.2% citrate in a 9:1 ratio for the preparation of platelet poor plasma (PPP), which was prepared consecutively by centrifuging twice at 2821 g for 10 min and then stored at  − 80 °C until further use. All methods were performed in accordance with the relevant guidelines and regulations.

### Thrombin generation

Calibrated Automated Thrombinography (CAT) was performed as previously described30. All wells contained 80 µl plasma and 20 µl tissue factor (TF; 1 or 5 pM; Innovin, Dade-Behring, Marburg, Germany) and phospholipids (4 µM; Synapse Research Institute, Maastricht, the Netherlands;31) or 20 µl of calibrator (100 nM; Synapse Research Institute, Maastricht, the Netherlands; 30). Thrombin generation (TG) was initiated by the addition of 20 µl of ZGGR-AMC (417 µM; Bachem, Bubendorf, Switzerland) and CaCl2 (16.7 mM).

The TG fluorescence data were converted to TG curves, as described elsewhere32 and further used to perform additional computational thrombin dynamics analysis to extract prothrombin conversion and quantify thrombin inactivation. The TG curves were quantified by the parameters lag time, time-to-peak, peak height, endogenous thrombin potential (ETP) and velocity index.

### Coagulation factor levels

Plasma FVIII, fibrinogen and AT levels were determined on the STA-R analyser, using respectively, STA ImmunoDef VIII with STA-CK Prest, STA Liquid Fibrinogen, and STA—Stahrom AT III and according to the manufacturer’s specifications (Diagnostica Stago, Asnières-sur-Seine, France). α2-macroglobulin (α2M) was measured in a functional assay (Synapse Research Institute, Maastricht, the Netherlands)11. AT, α2M and fibrinogen levels were used to perform thrombin dynamics analysis.

### Thrombin dynamics

The TG curve is the net result of prothrombin conversion and thrombin inactivation. Therefore, the course of prothrombin conversion can be calculated if thrombin formation and inactivation are known. Thrombin inactivation was determined by the previously described computational model which is based on the plasma AT, α2M and fibrinogen level, according to Eqs. (1)–(4).

$${\text{d}}\left( {{\text{T-AT}}} \right)/{\text{dt}} = {\text{k}}_{{{{\rm AT}}}} \cdot \, \left[ {{\text{AT}}} \right]_{{\rm t}} \cdot \left[ {{\text{T}}_{{\rm free}} } \right]_{{\rm t}}$$
(1)
$${\text{d}}\left( {{\text{T-}}{\upalpha }_{2} {\text{M}}} \right)/{\text{dt}} = {\text{k}}_{{{\upalpha }2{\text{M}}}} \cdot \, \left[ {{\upalpha }_{2} {\text{M}}} \right]_{{\rm t}} \cdot \, \left[ {{\text{Tfree}} } \right]_{{\rm t}}$$
(2)
$${\text{d}}\left( {{\text{T-MS}}} \right)/{\text{dt}} = {\text{k}}_{{\rm MS}} \cdot \, \left[ {{\text{T}}_{{\rm free}} } \right]_{{\rm t}}$$
(3)
$$- d\left( {{\text{T}}_{{\rm free}} } \right)/{\text{dt }} = {\text{k}}_{{\rm AT}} \cdot \, \left[ {{\text{AT}}} \right]_{{\rm t}} \cdot \, \left[ {{\text{T}}_{{\rm free}} } \right]_{{\rm t}} + {\text{ k}}_{{{\upalpha }2{\text{M}}}} \cdot \, \left[ {{\upalpha }_{2} {\text{M}}} \right]_{{\rm t}} \cdot \, \left[ {{\text{T}}_{{\rm free}} } \right]_{{\rm t}} + {\text{ k}}_{{\rm MS}} \cdot \, \left[ {{\text{T}}_{{\rm free}} } \right]_{{\rm t}}$$
(4)

Additionally, thrombin dynamics analysis was used to determine prothrombin conversion curves from TG test data and the model of thrombin inactivation, as described by Eqs. (5 and 6)11.

$${\text{d}}\left( {\text{T}} \right)/{\text{dt }} = \, - {\text{d}}\left( {\text{P}} \right)/{\text{dt}} - {\text{d}}\left( {{\text{T-inh}}} \right)/{\text{dt}}$$
(5)
$$- {\text{d}}\left( {\text{P}} \right)/{\text{dt }} = {\text{ d}}\left( {\text{T}} \right)/{\text{dt }} + {\text{ k}}_{{\rm AT}} \cdot \, \left[ {{\text{AT}}} \right]_{{\rm t}} \cdot \, \left[ {\text{T}} \right]{\text{t }} + {\text{ k}}_{{{\upalpha }2{\text{M}}}} \cdot \, [{\upalpha }_{2} {\text{M]}}_{{\rm t}} \cdot [{\text{T}}]_{{\rm t}}$$
(6)

The total inhibitory potential of each plasma was quantified by the thrombin decay constant (TDC) and prothrombin conversion curves were quantified by.

1. 1.

The total amount of prothrombin converted during the TG test (PCtot);

2. 2.

The maximum rate of prothrombin conversion (PCmax);

3. 3.

The amount of thrombin-AT complexes formed (T-AT); and

4. 4.

The amount of thrombin- α2M complexes formed (T-α2M).

### In silico experimentation

The computational model for thrombin inactivation by AT and α2M was used to perform in silico experiments that show the effect of plasma AT reduction on TG in haemophilia A patients. The in silico TG curve (∫d(T)/dt) was computed using thrombin dynamics Eqs. (1)–(6) while the plasma level of antithrombin ([AT]0) was varied in silico in the thrombin dynamics algorithm for thrombin inactivation (d(T-inh)/dt).

As AT levels are know to influence the course of prothrombin conversion indirectly, the individual prothrombin conversion curves were transformed to accommodate the effect of AT lowering33. We have shown previously that although the plasma AT level does not influence the total amount of prothrombin conversion (PCtot), it does affect the maximal rate of prothrombin conversion (PCmax) dose-dependently33. To correct for this effect we fitted the relationship between plasma AT level and PCmax in experimentally determined AT dose–response curves and transformed the prothrombin conversion curves obtained in the hemophilia A patients accordingly for each plasma level of AT.

The input of the model was the previously determined prothrombin conversion curve (d(P)/dt) of each individual patients and. Each individual prothrombin conversion curve together the patients variable AT level and α2M and fibrinogen levels were used to calculate a series of 14 TG curves, at 100% AT (of the patients original plasma level), 90%, 80%, 70%, 60%, 50%, 40%, 30%, 25%, 20%, 15%, 10%, 5% and 2.5%. Each in silico generated TG curve was quantified by the peak height, ETP and velocity index were derived from the in silico calculated curves. The TG parameters derived from in silico TG curves obtained at the original AT level of each patient did not differ from the original experimentally determined TG parameters in the individual patients.

### Statistics

GraphPad Prism (was used to perform statistical analyses. A Mann–Whitney U or Kruskal–Wallis test was performed to test for differences between groups, and correlations were assessed using the Spearman’s correlation coefficient.


text:
# Median question

• June 15th 2013, 10:20 AM
sscgeek
Median question
In a triangle ABC, AD is a median .Which is the correct answer ?

b) AB + AC < 2 AD

d) None of these
• June 15th 2013, 10:41 AM
Plato
Re: Median question
Quote:

Originally Posted by sscgeek
In a triangle ABC, AD is a median .Which is the correct answer ?
b) AB + AC < 2 AD
d) None of these

If you can use vectors then notice that $D$ is a midpoint so:
$\overrightarrow {AB} + \overrightarrow {BD} = \overrightarrow {AC} + \overrightarrow {CD} = \overrightarrow {AD}$

Using $\|\overrightarrow {BD}\|$ for the length of $\overrightarrow {BD}$ note also that $\|\overrightarrow {BD}\|=\|\overrightarrow {CD}\|$.
• June 16th 2013, 02:24 AM
ibdutt
Re: Median question
• June 16th 2013, 03:39 AM
MINOANMAN
Re: Median question
Ibdutt

Bravo..you did a good job...nice proof however you could use the Thales theorem as well
have a look here..
Intercept theorem - Wikipedia, the free encyclopedia.

However Plato is also right. If you consider vectors then the answer is c and not a.
In my opinion the original question is not clear. AB,AD AC are segments? or vectors?


text:
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 27 May 2017, 09:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Need help with SC Strategy

Author Message
Manager
Joined: 16 Feb 2011
Posts: 192
Schools: ABCD
Followers: 1

Kudos [?]: 203 [0], given: 78

Need help with SC Strategy [#permalink]

### Show Tags

23 Mar 2011, 17:47
I was trying to solve SC questions from OG12. I got approx 80-90% correct answers while solving the first fifty questions. However, as I am progressing, my success rate is going down steeply. To add, I got only 2/10 correct from 80-90 range. I know that OG12 problems are graded in increasing order of difficulty. Am I the only one who is facing these issues or is it that my basics are not right ?

Any tips will be greatly appreciated. I also tried to solve problems that I answered incorrectly on my first attempt. However, I get majority of them right on my second try. Not sure if I am treading the right path.

BTW, I have already gone through mGMAT SC Guide once. Sometimes I get frustrated and I feel as if I should open the grammar book.

Thanks
Voodoo Child
GMAT Forum Moderator
Status: Accepting donations for the mohater MBA debt repayment fund
Joined: 05 Feb 2008
Posts: 1883
Location: United States
Concentration: Operations, Finance
Schools: Ross '14 (M)
GMAT 2: 710 Q48 V38
GPA: 3.54
WE: Accounting (Manufacturing)
Followers: 61

Kudos [?]: 841 [0], given: 234

Re: Need help with SC Strategy [#permalink]

### Show Tags

23 Mar 2011, 18:24
This is common, as you mentioned, the difficult is in ascending order.

Have you see the SC strategy (see my sig)?

Are you keeping an error log? "Right on the second try" is a bad benchmark as you have exposure to the problem and know aspects of what's wrong (something wrong in the option you selected)

There's a reason you're missing the more difficult questions. You must resolve the WHY and the WHAT to move forward.
_________________

Strategy Discussion Thread | Strategy Master | GMAT Debrief| Please discuss strategies in discussion thread. Master thread will be updated accordingly. | GC Member Write Ups

GMAT Club Premium Membership - big benefits and savings

Moderator
Joined: 27 Aug 2010
Posts: 290
Schools: Tepper, McCombs, Kelley, Darden, Andersen
Followers: 22

Kudos [?]: 73 [0], given: 35

Re: Need help with SC Strategy [#permalink]

### Show Tags

23 Mar 2011, 22:28
I agree with mohater. Do you make sure that you read the explanations to all the questions.Irrespective of the fact that you get a question correct or not, you should make sure that you go through the explanation diligently. And after reading the explanation, you should have ask yourself, what are the two new things I learnt from this explanation/question. I can guarantee you that you'll be amazed to see that even if the question is easy, you'll definitely have learnt at least two new things on going through the explanations.
SVP
Affiliations: HEC
Joined: 28 Sep 2009
Posts: 1636
Concentration: Economics, Finance
GMAT 1: 730 Q48 V44
Followers: 101

Kudos [?]: 647 [0], given: 432

Re: Need help with SC Strategy [#permalink]

### Show Tags

24 Mar 2011, 01:42
And make sure to incorporate the Manhattan SC guide. Read it at least twice. The other suggestions (error log, fully read all the explanations, etc.) are very, very helpful. In fact, they are essential. And play a very active role in the verbal forums. Answer questions and fully defend your answers with detailed explanations.
_________________
Senior Manager
Joined: 17 Mar 2011
Posts: 449
Location: United States (DC)
Concentration: General Management, Technology
GMAT 1: 760 Q49 V45
GPA: 3.37
WE: Information Technology (Consulting)
Followers: 11

Kudos [?]: 183 [0], given: 5

Re: Need help with SC Strategy [#permalink]

### Show Tags

24 Mar 2011, 05:57
voodoochild wrote:
I was trying to solve SC questions from OG12. I got approx 80-90% correct answers while solving the first fifty questions. However, as I am progressing, my success rate is going down steeply. To add, I got only 2/10 correct from 80-90 range. I know that OG12 problems are graded in increasing order of difficulty. Am I the only one who is facing these issues or is it that my basics are not right ?

Any tips will be greatly appreciated. I also tried to solve problems that I answered incorrectly on my first attempt. However, I get majority of them right on my second try. Not sure if I am treading the right path.

BTW, I have already gone through mGMAT SC Guide once. Sometimes I get frustrated and I feel as if I should open the grammar book.

Thanks
Voodoo Child

This is not uncommon.

If you're fluent in English, the easy problems will be very easy. However once you get into the harder questions, you're required to know the rules, and be able to systematically apply them to the sentences. The questions are phrased that it gets harder and harder to just 'sound out' what the right answer is.

Keep working on the MGMAT guide, and be brutally thorough in reviewing problems you did.

For problems youve already done, go back and write out for each answer choice, EXACTLY why it's wrong. Then compare your reason with the OA.
Manager
Joined: 16 Feb 2011
Posts: 192
Schools: ABCD
Followers: 1

Kudos [?]: 203 [0], given: 78

Re: Need help with SC Strategy [#permalink]

### Show Tags

24 Mar 2011, 06:08
jko wrote:
voodoochild wrote:
I was trying to solve SC questions from OG12. I got approx 80-90% correct answers while solving the first fifty questions. However, as I am progressing, my success rate is going down steeply. To add, I got only 2/10 correct from 80-90 range. I know that OG12 problems are graded in increasing order of difficulty. Am I the only one who is facing these issues or is it that my basics are not right ?

Any tips will be greatly appreciated. I also tried to solve problems that I answered incorrectly on my first attempt. However, I get majority of them right on my second try. Not sure if I am treading the right path.

BTW, I have already gone through mGMAT SC Guide once. Sometimes I get frustrated and I feel as if I should open the grammar book.

Thanks
Voodoo Child

This is not uncommon.

If you're fluent in English, the easy problems will be very easy. However once you get into the harder questions, you're required to know the rules, and be able to systematically apply them to the sentences. The questions are phrased that it gets harder and harder to just 'sound out' what the right answer is.

Keep working on the MGMAT guide, and be brutally thorough in reviewing problems you did.

For problems youve already done, go back and write out for each answer choice, EXACTLY why it's wrong. Then compare your reason with the OA.

I think you guys are right. Fluency is not going to help long. I will have to make sure that I diligently study explanations for each of the questions. I re-read MGMAT yesterday and realized that I have forgotten many concepts. I think it's time for me to do some revision.

Thanks
Voodoo Child
Manager
Status: TIME FOR 700+
Joined: 06 Dec 2010
Posts: 204
Schools: Fuqua
WE 1: Research in Neurology
WE 2: MORE research in Neurology
Followers: 3

Kudos [?]: 46 [0], given: 55

Re: Need help with SC Strategy [#permalink]

### Show Tags

24 Mar 2011, 07:13
Have you tried SC grail from Aristotle prep? It is only 15$and accompanies MGMAT and OG, very useful _________________ Back to the grind, goal 700+ Manager Joined: 16 Feb 2011 Posts: 192 Schools: ABCD Followers: 1 Kudos [?]: 203 [0], given: 78 Re: Need help with SC Strategy [#permalink] ### Show Tags 26 Mar 2011, 15:32 Wishbone wrote: Have you tried SC grail from Aristotle prep? It is only 15$ and accompanies MGMAT and OG, very useful

nope. I am first going through OG 12.

Thanks
Re: Need help with SC Strategy   [#permalink] 26 Mar 2011, 15:32
Similar topics Replies Last post
Similar
Topics:
Need help: Math strategies 1 08 Sep 2015, 16:27
3 need help in my strategy 11 11 Dec 2011, 23:48
1 Strategy for SC!!! help needed 1 27 Aug 2011, 01:14
Need help with retake strategy 4 24 Nov 2011, 09:25
Need help for the plan and strategy 1 21 Apr 2009, 10:51
Display posts from previous: Sort by

# Need help with SC Strategy

Moderator: HiLine

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.


text:
1 answer

# C. The company's income tax rate is 20%. After making all the above adjustments, SPC's net...

###### Question:

C. The company's income tax rate is 20%. After making all the above adjustments, SPC's net income before taxes $10,000. No income tax has been paid or recorded. Record at the adjusting entry for income tax and 20% on that income before taxes of$10,000.
Fnewconnect.mheducation.com%252F#/activity/questi apter 4 HW 0 Saved wy 1. in the first account field.) 2 nts a. Prepaid Insurance shows a balance of zero at September 30, but Insurance Expense shows a debit balance of $2,340, representing the cost of a three-year fire insurance policy purchased on September 1 of the current year. b. On August 31 of this year, Cash was debited and Service Revenue was credited for$1,500. The S1,500 related to fees for a three- month period beginning September 1 of the current year. c. The company's income tax rate is 20%. After making the above adjustments, SPC's net income before tax is $10,000. No income tax has been paid or recorded. eBook View transaction list Print Journal entry worksheet eferences Record the adjusting entry for income tax of 20% on net income before tax of$10,000 Note: Enter debits before credits Transaction General Journal Debit Credit с Record entry Clear entry View general journal

## Answers

#### Similar Solved Questions

1 answer
##### Imagine that you are in a car that is traveling up a bridge that is inclined...
Imagine that you are in a car that is traveling up a bridge that is inclined at an angle of 14.5 degrees from the horizontal. The car's speed is 34.0 mi/hr (15.20 m/s). At time t = 0 you open your window and illegally drop a soda can from your rest frame over the edge of the bridge. Your height ...
1 answer
##### Please write your answer clearly and easy to read. Please only answer the ones you can....
Please write your answer clearly and easy to read. Please only answer the ones you can. I will upvote all the submitted answers. Question 5. Prove by contradiction that every circuit of length at least 3 contains a cycle Question 6. Prove or disprove: There exists a connected graph of order 6 in whi...
1 answer
##### A circular coil of 200 turns, with a radius of 8 cm, is dropped vertically into...
A circular coil of 200 turns, with a radius of 8 cm, is dropped vertically into a very long solenoid, which has a radius of 12 cm, 300 turns / m, and which conducts a current of 3 A. What is the value of the emf induced in the coil that is in free fall, due to the magnetic field of the solenoid ?. E...
1 answer
##### If 2.8 kg of CO2 gas is stored in a 25 L tank at 20 °C,...
If 2.8 kg of CO2 gas is stored in a 25 L tank at 20 °C, what is the required pressure of the tank?...
1 answer
##### For reference, the answers are 17.56 MPa and 41.25 MPa The cross section below has dimensions...
For reference, the answers are 17.56 MPa and 41.25 MPa The cross section below has dimensions h = 74 mm, t1 = 6 mm = 8 mm and b 91 mm. 2 % Matlab input: b-91; ybar Iz = = 55.47029702978297; 1.e81573240924e926"10"6; MZ = 716; The centroid position is given by: y 55.47029702970297 mm The momen...
1 answer
##### Delta Company produces a single product. The cost of producing and selling a single unit of...
Delta Company produces a single product. The cost of producing and selling a single unit of this product at the company’s normal activity level of 105,600 units per year is: Direct materials $1.90 Direct labor$ 2.00 Variable manufacturing overhead $0.90 Fixed manufacturing overhead$ 4.45 V...
1 answer
1 answer
##### The four wires that lie at the corners of a square of side a- 3.10 cm...
The four wires that lie at the corners of a square of side a- 3.10 cm are carrying equal currents i 1.80 A into (+) or out of the page, as shown in the picture. Calculate the component of the magnetic field at the center of the square....