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# Data Sufficiency

Are you preparing for campus placements,Banking,SSC, IAS, Insurance,Defence and other competitive exams? Then, make sure to take some time in practicing the Data Interpretation questions and answer in Quantitative Aptitude. Moreover, only those questions are included that are relevant and likely to be asked in any competitive exam. So, take these questions and answer, brush up your skills and practice to stay fully prepared for any your exam.

• Q1.Directions: What should come in place of question mark (?) in the following questions?${\left(38.05\right)}^{2}-{\left(29.9\right)}^{2}+{\left(20.9\right)}^{2}=?\left(L2\right)$

• Q2.Direction: A question is given followed by the information in three statements. You have to decide the information in which of the statements is necessary and sufficient to answer the question and mark answer accordingly.
What will be the ratio between the two digits in the two digit number?
Statements:
I. The largest digit is 9.
II. The sum of the digits in the number is 3 times their difference.

• Q3.Direction: A question is given followed by the information in three statements. You have to decide the information in which of the statements is necessary and sufficient to answer the question and mark answer accordingly.
Three friends, A, B and C started a partnership business investing money in the ratio of 3: 2: 1 respectively for a period of 3 years. What is the amount received by C as his share of profit?
Statements:
I. Total amount invested in the business in Rs. 24,750.
II. Profit earned at the end of 3 years is 2/3 of the total investment.
III. The average amount of profit earned per year is Rs. 5500.

• Q4.Direction: A question is given followed by the information in three statements. You have to decide the information in which of the statements is necessary and sufficient to answer the question and mark answer accordingly.
16 men and 28 women are working together on a construction site. After working for 3 days, 10 men and 16 women leave the work. How many more days will be required to complete the work?
Statements:
I. 38 men and 24 women together can complete the work in 9 days.
II. 32 men can complete two-third of the work in 8 days.
III. In 2 days, the work done by six men in equal to the work done by eight women.

• Q5.Direction: A question is given followed by the information in three statements. You have to decide the information in which of the statements is necessary and sufficient to answer the question and mark answer accordingly.
What is the length of a running train A crossing another running train B?
Statements:
I. These two trains take 24 seconds to cross each other.
II. These trains are running in opposite directions.
III. The length of the train A is 360 metres.

• Q6.Direction: A question is given followed by the information in three statements. You have to decide the information in which of the statements is necessary and sufficient to answer the question and mark answer accordingly.
Who among men, women or boys will complete same piece of work the fastest?
Statements:
I. 18 men and 16 women can complete the piece of work in 24 days.
II. 24 men and 18 boys can complete the same piece of work in 32 days.
III. 20 women and 18 girls can complete the same piece of work 22.5 days.


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# 8.5 - Coefficient of Determination

Now that we know how to estimate the coefficients and perform the hypothesis test, is there any way to tell how useful the model is?

One measure is the coefficient of determination, denoted $$R^2$$.

Coefficient of Determination $$R^2$$
The coefficient of determination measures the percentage of variability within the $$y$$-values that can be explained by the regression model.

Therefore, a value close to 100% means that the model is useful and a value close to zero indicates that the model is not useful.
It can be shown by mathematical manipulation that:

$$\text{SST }=\text{ SSR }+\text{ SSE}$$

$$\sum (y_i-\bar{y})^2=\sum (\hat{y}_i-\bar{y})^2+\sum (y_i-\hat{y}_i)^2$$

Total variability in the y value = Variability explained by the model + Unexplained variability

To get the total, explained and unexplained variability, first we need to calculate corresponding deviances. Drag the slider on the image below to see how the total deviance $$(y_i-\bar{y})$$ is split into explained $$(\hat{y}_i-\bar{y})$$ and unexplained deviances $$(y_i-\hat{y}_i)$$.

he breakdown of variability in the above equation holds for the multiple regression model also.

Coefficient of Determination $$R^2$$ Formula

$$R^2=\dfrac{\text{variability explained by the model}}{\text{total variability in the y values}}$$

$$R^2$$ represents the proportion of total variability of the $$y$$-value that is accounted for by the independent variable $$x$$.

For the specific case when there is only one independent variable $$X$$ (i.e., simple linear regression), one can show that $$R^2 =r^2$$, where $$r$$ is correlation coefficient between $$X$$ and $$Y$$. For Bob’s data, the correlation of the two variable is 0.994 and the R2 value is 98.89.

##### Correlations
 Pearson correlation 0.994 P-value 0
##### Model Summary
S R-sq R-sq(adj) R-sq(pred)
1.05958 98.89% 98.88% 98.82%

## Finding Correlation Section

1. Select Stat > Basic statistics > Correlation
2. Specify the two (or more) variables for which you want the correlation coefficient(s) calculated.
• Pearson correlation is the default.  An optional Spearman rho method is also available.
3. If it isn't already checked, put a checkmark in the box labeled Display p-values by clicking once on the box.
4. Select OK. The output will appear in the session window.

format: plain


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zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On right fractional calculus. (English) Zbl 1198.26006
Summary: Here are presented fractional Taylor type formulae with fractional integral remainder and fractional differential formulae, regarding the right Caputo fractional derivative, the right generalized fractional derivative of {\it J. A. Canavati} type [Nieuw Arch. Wiskd., IV. Ser. 5, 53--75 (1987; Zbl 0649.46026)] and their corresponding right fractional integrals.Then are given representation formulae of functions as fractional integrals of their above fractional derivatives, as well as of their right and left Weyl fractional derivatives.At the end, we mention some far reaching implications of our theory to mathematical analysis computational methods.Also we compare the right Caputo fractional derivative to right Riemann-Liouville fractional derivative. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
 26A33 Fractional derivatives and integrals (real functions)
Full Text:
References:
 [1] Anastassiou, G.: Quantitative approximations, (2001) · Zbl 0969.41001 [2] Canavati, J. A.: The Riemann -- Liouville integral, Nieuw archief voor wiskunde 5, No. 1, 53-75 (1987) · Zbl 0649.46026 [3] Kai Diethelm, Fractional differential equations. Available from: http://www.tu-bs.de/ diethelm/lehre/f-dgl02/fde-skript.ps.gz. · Zbl 1136.26302 [4] El-Sayed, A. M. A.; Gaber, M.: On the finite Caputo and finite Riesz derivatives, Electron J theor phys 3, No. 12, 81-95 (2006) [5] Frederico, G. S.; Torres, D. F. M.: Fractional optimal control in the sense of Caputo and the fractional Noether’s theorem, Int math forum 3, No. 10, 479-493 (2008) · Zbl 1154.49016 [6] Gorenflo R, Mainardi F, Essentials of fractional calculus. Maphysto Center; 2000. Available from: http://www.maphysto.dk/oldpages/events/LevyCAC2000/MainardiNotes/fm2k0a.ps. · Zbl 1030.26004 [7] Miller, K. S.: The Weyl fractional calculus, Lecture notes in mathematics 457, 80-89 (1975) · Zbl 0305.44004 [8] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives, theory and applications, (1993) · Zbl 0818.26003


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# Macro not working properly

I am running the following macro commands in batch processing mode

run(“Make Binary”);
run(“Outline”);
makeRectangle(340, 371, 300, 100);
run(“Clear Outside”);

I run the same macros on two different platforms Windows 10 and Windows 7. However both resulted in to different outputs as given in the image. While the output i was getting in Windows 7 platform is my desired result, I am not able to get the same result in Windows 10 platform. Is it a bug or how can I get back to the desired result in Windows 10 platform.


text:
# Hanging indentation in psalm-like verses

Working on psalm indentation with macro

\def\par{\ifvmode\noindent\else\endgraf\fi}
\obeylines

given by David Carlisle here I came across next problem of verses which doesn't fit in a single line.

I tried to put there additional indentation with \hangindent but didn't succeed.

Here is some MWE:

\documentclass[12pt,a4paper]{article}
\usepackage[
left=4cm,
right=4cm,
showframe]{geometry}

\begin{document}

\begingroup
\setlength{\parskip}{0pt}
\def\par{\ifvmode\noindent\else\endgraf\fi}
\obeylines
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor
\endgroup
\end{document}

I aim at something like that:

Something like this?

\documentclass[12pt,a4paper]{article}
\usepackage[
left=4cm,
right=4cm,
showframe]{geometry}

\begin{document}

\begingroup
\setlength{\parskip}{0pt}
\def\par{\ifvmode\hangindent40pt\noindent\else\endgraf\hangindent40pt\fi}
\obeylines
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor
\endgroup
\end{document}

• That's it! Thanks again. I was trying to put \hangindent somewhere in "preamble" of the group but didn't think of editing the conditional. – Precluch Mar 24 '17 at 21:17

This answer is a little redundant, since David Carlisle has provided a beautiful answer. But I'm so impressed at how this will help me typeset Bible quotes that I want to provide a fuller example of how I'd use this method to typeset biblical poetry. It's so much better than me previous efforts built around the list environment. Any suggestions for improvement welcome.

\documentclass[twocolumn]{article}
\usepackage[b5paper,margin=2cm]{geometry}
\usepackage{lettrine}
\pagestyle{empty}
\setlength\parindent{1em}
\renewcommand*{\thefootnote}{\emph{\alph{footnote}}}
\def\vs#1{\textsuperscript{#1}}
\def\ch#1{\lettrine[findent=0.5em,nindent=0em]{#1}{}}
\newlength\psalmleftskip
\setlength\psalmleftskip{1em}
\newlength\psalmindent
\setlength\psalmindent{1em}
\newenvironment{psalm}
{\raggedright
\leftskip\psalmleftskip
\parskip 0pt
\parindent\psalmindent
\def\vs##1{\llap{\textsuperscript{##1}}}
\def\par{%
\ifvmode
\def\vs####1{\llap{\textsuperscript{####1}}}
\noindent
\else
\def\vs####1{\hspace{-\psalmindent}\llap{\textsuperscript{####1}}\hspace{\psalmindent}}
\endgraf
\fi
\hangindent=3\psalmindent}
\obeylines}
{}
\begin{document}
\section*{Job}

\subsubsection*{Elihu}

\ch{32}So these three men stopped answering Job, because he was righteous in
his own eyes. \vs{2}But Elihu son of Barakel the Buzite, of the family of Ram,
became very angry with Job for justifying himself rather than God. \vs{3}He
was also angry with the three friends, because they had found no way to refute
Job, and yet had condemned him.\footnote{\emph{3} Masoretic Text; an ancient
had waited before speaking to Job because they were older than he. \vs{5}But
when he saw that the three men had nothing more to say, his anger was aroused.

\vs{6}So Elihu son of Barakel the Buzite said:\medskip

\begin{psalm}
I am young in years,
and you are old;

that is why I was fearful,
not daring to tell you what I know.

\vs{7}I thought, Age should speak;

\vs{8}But it is the spirit\footnote{\emph{8} Or \emph{Spirit}; also in verse 18} in a person,
the breath of the Almighty, that gives them understanding.

\vs{9}It is not only the old\footnote{\emph{9} Or \emph{many}; or \emph{great}} who are wise,
not only the aged who understand what is right.\medskip

\vs{10}Therefore I say: Listen to me;
I too will tell you what I know.

\vs{11}I waited while you spoke,

while you were searching for words,
\vs{12}I gave you my full attention.

But not one of you has proved Job wrong;
none of you has answered his arguments.

\vs{13}Do not say, We have found wisdom;
let God, not a man, refute him.'

\vs{14}But Job has not marshaled his words against me,
\end{psalm}

\newpage

\section*{Psalms}

\subsubsection*{\centering Psalm 63\footnote{In Hebrew texts 63:1--11 is
numbered 63:2--12.}}

\begin{center}
\emph{A psalm of David. When he was in the Desert of Judah.}
\end{center}

\begin{psalm}
\vs{1}You, God, are my God,
earnestly I seek you;

I thirst for you,
my whole being longs for you,

in a dry and parched land
where there is no water.\medskip

\vs{2}I have seen you in the sanctuary

\vs{3}Because your love is better than life,
my lips will glorify you.

\vs{4}I will praise you as long as I live,
and in your name I will lift up my hands.

\vs{5}I will be fully satisfied as with the richest of foods;
with singing lips my mouth will praise you.\medskip

\vs{6}On my bed I remember you;
I think of you through the watches of the night.

\vs{7}Because you are my help,

\vs{8}I cling to you;


text:
Home > Uncategorized > Liquid Water flow Solutions, Components, Steps and Routine maintenance

## Liquid Water flow Solutions, Components, Steps and Routine maintenance

Liquid Water flow Solutions, Components, Steps and Routine maintenance

Fluids Drainage Ways, Supplies, Functions and Routine service The fact, water is life is not actually new to our ears. In fact, normal water is required in a large number of paths of human being daily life from drinking alcohol to washing never to fail tool technology considerations, like an electrical source age group in hydroelectric flowers and plants.write me an essay online It is actually truly genuine that mineral water is life. H2o Discharge is considered the all natural or synthetic elimination of spot and undercover h2o from a location. Water drainage tactics are different extensively dependant upon the intention and also wanted effect. A water flow process are usually created and made to circumvent exterior runoff and toxins, deplete liquid directly into the soil, reduce the amount speed of perform-off or to assemble waters in basins and pond for storage space. This little exhibits how essential drinking water water flow techniques can be. Drainage methods may perhaps be categorized channel water flow and place drainage. Station drainage will involve use of concrete, stainlesss steel, polymer or composites to develop the water flow funnel. Water then generally flows over the channel and is particularly communicated in to the required idea. A great instance of these is the piping helpful to present waters from the fluids firms near. Have a look near therefore you is unable to pass up a seeping pipe all around. Do not forget to be enthusiastic. On the other hand, Time drainage appropriately generally known as wide open devices contain gullies that intercept top manage-out of drinking water. The galleys stick to the topographical design of your terrain floor and get connected to discharge water lines beneath the earth top. Culverts and route gutters would serve a seriously excellent illustration to lavish. Liquid flowing on the road gutters flows into culverts and then it’s sent to estuaries and rivers as well as the desired shops. Styling a water flow method is quite often pretty challenging. Civil Designers partaking these initiatives give good results beside designers, surveyors and other stakeholders in state to produce a good organize. A good quality discharge system schedule should incorporate information of the time of development. The mention of installer (also called the installer) also have to be included. It must recognise any shifts crafted from the initial method capacity, depth, class, videos and supplies to being used.

The blueprint will have to indicate spot section of the undertaking, its measurement and potential. It must discuss any doable construction dilemmas that might be encountered through the entire precise assembly approach. All attainable water inlets, outlets and old free of moisture wells in which the effluent fluids is diverted have to be lavish. Generally if the water ended up being to be outsoucring straight into the active all natural drainages like estuaries and rivers, then it must be prepared definitely. The pros really should think up a adept method of managing the job immediately after its finalization .You have to also keep in mind that project could become so essential that this requirements long term future extensions. This really is just but to talk about the technicians as well as skilled teams of qualified personnel experienced taken into account that from the start. The construction technique would be the epitome belonging to the design. It calls for the incorporation coming from all developing elements in order to create the desired drainage construction. The key design resource is cement Definite. Cement definite is a rate blend of concrete, sand and coarse aggregate). It possesses a great substantial compressive sturdiness which is totally free of rust. Typically, the earth is excavated depending on the design and style arrange and foundations within the structures put applying concrete. Reinforcements is usually necessary in great-tension zones to resist the impact of the the water. Steel taverns of this specs offered by the coming up with pros can be used. In other instances, ferrous precious metals can be utilized as support. Stones and bricks include the principal construction resources for strengthening the route surfaces with regards to opened discharge products while plumbing are mainly utilised in the idea drainages. Pipes number in sizes and fabric from metal pipes, definite water pipes, PVC`s and perhaps plastic materials .Generally, stainless steel pipes are described on the main constructions to stand up to weight and also lengthen the life-time for the mission even as it fits the ambitions. The building contractor hires accredited personnel who integrate materials to the wished-for end up. Repair of fluids discharge platforms is conducted by municipal team or standard water agencies. Upkeep perceives for it the surroundings is just not harmfully influenced, and also the principle of legislation is upheld from the people for the model. It needs to be conducted on a consistent basis to take out any contaminants, minimize clogging with the downstream and to guarantee the model operates properly without the need of surging. Any pointed out disadvantages all through the inspection within the construction should also be serviced. Frequent scrubbing of hook basins, draw inlets, in addition to other conveyance components like water pipes in divisions the place air-borne pollutants increase often ought to be facilitated. Several of the toxins involved are between other rubbish, alloys, blockages and natural and organic components. They ought to be withdrawn from the the water. Upon maintaining its essential that information of polished basins and route sectors be known. The sheer numbers of cleaned out basins and the volume of squander taken away should be documented downwards. The toxins compiled on the cleaning up activity with the discharge procedure must be stored in applicable storage containers, or completely unique places in ways that they can not be released here we are at the drainage .This type of water really needs to be filtered accompanied by a suited sieving unit right before it is discharged on the sewer. Incase release to your hygienic sewer is simply not helped, plus the the water needs to be motivated or vacuumed into a exclusive storing container and properly disposed off of. Minor vendors with small-scale constructions and number of grab basins carry out the washing of the water flow platforms personally. Buckets are of excellent us the following. Conversely, big fluids companies and municipalities call for technical devices to wash. This type of include vacuum cleaners, eliminating pumping systems, and buckets. Last but not least, repair of discharge units would merely named valuable if only it produced up new guidelines and policy that can be in settlement when using the recent legal guidelines. Offenders violating the explained protocols and policies must be punishable through regulations, being the setting must be protected from vices like air pollution. Other improvements could be meant to supervise competent water flow water and removing of pollutants from the channels. This would be an exact measure of an effective relief system and powerful, useful maintenance.

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text:
# Let X i , i = 1, ... , n, Y i , i = 1, ... , n be independent r.v.’s such that the X i ’s

Let Xi, i = 1, ... , n, Yi, i = 1, ... , n be independent r.v.’s such that the Xi’s

## Plagiarism Checker

Submit your documents and get free Plagiarism report

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text:
Cryptology ePrint Archive: Report 2003/075

Almost Security of Cryptographic Boolean Functions

Kaoru Kurosawa

Abstract: $PC(l)$ of order $k$ is one of the most general cryptographic criteria of secure Boolean functions. In this paper, we introduce its $\epsilon$-almost version. The new definition requires {\it only} that $f(X)+f(X+\Delta)$ is {\it almost} uniformly distiributed (while the original definition of $PC(l)$ of order $k$ requires that it is {\it strictly} uniformly distiributed). We next show its construciton. Better parameters are then obtained than normal $PC(l)$ of order $k$ functions.

Category / Keywords: secret-key cryptography / boolean functions

Contact author: kurosawa at cis ibaraki ac jp

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation

Short URL: ia.cr/2003/075

[ Cryptology ePrint archive ]


text:
If the diameter is 70cm, the circumference is 70cm(pi) = 70pi cm, or roughly 217cm. Transcript. Distance covered in on revolution/turn=circumference= πD=π×65 =204.2 cm =2.042 m =,how many turns will it 2km=2000 m. Hence revolutions/turns required for 2 km=2000/2.042 =979.42 turns The area of a circle is 616 sq cm, find its circumference? The length of the pipe is 14cm and its external radius is 9 cm. On the other hand, Light Bicycle is keen to post more and more useful bike-related articles so you can make decisions easier. In a right angled triangle $\triangle PQR$, PR is the hypotenuse of length 20 cm, $\angle PRQ$ = $30^{0}$, the area of the triangle is. agree to the. 2. The formerly popular 27 inch (630 mm) wheel size is now rare. What is the circumference? The area of rhombus is: 2. You can study other questions, MCQs, videos and tests for Railways on EduRev and even discuss your questions like The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. The cost of painting it at the rate of Rs.5 per 10 sq.cm will be: The volume of the metal of a cylindrical pipe is 748 cu.cm.. The 700c is an ideal wheel size as it is the ‘standard’ wheel size for most road bikes. How many revolutions will the wheel make during this journey? What size of bike do I need for my height of 5’6”? How many revolutions will the wheel make during the journey?1). If you ride on and around a circle with a 10 km diameter 12 times, how many revolutions does the wheel make? over here on EduRev! The actual ISO diameter of a traditional 26″ wheel is 559 millimeters. the bead radius) corresponds with the distance from the centre of the wheel to the centre of a brake block. I solely depend on you. 6 Answers. 6’2″ – 6’4″ = 19 – 21 inches; 6’4″ and taller = 21+ inches; Voilà! a.To the nearest revolution, how many times will the wheel turn if the bicycle is ridden for 3 miles? If the two wheels are front and rear wheel, both distances should be equal. Standard road bicycle wheel size today is 622 mm and it usually takes tyres of 23-622, or wider 25-622. (Take $\pi$ = $\frac{22}{7}$), 10. If the bike is moving at a velocity of 8.00 m/s, what is the centripetal acceleration on the perimeter of the bicycle wheel? The area of a circle is 616 sq cm, find its circumference? Examples of the 26-inch bike include Commencal Supreme Park (2015), Kona Stinky 26, and Rocky Mountain Maiden. m2) Of The System About An Axis Perpendicular To The Plane Of The Wheel Through Its Center? As with most bike wheel naming conventions, the term ’26 inch’ does not refer to the diameter of the wheel itself, but rather the approximate outside diameter of the tire that fits this wheel size. By comparing this dimension you can see if the brakes will reach when a different size of rim is fitted to your bike. Bike frames are measured from the middle of their bottom bracket to the end of their seat tube. Be sure of the type of bicycle you want: Mountain bike, city bike or road bike. The 92400 is meters converted to centimeters. The bigger wheels, however, have been skulking around the scene for decades. For example, if your offspring is between 95 and 100 cm tall, a 12-inch wheel fits perfectly. m. Find the length of the canvas required to build the tent, if the canvas is 2m in width. The diameter of a cycle wheel is 4 5 11 cm . 0 0 Light Bicycle can only speak for the rims we make. The diameter of a cycle wheel is 70 cm. the setup would look like this: 92400/2*21*3.14=700.6369426751592 the diameter of a cycle wheel is 70cm. The area of the hexagon is. If your wheel set is going to be used for both road and gravel, select a road rim and tire sizes 25mm-50mm. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire. It is to be painted inside as well as outside. If there were a wheel that had a circumference of 12.36375 cm, what would the diameter … Find out which wheel size is suitable for your new tyres. [The Radii Of Each Ballast Is … Get 1:1 help now from expert Physics tutors (mm)" boxes. the diameter of the wheel of a cycle is 63 cm find the number of times the wheel will rotate in travelling through a distance of 1 089 KM and the speed of the cycle in kilometre per hour if its wheel makes 500 revolutions per minute - Math - Circles Diameter of wheel of a cycle is 21 cm. The third number generally preceded by an "R" is the wheel diameter. C = 50.24 in; d = 50.24 in ÷ 3.14; C = 16 in 3 The radius of a circular rug is 4 ft. By continuing, I agree that I am at least 13 years old and have read and You can find them with 26” wheels, 27.5” wheels, or 29” wheels. the perimeter of the wheel is 2πr [r is radius] =2 *π *35 cm =70π cm . This wheel size is the largest available for conventional bicycles, giving a racing bike more stability at high speeds. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. We can use the equation c=pi(d) to get it, or use the more commonly cited formula c=2pi(r), with a few added steps. Communists, Nationalists, and China's Revolutions - History. Diameter of wheel of a cycle is 21 cm. circumference of wheel = πd = π * 70 cm. Harry Potter. find how many times the wheel revolve in order to cover a dist of 110cm 2. Diameter of wheel of a cycle is 21 cm. A bicycle wheel has a diameter of 64.0 cm and a mass of 1.80 kg. If the answer is not available please wait for a while and a community member will probably answer this The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. If the wheel of a car whose radius is 21 cm by taking 800 rpm, how long will it take to cover the same distance, π=22/7? 18750 3). Today when off road bicycles with wheels larger than standard MTB wheels started to be popular, it’s wheels are marketed as 29″, but in fact are 622 wheels with wider tyres (so that outer diameter is … Your 21 cm radius wheel will make approximately 701 revolutions traveling that 924 meters. How many revolutions will the wheel make during the journey?a)12325b)18750c)21000d)24350Correct answer is option 'B'. If you are traveling a speed of 10 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning? The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. The wheel of a truck has diameter of 84 cm, by taking 500 rpm it covers a certain distance in one hour. At first, measure the height of your child. Click on the Donate button and show your support with anything possible from your side. A bike with an 18″ frame is your ‘sweet spot’. 650b is a mountain bike wheel size that falls between 26in and 29in and is often (inaccurately) referred to as 27.5in. If your child measures more than 140 cm, you should choose a 26-inch wheel. How far will the bicycle travel if the wheel rotates 2000 times. Bikepacking/MTB/ The first number on a metric tyre is the width. are solved by group of students and teacher of Railways, which is also the largest student Thus, a wide range of small bike wheels are still found, ranging from 239 mm (9.4 in) diameter … How many revolutions will the wheel make during the journey?a)12325b)18750c)21000d)24350Correct answer is option 'B'. To use the calculator, select a wheel and tire size from the table or enter the wheel and tire size in mm in the "Dia. If the bike is traveling at a rate of 21 miles per hour, find the angular speed of the wheels. The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. The length of each side of the triangle is, If in a $\triangle ABC$, the medians CD and BE intersect each other at 0, then the ratio of the areas of $\triangle ODE$ and $\triangle ABC$ is. The diameter of Sheree's bicycle wheel is 0.705 m. Caculate how many turns the bicycle wheel will make if she rides the bicycle 1 km. Concept: Circumference of a Circle. How many revolutions will it make in moving 6.3km? (1 unit = 1 cm). Revolutions specifies, how often the wheel turns around at the covered distance. The cyclist takes .30 hours to reach his destination at the speed of 22 kmph. convert 1 km to cm). Its thickness is (Take $\pi$ = $\frac{22}{7}$), Each side of a regular hexagon is 1 cm. If in a $\triangle ABC$, the medians CD and BE intersect each other at 0, then the ratio of the areas of $\triangle ODE$ and $\triangle ABC$ is. diameter of wheel = d = 70cm. Find something that is 4 cm in diameter (or slightly smaller) and draw around it. The area of the hexagon is. Use a compass set to a radius of 2 cm. The number of revolutions your wheels need to make to go this distance is: 15.748 / 19.4 or 0.81 revolutions. Radius of a wheel is the span between center and edge, diameter ist twice the radius, the span from edge to opposite edge. Expert Answer 100% (10 ratings) Previous question Next question Get more help from Chegg. 12325 2). math. This website needs some kind support from All the visitors. Smaller tire sizes like the 25c is … Quick Answer: 700c is the size of your bike tire, according to the ‘French system’. Assume that the wheel is a hoop with all the mass concentrated on the outside radius. In this ThrillSpire article, we will give you a proper guide on the sizes of the bike frames. A bicycle with 40.20 cm diameter wheels is traveling at 28.00 km/hr. m. Find the length of the canvas required to build the tent, if the canvas is 2m in width. Since we're given the diameter, not the radius, the first formula makes more sense. And those benefits are undeniable. Today when off road bicycles with wheels larger than standard MTB wheels started to be popular, it’s wheels are marketed as 29″, but in fact are 622 wheels with wider tyres (so that outer diameter is … 21" Tire Diameter 185/60R13 = 21.7x7.3R13 215/50R13 = 21.5X8.5R13 225/45R13 = 21x8.9R13 225/50R13 = 21.9x8.9R13 255/40R13 = 21x10R13 If all three have a 15” frame, there will be a height difference between them due to their wheel size. A bicycle wheel has a diameter of 70.0 cm. These figures are useful for setting your cycle-computer and precisely calculating gears. The diameter of a bicycle wheel (including the tire) is 70cm.? You can make a list for us if you want, we will arrange updates later on and send you emails for the updates. 210004). convert 10 miles into inches: 10 miles = 10*5280 = 52800 feet = 633600 inches. A hemispherical bowl has 3.5 cm radius. circumference of wheel: (pi)d = (3.14)28 = 87.92 inches per revolution. In 1999, Wilderness Trail Bikes got the ball rolling in earnest when they produced the first real 29er mountain bike tire. The ISO for most tires is found on the sidewall along with the diameter and tire width. You have a couple options. To get the approximate diameter of the wheel with the tire on, you would take the diameter of tire x 2 (because it’s both on the top and bottom) + the diameter at the rim * pi (3.14) to get the cimcuference. a) At what angular speed do the wheels turn? So, to travel 110cm, it's going to take 110/70pi revolutions, or roughly 1/2 revolution. Now to solve: This means an internal rim width of at least 20mm. The diameter of a cycle wheel is 140 cm. Answers of Diameter of wheel of a cycle is 21 cm. Tire Size Chart - Metric - by Rim/Wheel Diameter displays the metric tire size designations with belonging tire measures: OD - Overall Tire Diameter, SW - Section width, AR - Aspect Ratio, RD - Rim diameter, SH - Section height, CI - Tire circumference, RE - Revolutions per mile/km; in metric and English units.. A bicycle wheel has a diameter of 57.7 cm and a mass of 2.66 kg. Alvi. The bicycle is placed on a stationary stand and a resistive force of 156 N is applied tangent to the rim of the tire. the bead radius) corresponds with the distance from the centre of the wheel to the centre of a brake block. This discussion on Diameter of wheel of a cycle is 21 cm. The length of each side of the triangle is, 3. The lengths of the diagonals of a rhombus are 8 cm and 6 cm.

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text:
# Student Colloquium

Thursday, February 11, 2016 — 4:30 PM EST

Michael Deveau, Department of Pure Math, University of Waterloo

"Calculus In Reverse"

In a typical first-year calculus course, we often introduce students to new results in a somewhat ad-hoc fashion. Do some of these theorems really belong in a calculus / real analysis course? What is it about the real numbers that makes these theorems work? We take a brief tour through some of the results of a standard calculus / real analysis course with a fresh perspective: the logician's program of Reverse Mathematics -- as interpreted by analysts, at least -- and investigate what makes $\mathbb{R}$ appropriate (or not) for calculus. In addition, we also discuss a pressing question: If we are ever contacted by an alien race, should we send them a copy of one of our calculus textbooks?

MC 5479

### December 2022

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text:
# Correlations for Volumetric Properties

## Molar Split Approximation

Given $$y_{i}$$ at reservoir conditions and assume that $$y_{n+}$$ goes to the liquid phase and $$y_{n-}$$ goes to the vapor phase at surface conditions.

### Derivation

Given the definition of the gas FVF and the real gas law, the definition of the gas FVF can be re-written as

From the molar material balance and the assumption that $$y_{n+}$$ goes to the liquid phase at surface conditions and the fact that the Z-factor at surface conditions is equal to 1 yields

Inserting equation \eqref{eq:step2} in equation \eqref{eq:step1} and re-arranging the fraction yields

### Method

The approximation for the dry gas FVF using the real gas law becomes

where the Z-factor can be calculated by an EOS or by correlation.

### Example

Given a mixture

$$y_i=[0.57116,0.04317,0.00416,0.01561,0.07881,0.13290,0.15417]$$

Assume that $$C_{5+}$$ goes to the liquid phase at surface conditions then $$y_{5+}=0.36589$$. The ratio of the dry and wet gas FVF then becomes

which indicates a widely different value of for the shrinkage of the gas!

## Cragoe Correlation

Note

The units used in this correlation are field units, i.e. pressure: (psia), temperature: (R), OGR: (STB/scf) and FVF: (ft3/scf).

### Method

where

and

In equation \eqref{cragoe_MW} $$\gamma_{API}$$ is the API gravity of the surface oil.

## Standing Oil FVF and GOR Correlations

In 1947 Standing published correlations for both oil FVF (for both saturated and undersaturated conditions), solution GOR and a bubble-point correlation1. The correlations were based on 105 different data-points for 22 different hydrocarbon systems. In the following sub-sections the oil FVF and solution GOR correlations are given.

Note

The units used in this correlation are temperature: (F), pressure: (psia), solution GOR: (scf/STB).

### Oil FVF (Saturated)

where $$\gamma_o$$ and $$\gamma_g$$ are the surface gas and oil specific gravities.

### Oil FVF (Underaturated)

where $$c_o$$ is the oil compressibility, $$p_b$$ is the bubble-point pressure and $$B_{ob}$$ is the oil FVF at the bubble-point pressure. The oil compressibility can be calculated by correlation or measured values.

Typically the bubble-point is calculated by correlation. Standing provides a correlation for the bubble-point given by re-arranging equation \eqref{eq:standing_GOR} given by

where $$\gamma_{API}$$ is the surface oil API gravity.

### Solution GOR

where $$\gamma_{API}$$ is the surface oil API gravity and $$\gamma_g$$ is the gas gravity specific gravities.

1. M.B. Standing. A pressure-volume-temperature correlation for mixtures of california oils and gases. In Drilling and Production Practice, paper API–47–275. American Petroleum Institute, 1947.


text:
# Analyzing Meshes¶

Very often there will be specific regions of a set of results that are the most of interest, and in those cases it can be helpful to pull out a particular region's data for visualization in a clearer way. The LineCrossSection and SurfaceCrossSection classes allow taking cross-sections of a mesh (or some other rasterizable object) along poly-lines drawn using the PolyDraw tool, letting you make an x/z or x/z/t plot from data laid out in x/y/z or x/y/z/t (respectively). These classes rasterize the data at a fixed resolution, and then sample the data at that resolution given the underlying polylines. The resolution may be defined in the units of the underlying coordinate system.

In [1]:
import holoviews as hv
import geoviews as gv
import cartopy.crs as ccrs
from colorcet import cm_n

from holoviews import opts

from earthsim.analysis import LineCrossSection, SurfaceCrossSection


text:
# Math Help - Difficult square number problem

1. ## Difficult square number problem

A pair of positive integers $(x, y)$ is called 'square' if both $x + y$and $xy$ are perfect square numbers. E.g. $(5, 20)$ is 'square' since $5 + 20 = 25$ and $5 x 20 = 100$, both which are perfect squares.

Prove no square pair exists in which one of its numbers is 3.

I'm not sure how to do this, but I think it involves mods in the solution.

2. Hello BG5965
Originally Posted by BG5965
A pair of positive integers $(x, y)$ is called 'square' if both $x + y$and $xy$ are perfect square numbers. E.g. $(5, 20)$ is 'square' since $5 + 20 = 25$ and $5 x 20 = 100$, both which are perfect squares.

Prove no square pair exists in which one of its numbers is 3.

I'm not sure how to do this, but I think it involves mods in the solution.

There may be a shorter route to the contradiction, but the following works OK.

Suppose that $(3,x)$ is a square pair. Then, for some $p, q$:

$3+x = p^2$ and $3x=q^2$

$\Rightarrow q$ is a multiple of $3$; say $q = 3r$

Then $3x = q^2 = 9r^2$

$\Rightarrow x = 3r^2$

$\Rightarrow 3 + x = 3+3r^2 = p^2$

$\Rightarrow 3(1+r^2) = p^2$

$\Rightarrow p$ is a multiple of $3$; say $p = 3s$

$\Rightarrow p^2 = 9s^2 = 3(1+r^2)$

$\Rightarrow 1+r^2 = 3s^2$

$\Rightarrow r^2 \equiv 2 \mod 3$

But this is impossible, since $0^2\equiv 0$ and $1^2 \equiv 2^2 \equiv 1 \mod 3$.

Hence the square pair $(3, x)$ does not exist.


text:
# Can anyone recommend a spell checker for tex files?

Doug McKenna doug at mathemaesthetics.com
Fri Aug 16 01:45:40 CEST 2019

Spell-checking TeX source code doing code-y things is no doubt fraught with difficulties doing the right thing.

Only two hours ago, I was going through a draft paper of mine in LaTeX, changing a word I had used ubiquitously, to a slightly less ambiguous word that I decided would be better.  But I hedged my bets.  Instead of just doing a simple text find and replace, I wrote a TeX macro to replace with, so that if I decided to undo my global change, I could just change the macro's definition to the previous word I was using.

But the word can be plural or not.

So for the plural instances, now my TeX source code is filled instances of the substitution macro that look like this:

\def\newword{widget}

...

... a whole lot of \newword s for English plurals

A spell-checker (or worse, corrector) is very likely going to flag that lone 's', which is not a word.  This would leave me in a mood somewhere between annoyed and murderous. :-)

Yes, I could have created macros for the plural words too (and the capitalized versions as well), but you get my point.  TeX is advertised as a Turing-complete macro language, and there will therefore be a near-infinite variety of creative uses that can't be out-thought by any one spell-checking algorithm.

- Doug McKenna


text:
# The problem

I'm writing a document where all of my equations are labeled, not by numbers, but by names, which I provide with amsmath's \tag command. I also use cleveref for ease of cross-referencing. And I just today decided I'd add hyperref. While this didn't break anything old (at least, not after I'd figured out where to put it), it didn't completely work: links to equations jump incorrectly. Why is this? And how can I fix it?

Edit: The extended problem. This isn't just with equations, it's with all mathematical environments. I make use of equation, align, align*, alignat, align*, and gather, and these all need to support appropriate links. And unfortunately, I just realized this, and the due date for this document is bearing down on me, which is my own fault; but the solution is sufficiently important to me that I'm adding a bounty. (The remainder of this question just refers to the shown MWE.tex; however, the problem is more general.)

# An example

In the following document, all three \eqref links jump to the first equation:

\documentclass{book}

\usepackage{amsmath}
\usepackage{hyperref}
\usepackage{cleveref}

\begin{document}

$$\label{eq:first}\tag{first} \text{First equation}$$

$$\label{eq:second}\tag{second} \text{Second equation}$$

$$\label{eq:third}\tag{third} \text{Third equation}$$

\begin{itemize}
\item A reference to~\eqref{eq:first}.
\item A reference to~\eqref{eq:second}.
\item A reference to~\eqref{eq:third}.
\end{itemize}

\newpage

For scrolling purposes.

\end{document}

If I either remove \usepackage{cleveref} or remove the \tags, everything works fine. But with both of them together, everything jumps to the first equation.

# Compilation messages

## With \usepackage{cleveref} and \tags

When I compile this example (in MWE.tex), I get the following warning messages in the log:

[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}pdfTeX warning (ext4): des
tination with the same identifier (name{equation.0.0.1}) has been already used,
duplicate ignored

\AtBegShi@Output ...ipout \box \AtBeginShipoutBox
\fi \fi
l.27 \newpage
pdfTeX warning (ext4): destination with the same identifier (name{
equation.0.0.1}) has been already used, duplicate ignored

\AtBegShi@Output ...ipout \box \AtBeginShipoutBox
\fi \fi
l.27 \newpage
] [2] (./MWE.aux) )

And sure enough, if I look at MWE.aux, it contains the following lines:

\newlabel{eq:first}{{{first}}{1}{\relax }{equation.0.0.1}{}}
\newlabel{eq:first@cref}{{[equation][2147483647][]{first}}{1}}
\newlabel{eq:second}{{{second}}{1}{\relax }{equation.0.0.1}{}}
\newlabel{eq:second@cref}{{[equation][2147483647][]{second}}{1}}
\newlabel{eq:third}{{{third}}{1}{\relax }{equation.0.0.1}{}}
\newlabel{eq:third@cref}{{[equation][2147483647][]{third}}{1}}

## With just \tags (no \usepackage{cleveref})

If I compile without cleveref, then I get the same warning:

[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}pdfTeX warning (ext4): des
tination with the same identifier (name{equation.0.0.1}) has been already used,
duplicate ignored

\AtBegShi@Output ...ipout \box \AtBeginShipoutBox
\fi \fi
l.27 \newpage
pdfTeX warning (ext4): destination with the same identifier (name{
equation.0.0.1}) has been already used, duplicate ignored

\AtBegShi@Output ...ipout \box \AtBeginShipoutBox
\fi \fi
l.27 \newpage
] [2] (./MWE.aux) )

However, the links work correctly, and the aux file contains

\newlabel{eq:first}{{{first}}{1}{\relax }{AMS.1}{}}
\newlabel{eq:second}{{{second}}{1}{\relax }{AMS.2}{}}
\newlabel{eq:third}{{{third}}{1}{\relax }{AMS.3}{}}

## With just \usepackage{cleveref}s (no \tags)

If I compile without using \tags, then I get no warning, the links work, and my aux file contains

\newlabel{eq:first}{{1}{1}{\relax }{equation.0.0.1}{}}
\newlabel{eq:first@cref}{{[equation][1][0]1}{1}}
\newlabel{eq:second}{{2}{1}{\relax }{equation.0.0.2}{}}
\newlabel{eq:second@cref}{{[equation][2][0]2}{1}}
\newlabel{eq:third}{{3}{1}{\relax }{equation.0.0.3}{}}
\newlabel{eq:third@cref}{{[equation][3][0]3}{1}}

## With nothing (neither \usepackage{cleveref} nor \tags)

If I compile without using either \usepackage{cleveref} or \tags, then I get no warning, the links work, and my aux file contains

\newlabel{eq:first}{{1}{1}{\relax }{equation.0.0.1}{}}
\newlabel{eq:second}{{2}{1}{\relax }{equation.0.0.2}{}}
\newlabel{eq:third}{{3}{1}{\relax }{equation.0.0.3}{}}

## Without \usepackage{hyperref}, but with everything else

If I instead remove just \usepackage{hyperref}, then I get no warning, there are no links, and my aux file contains

\newlabel{eq:first}{{{first}}{1}}
\newlabel{eq:first@cref}{{[equation][2147483647][]{first}}{1}}
\newlabel{eq:second}{{{second}}{1}}
\newlabel{eq:second@cref}{{[equation][2147483647][]{second}}{1}}
\newlabel{eq:third}{{{third}}{1}}
\newlabel{eq:third@cref}{{[equation][2147483647][]{third}}{1}}

## Replacing equation with gather

The hyperref README reports that the equation environment "[isn't] supported too well," and suggests replacing it with the gather environment. Doing that successfully gets rid of the error message, but doesn't fix the behavior of the links; they still jump to the wrong place. The aux file contains

\newlabel{eq:first}{{{first}}{1}{\relax }{Doc-Start}{}}
\newlabel{eq:first@cref}{{[equation][2147483647][]{first}}{1}}
\newlabel{eq:second}{{{second}}{1}{\relax }{Doc-Start}{}}
\newlabel{eq:second@cref}{{[equation][2147483647][]{second}}{1}}
\newlabel{eq:third}{{{third}}{1}{\relax }{Doc-Start}{}}
\newlabel{eq:third@cref}{{[equation][2147483647][]{third}}{1}}

# What's happening?

Admittedly, that's part of my question, but it looks to me like hyperref and \tag don't play well together: if I have both, I get the error message about duplicates. But it doesn't seem to cause any problems in the document unless cleveref is present as well.

I should also add a couple of caveats:

• This is an 85-page document. I really don't want to deal with changing out any of my packages at this point, but if it works….

• I'm compiling this document on a school machine, and so I don't have control over the main TeX install. I have installed some updated versions to my local texmf tree, however. Here are all the package versions in my log file:

• amstext 2000/06/29 v2.01
• amsbsy 1999/11/29 v1.2d
• amsopn 1999/12/14 v2.01
• hyperref 2011/04/09 v6.82f
• ltxcmds 2011/11/09 v1.22
• ifpdf 2011/01/30 v2.3
• pdftexcmds 2011/11/29 v0.20
• infwarerr 2010/04/08 v1.3
• ifluatex 2010/03/01 v1.3
• keyval 1999/03/16 v1.13
• kvsetkeys 2012/04/25 v1.16
• etexcmds 2011/02/16 v1.5
• pdfescape 2011/11/25 v1.13
• ifvtex 2010/03/01 v1.5
• ifxetex 2009/01/23 v0.5
• hycolor 2011/01/30 v1.7
• xcolor-patch 2011/01/30
• hopatch 2011/06/24 v1.1
• letltxmacro 2010/09/02 v1.4
• kvoptions 2011/06/30 v3.11
• intcalc 2007/09/27 v1.1
• url 2006/04/12 ver 3.3
• bitset 2011/01/30 v1.1
• bigintcalc 2012/04/08 v1.3
• atbegshi 2011/10/05 v1.16
• atveryend 2011/06/30 v1.8
• rerunfilecheck 2011/04/15
• uniquecounter 2011/01/30 v1.2
• cleveref 2012/03/07{} v0.18.5{}
• nameref 2010/04/30 v2.40
• refcount 2011/10/16 v3.4
-
I just noticed that the hyperref README suggests replacing equation by gather; that doesn't fix the behavior of the links, but I added information about what happens when I do that. – Antal Spector-Zabusky May 7 '12 at 4:48
I realized that what I was asking for was insufficient, so I've extended the question and added a bounty. – Antal Spector-Zabusky May 18 '12 at 19:41

I have a solution. However this might not be the most elegant way.

You have to define your own numbering scheme for hyperref so that each number is unique:

\listfiles
\documentclass{book}

\usepackage{amsmath}
\usepackage{hyperref}
\usepackage{cleveref}

%%% define a new counter and use it for \theHequation which hyperref uses for the links
\newcounter{Hequation}
\renewcommand{\theHequation}{\thechapter.\arabic{Hequation}}
\makeatletter
\makeatother

\begin{document}
$$\tag{first}\label{eq:first} \text{First equation}$$

$$\tag{second}\label{eq:second} \text{Second equation}$$

$$\label{eq:firstreal} \text{First equation without tag}$$

$$\tag{third}\label{eq:third} \text{Third equation}$$

$$\label{eq:secondreal} \text{Second equation without tag}$$

\begin{itemize}
\item A reference to~\eqref{eq:first}.
\item A reference to~\eqref{eq:second}.
\item A reference to~\eqref{eq:third}.
\item A reference to~\eqref{eq:firstreal}.
\item A reference to~\eqref{eq:secondreal}.
\end{itemize}

\newpage

For scrolling purposes.

\end{document}

As you can see \equation has to be redefined as well. Then equations with and without \tag can be mixed-up without any problems.

Best regards
Martin

-
This seems to work—thanks! A question, though: why are you patching \tag as well as \equation? Intuitively, it seems like you should only need to patch \equation to maintain this new unique \theHequation; and if I comment out the patch to \tag, everything seems to still work at a quick glance. – Antal Spector-Zabusky May 7 '12 at 19:10
Yes, you are right. Patching \equation is enough in this special situation, because \tag is always inside the equation environment. If you want to extend this mechanism to other amsmath environments, you have to patch other macros as well. – Martin May 8 '12 at 7:19
As you noticed, this only works for equation. Unfortunately, I only noticed this now too, which is my own fault but is unfortunate. I've updated the question to reflect my actual needs (I need correct links to most of the possible environments), and I've added a bounty. If you have the solution and/or the time, I'd love to have it... :-) – Antal Spector-Zabusky May 18 '12 at 19:42
I awarded you the bounty because your solution is what gave me the ability to understand what was going on and come up with a half-assed fix; thank you! (I'd still love to see if/how this generalizes to a nicer solution, but my urgent deadline is past, so it's just academic at this point. And/or if I need it in the future.) – Antal Spector-Zabusky May 25 '12 at 4:05

The correct way to use \tag with hyperref and amsmath is to use the starred math environments that are unnumbered. Then, they do not increment the equation counter, which implicitly defines an anchor based on the new counter value, only for \tag to decrement the counter again (there's nothing it can do about the already defined anchor, but one can use the hypertexnames=false option to hyperref to partially alleviate this if necessary).

Even with the above, there are incompatibility problems between hyperref, cleveref and amsmath. As Martin has noted, the problem is that cleveref directly implements amsmath macros and changes them, thus ignoring hyperref's work. One option then is to further patch the macros that amsmath provides to incorporate both hyperref's enhancements and cleverefs addition, which I have done in the following:

\documentclass{article}

\usepackage{amsmath}
\usepackage{hyperref}
\usepackage{cleveref}

\makeatletter

\def\make@df@tag@@#1{%
\gdef\df@tag{%
\maketag@@@{\Hy@make@anchor#1}%
\def\@currentlabel{#1}%
\def\cref@currentlabel{[equation][2147483647][]#1}%
}%
}
\def\make@df@tag@@@#1{%
\gdef\df@tag{%
\tagform@{\Hy@make@anchor#1}%
\toks@\@xp{\p@equation{#1}}%
\edef\@currentlabel{\the\toks@}%
\edef\cref@currentlabel{[equation][2147483647][]\the\toks@}
}%
}
\makeatother

\begin{document}

\begin{equation*}\label{eq:first}\tag{first}
\text{First equation}
\end{equation*}

\begin{equation*}\label{eq:second}\tag{second}
\text{Second equation}
\end{equation*}

\begin{equation*}\label{eq:third}\tag{third}
\text{Third equation}
\end{equation*}

$$\label{eq:fourth} \text{Fourth equation}$$

\begin{itemize}
\item A reference to~\eqref{eq:first}.
\item A reference to~\eqref{eq:second}.
\item A reference to~\eqref{eq:third}.
\item A reference to~\eqref{eq:fourth}.
\end{itemize}

\newpage

For scrolling purposes.

\end{document}

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Fantastic answer! Could you please explain how you found that? – mafp Mar 12 '13 at 21:43
@mafp: Glad it was of some help. I'm afraid it was a case of examining the various source files for each of the packages involved. Probably the issues with the interactions were never anticipated hence not documented or resolved. – cyberSingularity Mar 12 '13 at 21:56

For reference, this issue seems to have been fixed in recent versions of cleveref (at least since 0.18.10; not yet in CTAN but available from my web site). The redefinitions in the other answers are no longer be necessary. I haven't tracked down precisely which version of cleveref fixed this bug.

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Awesome! I just checked it out; with hyperref v6.82q, I get the spurious warnings, but things seem to work. Thanks! – Antal Spector-Zabusky Nov 24 '13 at 19:18

Since I had to find a solution to this for the final version of my document, here's the solution I found; it produces a lot of errors in the log file, but they don't appear to correspond to errors in the resulting document. I'm still curious about the Right Way™ to do this, though.

\makeatletter
\newif\if@plaintag
\@plaintagfalse
\let\plaintagform@\tagform@
\newcommand{\plaintag}[1]{\begingroup\let\tagform@\plaintagform@\tag{#1}\endgroup}
\def\tagform@#1{\if@plaintag\else\refstepcounter{equation}\fi%
\maketag@@@{[\textsc{\ignorespaces #1}]}}
\newcommand{\ptag}[1]{\@plaintagtrue\tag{#1}\@plaintagfalse}
\makeatother

Since I was redefining \tagform@ anyway (to render \maketag@@@ around small caps in square brackets), I forced it to include \refstep{equation} (modulo an if statement, for \tagged but unlabled equations). I also placed all \tags before \label`s (I'm not sure if this is necessary, but it didn't hurt). As a result, despite lots of warnings about duplicate labels, everything seemed to work properly; stepping the equation counter made the link destination correct.

-
This works, but is clearly sort of ugly. If there's a better solution, I'm all ears (really!), but this is what ended up in my document. – Antal Spector-Zabusky May 25 '12 at 4:05
I tried to create a solution by redefining hyperref's and cleverref's macros. I think, the problem is, that cleveref directly implements amsmath macros and changes them, thus ignoring hyperref's work. – Martin May 25 '12 at 7:42


text:
# Hits Array!

#1

It's telling me that my second loop is not pushing to the hits array...can anyone help?! I've been staring at it for an hour and a half lol.

var text = "Hey, how are you doing? my name is Mike.";
var myName = "Mike";
var hits = []
for(var i = 0; i if (text[i] ==="M") {
for(var j = i; j + (myName.length +i); j++) {
hits.push(text[j]);
}
}
}

#2

``````for(var j = i; j + (myName.length +i); j++) {
^``````

change the condition to reflect a condition statement.

so instead of `j + (myName.length + i) ;` try `j < (myName.length + i) ;`

``````for(var j = i; j < (myName.length +i); j++) {
^``````


text:
# AP Physics B : Understanding Wavelength, Frequency, and Velocity

## Example Questions

### Example Question #1 : Ap Physics 2

In the electromagnetic spectrum, __________ have the highest frequency and __________ have the greatest energy per photon.

X-rays . . . radio waves

infrared light . . . ultraviolet light

microwaves . . . microwaves

ultraviolet light . . . X-rays

gamma rays . . . gamma rays


text:
5

# Moacrigiven Foy-echelon TormWrite the systemequations (or Wnich thc niven matrixquamenicc matrix- (Enter each jnswcrtcrnsX,Ya Z, and #.)+x+ 2y+ 32y-2Zw + 2(6) Usc b...

## Question

###### Moacrigiven Foy-echelon TormWrite the systemequations (or Wnich thc niven matrixquamenicc matrix- (Enter each jnswcrtcrnsX,Ya Z, and #.)+x+ 2y+ 32y-2Zw + 2(6) Usc back-substitutionsolvc (nc Syscem(xYr z, W)4,3 1,3

moacri given Foy-echelon Torm Write the system equations (or Wnich thc niven matrix quamenicc matrix- (Enter each jnswcr tcrns X,Ya Z, and #.) +x+ 2y+ 32 y-2 Zw + 2 (6) Usc back-substitution solvc (nc Syscem (xYr z, W) 4,3 1,3

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text:
1. ## Calculus Word Problems

A hotel has 72 rooms.
Rooms are usually $90 per night. But if the owner raises the price to$95 per room per night, he finds that there will be 2 rooms fewer than usual($90 a room per night) hired. I am not sure whether for EVERY$95 dollar room, 2 rooms are left vacant, or are 2 rooms of the 72 rooms in total left vacant.

I think our teacher said that the Income formula that we have to calculate is:
Income = 108x - [or maybe +] (2x^2)/5
-----------------------------

1. Find the formula to calculate the income

2. Calculate the maximum Income

------------------------------

Could someone please explain calculus word problems like this to me in detail?

Thank You!

2. Originally Posted by janvdl
A hotel has 72 rooms.
Rooms are usually $90 per night. But if the owner raises the price to$95 per room per night, he finds that there will be 2 rooms fewer than usual($90 a room per night) hired. ... 1. Find the formula to calculate the income 2. Calculate the maximum Income Hello, I assume: a) that each room is rented for$90
b) that the price could be increased by multiple of $5: let x be the times that the price is increased: let i be the income: i(x) = (72 - 2x)(90 - 5x) = -10x² + 180x + 6480 The original situation is i(0) =$6480

The graph of this function is a parabola opening downward so the maximum value is at it's vertex. Use derivation:
i'(x) = -20x + 180. You'll get the maximum if i'(x) = 0 ==> x = 9

i(9) = $7290 when only 72 - 18 = 54 rooms are rented for a price of$(90-5*9) = $45 3. Sorry Earboth, my mistake. You are correct in what you did, but it still doesnt give me the income formula that I should have got... 4. Hello, janvdl! The problem is badly worded, but I'm familiar with this type. A hotel has 72 rooms. .Rooms are usually$90 per night.
But if the owner raises the price to $95 per room per night, he finds that there will be 2 fewer rooms rented than usual. (1) Find the formula to calculate the income (2) Calculate the maximum Income The problem is usually stated like this . . . When the owner charges$90 per room, all 72 rooms are rented.
Then he finds that for every $5 increase in the rate, he loses 2 guests. Let x = number of five-dollar increases in the rate. The rate will be: .90 + 5x dollars per night. He will lose 2 guests for every increase. . . Hence, he will have only: .72 - 2x guests. His income will be: .(90 + 5x)(72 - 2x) dollars. Therefore, the income function is: .I .= .6480 + 180x - 10x² .(1) Maximize the income function: .I' = 0 We have: .180 - 20x .= .0 . . . . x = 9 .** The maximum income is: .I .= .6480 + 180·9 - 10·9² .= .$7290 .(2)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**

To maximize his income, the owner should raise the rate nine times.
He will charge: .90 + 9·5 .= .$135 per night. As a result, he will lose 9·2 = 18 guests. . . He will have only: 72 - 18 .= .54 guests. But he will receive: .$135 × 54 .= .$7290 [Originally, his income was: .$90 × 72 .= .\$6450]

5. Ah, ok i understand now.

Thanks a lot to both of you!