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# BPSK consecutive same symbols

I have a question regarding BPSK. If we want to modulate the bit stream $$[0, 0]$$ with $$T_\text{ bit}=0.25 \text{ sec}$$ and the carrier frequency of the cosine that carries the BPSK signal is $$2\ \rm Hz$$ then the resulting waveform would be the one with the discontinuity or would the signal continue as it is until it reaches $$0.5\ \text{sec}$$? See pics below, it makes sense to me that we would have a discontinuity at $$0.25\ \text{sec}$$ because otherwise the receiver which samples the transmitted signal at every $$T_\text{bit}$$ would confuse the second zero as an 1:

• Are you sure it makes much sense to have a symbol rate greater (4 Hz) than the carrier (2 Hz) for BPSK? Jan 16 at 17:31
• That is what is given to us
– Jmk
Jan 16 at 17:40
• then what is given to you makes no sense. The general assumption is that the carrier frequency is much larger than the signal bandwidth, and that's not the case here. Jan 16 at 17:52
• I understand that but what i need to know is whether the graph would have a discontinuity, as i understand from the receiver block diagram it samples the signal for every Ts so if there is no "break" it would guess the bit to be 1 not 0.
– Jmk
Jan 16 at 17:57
• We can assume for the sake of the question just that carrier frequency is not a multiple of the bit rate and we would still have the same question.
– Jmk
Jan 16 at 18:01

The canonical baseband version of BPSK is that we wish to transmit a sequence $$\{a_k\}$$ of bits ($$0$$ or $$1$$) at a rate of $$1$$ bit every $$T$$ seconds using a pulse $$g(t)$$ of duration $$T$$ and so the transmitted baseband signal is $$s_{\text{baseband}}(t) = \sum_{k=-\infty}^\infty (-1)^{a_k}g(t-kT).$$ This is a sequence of nonoverlapping pulses of the form $$\pm g(\cdot)$$ spaced $$T$$ seconds apart. If, for example, $$g(t)$$ has value $$1$$ for $$t \in [0,T)$$, then $$s(t)$$ is a sequence of rectangular pulses of duration $$T$$ with the $$k$$-th pulse lasting from $$t=kT$$ to $$t=(k+1)T$$. Let's use this specific $$g(t)$$ for the rest of this answer. Note that $$s_{\text{baseband}}(t)$$ has value $$0$$ or $$1$$ for all $$t$$, and that it changes from one value to the other at times tenant are multiples of the bit duration $$T$$. Some elementary books on digital communication extend these notions to the passband signal too, saying that the passband BPSK signal during $$[0,T)$$ is of the form (say) $$\pm g(t)\cos(2\pi f_ct)$$ (where $$f_c$$ is the carrier frequency) and so during $$[T,2T)$$, the passband BPSK signal is just this passband RF burst delayed in time by $$T$$ seconds. That is, such texts take the passband BPSK signal to be $$s_{\text{passband}}(t) = \sum_{k=-\infty}^\infty (-1)^{a_k}g(t-kT)\cos(2\pi f_c(t-kT)).$$ Such a re-setting of the carrier phase to $$0$$ every $$T$$ seconds leads to discontinuities such as seen in the OP's first figure which correspond to $$a_0=a_1 =1$$.
In practice, and even in more advanced textbooks on digital communications, the BPSK passband signal is of the form $$s_{\text{passband}}(t) = s_{\text{baseband}}(t)\cos(2\pi f_ct) = \left(\sum_{k=-\infty}^\infty (-1)^{a_k}g(t-kT)\right)\cos(2\pi f_ct)$$ which makes the modulation aspect very clear: there is an oscillator that is producing the carrier signal $$\cos(2\pi f_ct)$$, and this is being modulated by the baseband BPSK signal. Sure looks like amplitude modulation to the untrained eye, but it is indeed phase modulation, because the baseband signal has value $$\pm 1$$ and since $$\cos(2\pi f_ct-\pi)=-\cos(2\pi f_ct)$$, we can write
$$s_{\text{passband}}(t) = \cos\left(2\pi f_ct - \pi\sum_{k=-\infty}^\infty a_kg(t-kT)\right)$$ where that inner sum has value $$1$$ or $$0$$ for all $$t$$ and so $$s_{\text{passband}}(t)$$ is a sinusoidal signal whose phase at all times is either $$0$$ or $$\pi$$, and the phase can flip from $$0$$ to $$\pi$$ or vice versa only at $$T$$ second intervals. With $$a_0=a_1=1$$, the phase remains at $$\pi$$ during $$[0,2T)$$ leading to the second plot provided by the OP.
• Is the last equation missing a $pi$ in front of the sum? Also - one thing I think people find confusing (at least I have before) - I know you noted at the top that you're using a pulse g(t) =1 over [0,T) for your answer, but the final equations showing how it is actually phase modulation does not hold when a different g(t) is used. This is often done, for example when doing RRC filtering. I would argue this is true of most real-world implementations of BPSK (or at least what we tend to call BPSK) and its one thing that's not really well spelled out in textbooks. Interested in your thoughts. Jan 18 at 20:09


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A second-order LTI system is described by the following state equations,

$\frac{d}{dt}x_1(t)-x_2(t)=0$

$\frac{d}{dt}x_2(t)+2x_1(t)+3x_2(t)=r(t)$

where $x_1(t)$ and $x_2(t)$ are the two state variables and $r(t)$ denotes the input. The output $c(t)$=$x_1(t)$. The system is

1. undamped (oscillatory)
2. underdamped
3. critically damped
4. overdamped

recategorized

format: plain


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# Worksheet on Simple Word Problems on Ratio

Practice the questions given in the worksheet on simple word problems on ratio. The word problem on ratio are related to divide different types of quantities according to the ratio.

1. Divide 64 cm in the ratio 5 : 3.

2. Divided 81 into three parts in the ratio 2 : 3 : 4.

3. The angles of a triangle are in the ratio 3 : 2 : 7. Find each angle.

4. Divided $104 among X, Y and Z in the ratio 1/2 : 1/3 : 1/4. 5. Divide$150 between David and Ken in the ratio 3 : 7.

6. $720 is divided between x and y in the ratio 4 : 5. How many dollars will each gets? 7. Two numbers are in the ratio 5 : 7. Their difference is 10. Find the numbers. 8. The sides of a triangle are in the ratio 3 : 2 : 4. If the perimeter of the triangle is 27 cm, find each side of it. 9. In a class, the ratio of boys to the girls is 7 : 8. What part of the whole class are girls? 10. Divide a sum of$1,350 among Ashley, Benny and Carol such that Benny gets equal to one-third of Ashley and Carol gets equal to half of Benny.

11. The price of bread increased from $12 to$13. Find the ratio of the increase in price to the original price.

Answers for the worksheet on simple word problems on ratio are given below to check the exact answers of the above ratio problems.

1. 40 cm and 24 cm

2. 18, 27 and 36

3. 45°, 30°, 105°

4. $48,$32 and $24 5. David$45; Ken $105 6. x gets$320 and y gets $400 7. 25, 35 8. 9 cm, 6 cm and 12 cm 9. 8/15 10. Ashley, =$900, Benny = $300 and Carol =$150

11. 1 : 12


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## Tuesday, January 02, 2007

### Chemistry in HTML: JavaScript from the server

Recently I blogged about a Greasemonkey script to take advantage of semantic markup of chemistry in blogs (and HTML in general), and later made some plans how this can be extended. One of the ideas was to make this userscript available from the server, instead of having people need to install Greasemonkey and the script separately. So, here it is.

sechemtic.js

Consider this (X)HTML:
 <title>m1</title>


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# Centroid of Triangle

In Î”ABC, the mid-points of the sides BC, CA, and AB are D, E, and F respectively. The lines AD, BE, and CF are called medians of the triangle ABC, the points of concurrency of three medians is called centroid. Generally it is represented by G.

Also, AG = AD, BG = BE, and CG = CF

Apollonius theorem

AB2 + AC2 = 2(AD2 + BD2)

# Escribed circles of a triangle and their radii

The circle which touches the side BC and two sides AB and AC produced of a triangle ABC is called the escribed circle opposite to the angle A. Its radius is denoted by r1. Similarly, r2 and r3 denote the radii of the escribed circles opposite to the angles B and C respectively. The centers of the escribed circles are called the ex-centers. The center of the escribed circle opposite to the angle A is the point of intersection of the external bisectors of angles B and C. The internal bisector of angle A also passes through the same point. The center is generally denoted by I1.

In a Î”ABC, we have
1. r1 =
2. r1 = s tan
3. r1 = 4R sin cos cos ,

r2 = 4R cos sin cos ,

r3 = 4R cos
m â€“ n Theorem

Let D be a point on the side BC of a Î”ABC such that BDDC = m : n and âˆ ADC = Î¸, âˆ BAD = Î±, and âˆ DAC = Î². Then
1. (m + n) cot Î¸ = m cot Î± â€“ n not Î²
2. (m + n) cot Î¸ = n cot B â€“ m cot C


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# Renaming an obj based on a Vertex Group script

I have a model with parts named obj0, obj1 etc which I am creating vertex groups with the same name for. I'm joing them together to edo and then After editing the model I split by vertices. I'm trying to rename all the original parts their name based on their vertex group name now using a script to save time. The following is what I have so far.

I have this which works when there's just one vertex group in the obj, but after splitting by vertex it keeps the remaining ones in. How would I edit this code so that the obj is renamed from the VertexGroups.active_index selected instead of the at the top of the list?

Thank you.

• why did you post your script as an image? Please post your code as text in a code block in the question. – David Mar 24 '18 at 19:56

import bpy


text: The microstructure of a lead-tin alloy at 180$$^{\circ}$$C consists of primary $$\beta$$ and eutectic structures. If the mass fractions of these two microconstituents are 0.57 and 0.43, respectively, determine the composition of the alloy.


text:
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Found in: Page 1000

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Integrated Concepts(a) On a day when the intensity of sunlight is $${\rm{1}}{\rm{.00\;kW/}}{{\rm{m}}^{\rm{2}}}$$, a circular lens $${\rm{0}}{\rm{.200\;m}}$$ in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of $${\rm{20}}{\rm{.}}{{\rm{0}}^{\rm{^\circ }}}$$. Assuming the sunlight is unpolarised and the polarizers are $${\rm{100\% }}$$efficient, what is the initial rate of heating of the water in $$^\circ {\rm{C}}/{\rm{s}}$$, assuming it is $$80.0\%$$ absorbed? The aluminium beaker has a mass of $$30.0$$grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.

1. The initial rate of heating of the water is $$0.02\frac{{^\circ {\rm{C}}}}{{\rm{s}}}$$.
2. Yes, the polarizing filters get hot.

See the step by step solution

## Step 1: Definition electric and magnetic field

Light reflected or transmitted through a particular medium so that all vibrations are confined to a single plane.

## Step 2: Finding energy absorbed

(a)

Let us first calculate the total energy absorbed in one second ( power) by the water and the beaker. Two polarizing sheets of plastic reduce the intensity of the light and then the lens focuses the light on the water and that means that only the light that passes through the lens heats the water and the beaker. The power is then:

\begin{align}P &= IA\eta \\ &= {I_0}{\cos ^2}\theta {r^2}\pi \eta \\ &= {10^3}\;\frac{{\rm{W}}}{{{{\rm{m}}^2}}} \times {\cos ^2}{20^\circ } \times {(0.1\;\;{\rm{m}})^2} \times \pi \times (0.8)\\ &= 22.19\;\;{\rm{W}}\end{align}

Next, let us find the change in temperature of the water and the beaker in one second. We will assume that the water and the beaker stay in thermal equilibrium at all time (that they have the same temperature).

The total heat that we have to deliver to the water and the beaker is:

$$Q = {m_w}{c_w}\Delta T + {m_a}{c_a}\Delta T$$

## Step 2: Finding initial rate of heating

If we look at the heat delivered to the water and the beaker in one second we get:

\begin{align}\frac{Q}{{\Delta t}} &= {m_w}{c_w}\frac{{\Delta T}}{{\Delta t}} + {m_a}{c_a}\frac{{\Delta T}}{{\Delta t}}\\\frac{Q}{{\Delta t}} &= \frac{{\Delta T}}{{\Delta t}}\left( {{m_w}{c_w} + {m_a}{c_a}} \right)\end{align}

But this is just our power delivered $$P$$:

\begin{align}P &= \frac{{\Delta T}}{{\Delta t}}\left( {{m_w}{c_w} + {m_a}{c_a}} \right)\\\frac{{\Delta T}}{{\Delta t}} &= \frac{P}{{{m_w}{c_w} + {m_a}{c_a}}}\end{align}

Plugging in the values (Table 14.1 from page 523. of the textbook) we get:

\begin{align}\frac{{\Delta T}}{{\Delta t}} &= \frac{{22.19\;\;{\rm{W}}}}{{(0.25\;\;{\rm{kg}})\left( {4186\;\frac{{\rm{J}}}{{{\rm{kg}}{ \cdot ^\circ }{\rm{C}}}}} \right) + (0.03\;\;{\rm{kg}})\left( {900\;\frac{{\rm{J}}}{{{\rm{kg}}{ \cdot ^\circ }{\rm{C}}}}} \right)}}\\ &= 0.02\;\frac{{^\circ {\rm{C}}}}{{\rm{s}}}\end{align}

## Step 3: Finding polarisation filter heats or not

b) The polarizing filter gets hot. They absorb some of the light energy as molecular kinetic energy (vibration), but temperature is a measure of kinetic energy.

$$\left( {{E_k} = \frac{3}{2}{k_b}T} \right)$$

So, if the kinetic energy increases then the temperature increases as well.


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## Model Structure

The LMIC reports are generated using an age-structured SEIR model. The developed model is an extension of the model used in our previous report (see Report 12) and the source code for the model can be found at https://github.com/mrc-ide/squire. In this model, the infectious class is divided into different stages reflecting progression through different disease severity pathways. These compartments are:

• S = Susceptibles
• E = Exposed (Latent Infection)
• $$I_{Mild}$$ = Mild Infections (Not Requiring Hospitalisation) – including asymptomatic infection
• $$I_{Case}$$ = Infections that will subsequently require hospitalisation
• $$I_{Hospital}$$ = Hospitalised Infection (Requires General Hospital Bed)
• $$I_{ICU}$$ = Hospitalised Infection in critical care/ICU (Requires critical care/ICU Bed)
• $$I_{Rec}$$ = Hospitalised Infection Recovering from critical care/ICU Stay (Requires General Hospital Bed)
• R = Recovered

Given initial inputs of hospital/ICU bed capacity and the average time cases spend in hospital, the model dynamically tracks available hospital and ICU beds over time. Individuals newly requiring hospitalisation (either a hospital or ICU bed) are then assigned to either receive care (if the relevant bed is available) or not (if maximum capacity would be exceeded otherwise). Whether or not an individual receives the required care modifies their probability of dying.

## Interventions

### Version 5

We continue the extensions made in version 4, by extending $$R_t\sigma$$ to consider more flexible mobility independent changes to transmission after $$pld$$. Starting one week after $$pld$$ we fit a shift to $$R_t$$ every 14 days, which is maintained after the 14 day period. In this way we model mobility independent changes to that change every 2 weeks. The last mobility independent change is maintained for the last 4 weeks prior to the current day to reflect our inability to estimate the size of this parameter, $$R_t\rho_n$$ below, due to the approximate 21 day delay between infection and death. $$R_t$$ is now given by:,

$R_{t,i} = R_{0,i} . f(-M_{eff}.(1-M_i(t)) -M_{eff.pld}.(M_i(t) - M_{pld}) - R_t\rho_1 - R_t\rho_2\ \ ... \ -R_t\rho_n)$ where $$R_t\rho_1$$ is the first mobility independent change in transmission, which starts 7 days after $$pld$$, i.e. is equal to 0 before this, and is in effect for the remainder of the simulation. $$R_t\rho_2$$ is the second mobility independent change in transmission, which starts 21 days after $$pld$$, i.e. 2 weeks after $$R_t\rho_1$$. We use strong priors, ($$N(0, 0.2)$$, where $$N$$ is the normal distribution with a mean of 0 and a standarad deviation of 0.2) to ensure that where mobility is still informative of transmission (where mobility is increasing transmission is also increasing) it is the mobility parameters that are driving the epidemic trajectory rather than the mobility independent changes in transmission.

### Version 4

We assume that transmission can decouple further from mobility, such that after lockdown transmission can be lower than $$R_0$$ at 100% mobility:

$R_{t,i} = R_{0,i} . f(-M_{eff}.(1-M_i(t)) -M_{eff.pld}.(M_i(t) - M_{pld}) - R_t\sigma)$ where $$M_{pld}$$ is the mobility at its nadir (at post lockdown date, $$pld$$) and is only in effect after $$pld$$ such that when $$t <= pld$$, $$M_{eff.pld} = 0$$.

$$R_t\sigma$$ is a one time signmoidal shift in $$R_t$$ that occurs over 30 days after post lockdown date to reflect mobility independent changes to transmission resulting from changing behaviour. $$R_t\sigma$$ is thus equal to 0 prior to $$pld$$ and is equal to the maximum value of $$R_t\sigma$$ for all time points more than 30 days after $$pld$$.

### Version 3

We assume that the impact of mobility on transmission will be different after lockdown ends, with a new $$M_{eff}$$ parameter, $$M_{eff.pld,i}$$ estimated for after lockdown, with $$R_t$$ given by:

$R_{t,i} = R_{0,i} . f(-M_{eff,i}.(1-M_i(t))),\ when\ t < Post\ Lockdown\ Date$ $R_{t,i} = R_{0,i} . f(-M_{eff.pld,i}.(1-M_i(t))),\ when\ t > Post\ Lockdown\ Date$ where the post lockdown date is inferred as when mobility is at its nadir.

### Version 2

We incorporate interventions using mobility data made publically available from Google, which provides data on movement in each country and includes the percent change in visits to places of interest (Grocery & Pharmacy, Parks, Transit Stations, Retail & Recreation, Residential, and Workplaces). Similar to Version 1, we assume that mobility changes will reduce contacts outside the household, whereas the increase in residential movement will not change household contacts. Consequently, we assume that the change in transmission over time can be summarised by averaging the mobility trends for all categories except for Residential and Parks (in which we assume significant contact events are negligable). Formally, $$R_t$$ (time varying reproductive number) for country $$i$$ is given by:

$R_{t,i} = R_{0,i} . f(-M_{eff,i}.(1-M_i(t)))$ where $$f (x) = 2 exp(x)/(1 + exp(x))$$ is twice the inverse logit function. $$M_i(t)$$ is the average mobility trend at time $$t$$ (in which 1 represnts 100% mobility (i.e. no change) and 0 represents 0% mobility) and $$M_{eff,i}$$ is the mobility effect size for country $$i$$. In countries in which mobility data is not available, we use a Boosted Regression Tree model, trained to government policy data from the ACAPS Government measures Dataset, to predict the change in mobility. In scenario projections going forwards we use the mean of the last 7 days mobility as the assumed mobility in the absence of changs in interventions.

### Version 1

In version 1 of these reports, we incorporated the impact of interventions that have been put in place using data from the Oxford Coronavirus Government Response Tracker. We currently make assumptions about the efficacy of these interventions and so the projections should be interpreted as scenarios rather than predictions. Work is ongoing for version 2 to integrate formal statistical fitting to improve these projections. In summary, school closures are assumed to cause a 10% reduction in contacts. Work closure is assumed to cause 30% reduction in contacts. Banning of public events is assumed to lead to a 5% reduction in contacts while restrictions on movement or a lockdown is not in force. Restrictions of movement is assumed to cause an additional 37.5% reduction in contacts on top of the 40% reduction due to school and work closure, leading to a total 77.5% reduction.

## Model Parameters

The parameter table below summarises the current best estimates incorporated in the package as of 2020-09-19. These will be updated as our understanding of the epidemic develops.

Parameter Value Reference
Basic reproductive number, $$R_0$$ 3.0 Report 13
Mean Incubation Period 4.6 days Report 9; Linton et al.; Li et al. The last 0.5 days are included in the I_MILD and I_CASE states to capture pre-symptomatic infectivity
Generation Time 6.75 days Report 9
Mean Duration in $$I_{MILD}$$ 2.1 days Incorporates 0.5 days of infectiousness prior to symptoms; with parameters below ~95% of all infections are mild. In combination with mean duration in $$I_{CASE}$$ this gives a mean generation time as above
Mean Duration in $$I_{CASE}$$ 4.5 days Mean onset-to-admission of 4 days from UK data. Includes 0.5 days of infectiousness prior to symptom onset
Mean Duration of Hospitalisation for non-critical Cases ($$I_{HOSP}$$) if survive 9.5 days Based on unpublished UK data
Mean Duration of Hospitalisation for non-critical Cases ($$I_{HOSP}$$) if die 7.6 days Based on unpublished UK data
Mean duration of Critical Care ($$I_{ICU}$$) if survive 11.3 days Based on UK data adjusted for censoring
Mean duration of Critical Care ($$I_{ICU}$$) if die 10.1 days Based on UK data
Mean duration of Stepdown post ICU ($$I_{Rec}$$) 3.4 days Based on unpublished UK data
Mean duration of hospitalisation if require ICU but do not receive it 1 day Working assumption
Probability of dying in critical care 50% Based on UK data
Probability of death if require critical care but do not receive it 95% Working assumption based on expert clinical opinion*
Probability of death if require hospitalisation but do not receive it 60% Working assumption based on expert clinical opinion*
Multiplier of duration of stay for LIC and LMIC settings compared to HIC 50% Working assumption based on expert clinical opinion*

*N.B. Given the substantially weaker health systems in LIC and LMIC, it is likely that disease outcomes will differ from the UK. The estimates listed above for the key parameters determining the severity outcomes are the result of a rapid expert clinical review. Eight clinical experts with experience both in treating COVID-19 patients in the UK and with previous experience in clinical practice in LIC/LMICs were asked to provide their assessment of severity outcomes in LMICs. Although there was broad consensus on these outcomes, it should be noted that there was also consensus that this is likely to be highly heterogeneous both within and between countries due to other factors that are difficult to quantify and for which data sources do not readily exist as of 2020-09-19.

### Age-Specific Parameters

Age-Group Proportion of Infections Hospitalised Proportion of hospitalised cases requiring critical care Proportion of non-critical care cases dying
0 to 4 0.001 0.050 0.013
5 to 9 0.001 0.050 0.013
10 to 14 0.001 0.050 0.013
15 to 19 0.002 0.050 0.013
20 to 24 0.005 0.050 0.013
25 to 29 0.010 0.050 0.013
30 to 34 0.016 0.050 0.013
35 to 39 0.023 0.053 0.013
40 to 44 0.029 0.060 0.015
45 to 49 0.039 0.075 0.019
50 to 54 0.058 0.104 0.027
55 to 59 0.072 0.149 0.042
60 to 64 0.102 0.224 0.069
65 to 69 0.117 0.307 0.105
70 to 74 0.146 0.386 0.149
75 to 79 0.177 0.461 0.203
80+ 0.180 0.709 0.580
Source Verity et al. 2020 corrected for non-uniform attack rate in China (see Report 12) Adjusted from IFR distributional shape in Verity et al. 2020 to give an overall proportion of cases requiring critical care of ~30% to match UK data Calculated from IFR in Verity et al. 2020 corrected for non-uniform attack rate in China (see Report 12) given the 50% fatality rate in critical care.


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# How to write absolute value equations as piecewise equations calculator

Identities are introduced in the first chapter, and revisited throughout. Then explain why the equation the student originally wrote does not model the relationship described in the problem.

The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

Here are more examples, with explanations. Here are some examples: Students will connect previous knowledge from Algebra I to Geometry through the coordinate and transformational geometry strand.

Grade 5 Arkansas 5. Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions. Then we need to get everything to the left side to have 0 on the right first.

You may also be asked to take an absolute value graph and write it as a piecewise function: This means we can write this absolute value function as a piecewise function.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Check the answers; the work!

The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.

In other words, they do not assume you've got any prior knowledge other than the standard set of prerequisite material needed for that class. Got It The student provides complete and correct responses to all components of the task.

There are a couple of calculus examples in the first four sections, but in all of these cases I've also tried to provide non Calculus examples as well.

So the whole piecewise function is: Try it; it works!

Write and solve an equation to find the times after Erin starts filming that the bird is 50 feet horizontally from her. Write a function that models this situation.

The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.

The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations. Grade 4 Arkansas 4. In addition, students will study polynomials of degree one and two, radical expressions, sequences, and laws of exponents.

Applications of Absolute Value Functions Absolute Value Functions are in many applications, especially in those involving V-shaped paths and margin of errors, or tolerances.

Learn these rules, and practice, practice, practice! In proof and congruence, students will use deductive reasoning to justify, prove and apply theorems about geometric figures.

Students will connect functions and their associated solutions in both mathematical and real-world situations. These notes assume no prior knowledge of differential equations. That costs more than a human haircut at least my haircuts!

If you are an instructor and are using this book with your class, please drop us an email so we can track use and keep you updated with changes.

Also included are reminders on several integration techniques.Expressing absolute value equations as piecewise functions. Ask Question. up vote 1 down vote favorite.

1. I'm not sure how to express this function in piecewise form without using absolute values: Re-write paper to make it truly double blind A Riddle of Riddles If my business hours start atat what time should the office be open for.

An absolute value equation is an equation that contains an absolute value expression.

The equation You can write an absolute value inequality as a compound inequality. \left | x \right |. Get the free "Absolute value equations calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. Algebra Examples. Step-by-Step Examples.

Algebra. Absolute Value Expressions and Equations. Write the Absolute Value as Piecewise. The piecewise polynomials are when and when. Learn how to solve absolute value equations and how to graph absolute value functions. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.

Absolute value & piecewise functions. Possible mastery points. A list of progress levels towards mastery. Each section. Determining Linear Equations of Lines in Slope-intercept Form.

Determining Linear Equations in Slope-Intercept Form - Part 1 (LA) Ex: Determine a Linear Equation From a Table of Values (Slope-Intercept Form) (09x).

How to write absolute value equations as piecewise equations calculator
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text:
A geometric viewpoint on computation?

Let me try to explain what I am trying to do in this work related to “computing with space“. The goal is to understand the process of emergence, in its various precise mathematical forms, like:

– how the dynamics of a big number of particles becomes the dynamics of a continuous system? Apart the physics BS of neglecting infinities, I know of very few mathematically correct approaches. From my mixed background of calculus of variations and continuous media mechanics, I can mention an example of such an approach  in the work of Andrea Braides    on the $\Gamma$-convergence of the energy functional of a discrete system to the energy functional of a continuous system and atomistic models of solids.

– how to endow a metric space (like a fractal, or sub-riemannian space) with a theory of differential calculus? Translated: how to invent “smoothness” in spaces where there is none, apparently? Because smoothness is certainly emergent. This is part of the field of non-smooth calculus.

– how to explain the profound resemblance between geometrical results of Gromov on groups with polynomial growth and combinatorial results of Breuillard, Gree, Tao on approximate groups? In both cases a nilpotent structure emerges from considering larger and larger scales. The word “explain” means here: identify a general machine at work in both results.

– how to explain the way our brain deals with visual input?  This is a clear case of emergence because the input is the excitation of some receptors of the retina and the output is almost completely not understood, except that we all know that we see objects which are moving and complex geometrical relations among them. A fly sees as well, read From insect vision to robot vision by N. Franceschini, J.M. Pichon, C. Blanes. Related to this paper, I cite from the abstract (boldfaced by me):

We designed, simulated, and built a complete terrestrial creature which moves about and avoids obstacles solely by evaluating the relative motion between itself and the environment. The compound eye uses an array of elementary motion detectors (EMDS) as smart, passive ranging sensors. Like its physiological counterpart, the visuomotor system is based on analogue, continuous-time processing and does not make use of conventional computers. It uses hardly any memory to adjust the robot’s heading in real time via a local and intermittent visuomotor feedback loop.

More generally, there seems to be a “computation” involved in vision, massively parallel and taking very few steps (up to six), but it is not understood how this is a computation in the mathematical, or computer science sense. Conversely, the visual performances of any device based on computer science computation up to now, are dwarfed by any fly.

I identified a “machine of emergence” which is in work in some of the examples given above. Mathematically, this machine should have something to do with emergent algebras, but what about the computation part?

Probably geometers reason like flies: by definition, a geometrical statement is invariant up to the choice of maps. A sphere is not, geometrically speaking, a particular atlas of maps on the sphere. For a geometer, reproducing whatever it does by using ad-hoc enumeration by  natural numbers, combinatorics  and Turing machines is nonsense, because profoundly not geometrical.

On the other hand, the powerful use and control of abstraction is appealing to the geometer. This justifies the effort to import abstraction techniques from computer science and to replace the non-geometrical stuff by … whatever is more of a geometrical character.

For the moment, such efforts are mostly a source of frustration, a familiar feeling for any mathematician.

But at some point, in these times of profound changes in, mathematics as well as in the society, from all these collective efforts will emerge something beautiful, clear and streamlined.