Suppose a change of coordinates T:R2→R2 from the uv-plane to the xy-plane is given by x=e−2ucos(5v), y=e−2usin(5v). Find the absolute value of the determinant of the Jacobian for this change of coordinates.

Answers

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The solution is  [tex]\frac{\delta  (x,y)}{\delta (u, v)} | = 10e^{-4u}[/tex]

Step-by-step explanation:

From the question we are told that

        [tex]x =  e^{-2a} cos (5v)[/tex]

and  [tex]y  =  e^{-2a} sin(5v)[/tex]

Generally the absolute value of the determinant of the Jacobian for this change of coordinates is mathematically evaluated as

     [tex]| \frac{\delta  (x,y)}{\delta (u, v)} | =  | \ det \left[\begin{array}{ccc}{\frac{\delta x}{\delta u} }&{\frac{\delta x}{\delta v} }\\\frac{\delta y}{\delta u}&\frac{\delta y}{\delta v}\end{array}\right] |[/tex]

        [tex]= |\ det\ \left[\begin{array}{ccc}{-2e^{-2u} cos(5v)}&{-5e^{-2u} sin(5v)}\\{-2e^{-2u} sin(5v)}&{-2e^{-2u} cos(5v)}\end{array}\right]  |[/tex]

[tex]Let \   a =  -2e^{-2u} cos(5v),  \\ b=-2e^{-2u} sin(5v),\\c =-2e^{-2u} sin(5v),\\d=-2e^{-2u} cos(5v)[/tex]

So

     [tex]\frac{\delta  (x,y)}{\delta (u, v)} | = |det  \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] |[/tex]

=>    [tex]\frac{\delta  (x,y)}{\delta (u, v)} | = | a *  b  - c* d |[/tex]

substituting for a, b, c,d

=>    [tex]\frac{\delta  (x,y)}{\delta (u, v)} | =  | -10 (e^{-2u})^2 cos^2 (5v) - 10 e^{-4u} sin^2(5v)|[/tex]

=>   [tex]\frac{\delta  (x,y)}{\delta (u, v)} | =  | -10 e^{-4u} (cos^2 (5v)   + sin^2 (5v))|[/tex]

=>  [tex]\frac{\delta  (x,y)}{\delta (u, v)} | = 10e^{-4u}[/tex]

Suppose A Change Of Coordinates T:R2R2 From The Uv-plane To The Xy-plane Is Given By X=e2ucos(5v), Y=e2usin(5v).

Related Questions

The expression (q16)(q−5)2 is equivalent to qn. What is the value of n? 42 22 -160 13

Answers

Answer:

  22

Step-by-step explanation:

In order to get one of the answer choices, it appears we need to interpret your input as ...

  [tex](q^{16}q^{-5})^2 = (q^{16-5})^2=q^{11\cdot 2}=q^{22}[/tex]

The value of n is 22.

__

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

Answer:

6

Step-by-step explanation:

Jaquarius has a pair of limited edition Jordan tennis shoes that are 12 inches long each. What is the total length of both of his shoes in feet?

Answers

Answer:

Total length of shoes in feet = 2 feet

Length of each shoe = 1 feet

Step-by-step explanation:

Given:

Length of each shoe = 12 inches

Find:

Total length of shoes in feet

Computation:

Total length of shoes = [12 + 12] inches

Total length of shoes = 24 inches

12 inches = 1 feet

Total length of shoes in feet = 24 / 12

Total length of shoes in feet = 2 feet

Length of each shoe = 1 feet

Write 2^-3 in word form

Answers

Answer:

two raised to the power of -3

Two to the power of negative 3

Step-by-step explanation:

[tex]2^-^3 = \frac{1}{2^3}[/tex]

1 divided by 2 to the power of 3

The following table presents the time taken to review articles that were submitted for publication to a particular journal during a recent year. A few articles took longer than 6 months to review; these are omitted from the table. Consider the data to be a population. (image) (a) Approximate the variance of the times. Round the answer to at least two decimal places. The variance is (b) Approximate the standard deviation of the times. Round the answer to at least two decimal places. The standard deviation is

Answers

Answer:

Variance = 0.1645

Standard deviation = 0.4056

Step-by-step explanation:

Kindly check attached picture for detailed explanation

What is your average speed in miles per hour and in feet per second if you travel a mile in 16 ​minutes?

Answers

Step-by-step explanation:

Mile Per Hour to Foot Per Second Conversion Table

Miles Per Hour Feet Per Second

16 mph 23.47 ft/s

17 mph 24.93 ft/s

18 mph 26.4 ft/s

19 mph 27.87 ft/s

Name the rays on line c.

Answers

Answer:

BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD

Step-by-step explanation:

"BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD" Are all the possible rays on line c.

zane bought a pair of jeans that originally cost $56. he used a coupon for 25% off and paid$8 in sales tax

Answers

Answer:

$38.64

Step-by-step explanation:

so the equation needed to solve is $56*0.25 and that number is 14. Since it is a coupon you subtract 14 from 56 and end up with 42. Now multiply 0.08*42 and you got your sales tax, $3.36. now subtract that from 42 and you have your answer

Answer:

He paid 50 dollars

Step-by-step explanation:

25% off = 75/100 x 56 = 42

42 + 8 = 50

if this question is about what percentage the tax is, then the answer would be 19.05%

x/100 x 42 = 50

42x/100 = 50

42x = 5000

x = 5000/42

x = 119.05

119.05 - 100 = 19.05%

HELP ASAP ILL GIVE YOU ALL!!! What is the coefficient of (6x^2-4x-5)-

Answers

Answer:

32x-5

Step-by-step explanation:

6x^2-4x-5

36x-4x-5

32x-5

32x-5 would be the answer I’m pretty sure

which number represents a whole number​

Answers

Answer: The answer is D

Step-by-step explanation:

I divided 24 by 3 and it gave me 8 which is a whole number.

While riding on a carousel, Angela travels a distance of 65 meters every 15 seconds. What is her speed in kilometers per hour? A. 3.9 km/hr B. 14.4 km/hr C. 15.6 km/hr D. 156.0 km/hr

Answers

C - 15.6

65 meters = 0.065
0.065 x 4 = 0.26 (in 1 minute)
0.26 x 60 = 15.6 (in a hour)
15.6km per hour

Can someone help my son with this it’s homework and he don’t understand it

Answers

Hey there! I think the answer is (-1,3)

6. Joe runs 3/4 mile in 1/2 hour. Find his average speed in miles per hour.

Answers

Answer:

1.5 MPH

Step-by-step explanation:

3/4 = 0.75

3/4 x 2 = 0.75 x 2 = 1.5

A particular computer takes 14 minutes to download a 42​-minute TV show. How long will it take the computer to download a 2.5​-hour ​movie?

Answers

Answer

about 15 min to 1 hour

Which statement about this system of equations is true?


A. The system has a unique solution at (0,6)

B. The system has a unique solution at (0,-4)

C. The system has no solution

D. The system has infinitely many solutions

Answers

Answer:

The system has NO solution

Answer C in your list

Step-by-step explanation:

Notice that the lines are parallel, they will not intercept, and therefore there is no answer to the system

A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow.
Student Math Writing
1 540 474
2 432 380
3 528 463
4 574 612
5 448 414
6 502 526
7 480 430
8 499 453
9 610 615
10 572 541
11 390 335
12 593 613
(a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.)
(b) Calculate the test statistic.

Answers

Answer:

Calculated t=  0.011659

t ≥ t ( 0.025,11) = 2.201

So the null hypothesis is accepted.

Step-by-step explanation:

Student     Math      Writing            Difference                            d²

                                             math score − writing score

1                 540          474               66                                      4356

2                432         380                52                                      2704

3               528           463              65                                       4225

4               574             612             -38                                  1444

5               448            414              34                                    1156

6               502            526            -24                                   576

7               480            430              50                                 2500

8              499            453             46                                    2116

9              610             615             -5                                       25

10             572             541             31                                      961

11              390             335            55                                  3025

12             593             613          -20                                     400            

∑              6168          5856          312                                     23488                

1) We state our null and alternative hypothesis as

H0: ud= 0                   Ha: ud≠0

2) The significance level alpha is set at α= 0.05

3) The test statistic under H0 is

t= d`/ sd/√n

which has t distribution with n-1 degrees of freedom.

4) The critical region is t ≥ t ( 0.025,11) = 2.201

5) Computations

d`= ∑di/n= 312/12= 31.2

Variance = ∑(di- d`)²/n-1= 1/n-1 [ ∑di²-( ∑di)²/n]

= 1/11[ 23488- (312)²/12]

= 1/11[ 23488- 8112] = 1/11[15376]= 5976.7272

Standard Deviation= √ 5976.7272= 77.2510= 77.25

Now t= 3.12/77.25/√12= 0.011659

The calculated t value= 0.011659 falls in the acceptance region . So we accept our null hypothesis  and reject the alternative hypothesis.

What is 8.6 increased by 75%

Answers

Answer:

15.05

Step-by-step explanation:

8.6 is 100% of 8.6.

To increase it by 75%, you'll end up with 175% of 8.6

175% of 8.6 =

= 1.75 * 8.6

= 15.05

What does point A represent on the graph? Jordan needs 3 cups of diced chicken for 2 salads. Jordan needs 2 cups of diced chicken for 3 salads. Jordan needs 3 cups of diced chicken for 1 and one-half salads. Jordan needs 1 and one-half cups of diced chicken for 3 salads.

Answers

Answer:

The answer is 3

Step-by-step explanation:

1 1/2 cups of chicken for 3 salads

Prove that the EOQ cost function can be rewritten as
g(Q) = h/2 * Q(Q - underroor 2K/h) + underroot 2Kh
Use this to prove without using calculus.

Answers

Answer:

the EOQ cost function [tex]\mathbf{g(Q)= \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}}[/tex]

Step-by-step explanation:

Given that:

[tex]g(Q) = \dfrac{h}{2 \lambda Q} \begin {pmatrix} Q- \sqrt{\dfrac{2 K \lambda}{h}} \end {pmatrix}^2 + \sqrt{\dfrac{2 Kh}{\lambda}}[/tex]

Total cost = Purchase Cost + Ordering Cost + Holding Cost

i.e

T = [tex]P \lambda + h \dfrac{Q}{2}+\dfrac{\lambda K}{Q}[/tex]

By differentiating with respect to Q and equating to zero, we have:

[tex]0 = 0 +\dfrac{h}{2}- \dfrac{\lambda K}{Q^2}[/tex]

[tex]Q* = \sqrt{\dfrac{2 k \lambda}{h}}[/tex]

Now;

[tex]T = P \lambda + \dfrac{h}{2Q}(Q-Q^*)^2 + hQ^*[/tex]

[tex]T = \dfrac{h}{2Q}(Q- \sqrt{\dfrac{2 \lambda K}{h}})^2 + \sqrt{2 hK \lambda } + P \lambda[/tex]

[tex](\dfrac{T - P \lambda}{\lambda }) = \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}[/tex]

Therefore:

the EOQ cost function [tex]\mathbf{g(Q)= \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}}[/tex]

Find the missing number to make the average correct. The average of 11, 17, 18, and ? is 17.

Answers

Answer:

The missing number is:

22

Step-by-step explanation:

There are 3 numbers and one more

4 numbers and your average is 17

then:

17*4 = 68

then:

11 + 17 + 18 + a = 68

46 + a = 68

a = 68 - 46

a = 22

Check:

(22 + 11 + 17 + 18)/4 = 17

68/4 = 17

you must be at least 18 years old to vote

Answers

Answer:

To vote you need to be a US citizen and be at least 18 years old by election day

Answer:

18 years old to vote

Step-by-step explanation:

You must be 18 years old to vote and you have to be a citizen. Also to vote, you have to be a resident of Florida. So therefore, yes you have to be 18 years old to vote.

Hope this Helps!

12. Higher order Thinking is the Product of two irrational numbers always an irrational number ? Explain​

Answers

Answer:

Not always but sometimes

Step-by-step explanation:

The product of two irrational numbers is sometimes and not always an irrational number.

So, Let us take two Example:

Example # 1:

Let the two irrational numbers be [tex]\sf \sqrt{37} \ and \ \sqrt{2}[/tex]

So, Multiplying these will give us

=> [tex]\sf \sqrt{37} * \sqrt{2}[/tex]

=> [tex]\sf \sqrt{74}[/tex]

Which is an irrational number.

Example # 2:

Let the two irrational numbers be [tex]\sf \sqrt{2} \ and \ \sqrt{2}[/tex]

So, Multiplying them would give us:

=> [tex]\sf \sqrt{2} * \sqrt{2}[/tex]

=> [tex]\sf (\sqrt{2} )^2[/tex]

=> 2

Which is a rational number.

This means that the product of two irrational numbers is not always an irrational number but sometimes an irrational number.

There are two different music download companies that offer a monthly plan for downloading songs. S-Jams charges $1.29 per song plus $10 monthly fee. C-tunes charges $0.99 per song plus $16 monthly fee. When will the company’s plans cost the same? Write an expression for the cost of S-Jams.

Answers

Answer:

Thus, when both S-jams and C-tunes have 20 songs downloaded in a month  , the cost will be same.

an expression for the cost of S-Jams $0.99n + $16

Step-by-step explanation:

For

S-Jams

cost of 1 song = $1.29

let there be n songs downloaded in a month

then

cost of n songs = n*cost of 1 song  = $1.29n

monthly fee = $10

Total cost of S-Jams = $1.29n+$10

________________________________________

For

C-Tunes

cost of 1 song = $0.99

let there be n songs downloaded in a month

then

cost of n songs = n*cost of 1 song  = $0.99n

monthly fee = $16

Total cost for C-Tunes= $0.99n + $16

we have to find When will the company’s plans cost the same.

Total cost of S-Jams = Total cost of C- Tunes

1.29n+10 = 0.99n + 16

=> 1.29n - 0.99n = 16-10

=> 0.30n = 6

=> n = 6/0.3 = 20

Thus, when both S-jams and C-tunes have 20 songs downloaded in a month  , the cost will be same.

an expression for the cost of S-Jams $0.99n + $16

HELP ASAP!!! To make a quiche, you need 1 tablespoon of butter for every 6 eggs. Write a ratio that compares these two quantities. Which ratios are equivalent to this ratio? Check all that apply. StartFraction 12 eggs Over 2 tablespoons EndFraction StartFraction 15 eggs Over 3 tablespoons EndFraction StartFraction 24 eggs Over 4 tablespoons EndFraction StartFraction 9 eggs Over 1.5 tablespoons EndFraction

Answers

Answer:

Options A, C and D.

Step-by-step explanation:

It is given that, we need 1 tablespoon of butter for every 6 eggs to make a quiche.

Ratio that compares these two quantities [tex]=\dfrac{6\text{ eggs}}{1\text{ tablespoons} }[/tex]

We need to find the ratios which are equivalent to this ratio.

[tex]\dfrac{6\text{ eggs}}{1\text{ tablespoons} }\times \dfrac{2}{2}=\dfrac{12\text{ eggs}}{2\text{ tablespoons} }[/tex]

[tex]\dfrac{6\text{ eggs}}{1\text{ tablespoons} }\times \dfrac{3}{3}=\dfrac{18\text{ eggs}}{3\text{ tablespoons} }\neq \dfrac{15\text{ eggs}}{3\text{ tablespoons} }[/tex]

[tex]\dfrac{6\text{ eggs}}{1\text{ tablespoons} }\times \dfrac{4}{4}=\dfrac{24\text{ eggs}}{4\text{ tablespoons} }[/tex]

[tex]\dfrac{6\text{ eggs}}{1\text{ tablespoons} }\times \dfrac{1.5}{1.5}=\dfrac{9\text{ eggs}}{1.5\text{ tablespoons} }[/tex]

Therefore, the correct options are A, C and D.

Answer:

A,C,D

HOPE THIS HELPS!

6. aA box in a certain supply room contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs. Suppose that three bulbs are randomly selected. a. What is the probability that exactly one of the selected bulbs are rated 75-watt? b. What is the probability that all three of the elected bulbs have the same rating? c. What is the probability that one bulb of each type is selected? d. What is the probability that at least two of the selected bulbs are rated 75-watt?

Answers

Answer:

A) 0.2967

B) 0.0747

C) 0.2637

D)0.6933

Step-by-step explanation:

We are told the box contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs.

Thus, total number of bulbs = 4 + 5 + 6 = 15 bulbs

This is a combination problem.

Thus;

A) probability that exactly one of the selected bulbs are rated 75-watt will be = ((6C2) × (9C1))/(15C3)

= (15 × 9)/455

= 0.2967

B) probability that all three of the elected bulbs have the same rating;

Number of ways to select three 40 watt bulbs out of the 4 in the box = 4C1 = 4!/(3! × 1!) = 4

Number of ways to select three 60 watt bulbs out of the 5 in the box = 5C1 =

5!/(3! × 2!) = 10

Number of ways to select 75 watt bulbs out of the 6 in the box = 6C1 = 6!/(3! × 3!) = 20

Total number of ways = 4 + 10 + 20 = 34.

Thus, probability that all three of the elected bulbs have the same rating = 34/15C3 = 34/455

= 0.0747

C) probability that one bulb of each type is selected =

[(4C1) × (5C1) × (6C1)]/(15C3)

= (4 × 5 × 6)/455

= 0.2637

D) probability that at least two of the selected bulbs are rated 75-watt =

[(4C1 × 5C1 × 6C2)/15C3] + 6C3/15C3

= (4 × 5 × 15/455) + 20/455

= 0.6493 + 0.044

= 0.6933

Peter bought 45 greeting cards at 3 for $2.00. he sold them for 5 for $4.00. how much money did he make

Answers

Step 1) Set up a proportion to find how much Peter spent

45 cards / x dollars = 3 cards / 2 dollars

Step 2) Cross-multiply to solve the proportion

3x = 90

x = $30

Step 3) Set up a proportion to find how much Peter made

45 cards / x dollars = 5 cards / 4 dollars

5x = 180

x = $36

Step 4) Subtract the amount Peter made by the amount he spent

36 - 30 = $6

Answer: Peter made $6

($2/3) * 45 = $30

($4/5) * 45 = $36

$36 - $30 = $6

what is the solution of the equation? 3(y-5)+2=5​

Answers

Answer:

Y=- 6

3(y-5)+2=5

multiply

3y-15+2=5

add

3y-13=5

add pos 13 to the neg 13 to

cancel it out and add +13 to 5

3y=18

divide -3 to pos 3 and 18 to cancel it out

y= -6

Which point would represent the value of v—72 Include the letter of the answer and then justify your response using complete sentences.??

Answers

Answer:

Verbal expression x more than 7 can be represented ... If a team scores 27 points in a game, then 6T + p ... Algebraic expressions include variables, numbers, ... the sides of a cube all have the same length, V = x • x • x, or x ... Write a sentence describing what the length of ... REASONING Explain how to evaluate a[(b − c)

Step-by-step explanation:

Priya and Tyler are discussing the figures shown below. Priya thinks that B, C, and
D are scaled copies of A. Tyler says B and D are scaled copies of A. Do you agree
with Priya, or do you agree with Tyler? Explain your reasoning.
A
B
C
D

Answers

Answer:

No, I do not agree with them. Both are wrong.

Step-by-step explanation:

For a shape or figure to be considered a scaled copy of another, the length of all the segments of scaled copy must be equal to the length of all corresponding segments of the original figure multiplied by the same scale factor.

By examining the scaled copies B, C, and D, we would conclude that only D can be referred to as a scaled copy of D, because all the segments are exactly twice the corresponding segments of A. C and B do not have all its segment scaled in the same proportion.

Therefore, we cannot agree with Priya, nor Tyler. They are both wrong.

P (x) is a polynomial. Here are a few values of P (x): P(-5)=-2 and P (5)=-1 What is the remainder when P(x) is divided by (x+5)? (Answer choices in the picture)

Answers

Answer:

– 2

Step-by-step explanation:

From the question given above, the following data were obtained:

P(x) = polynomial

P(–5) = – 2

P(5) = –1

Remainder when P(x) is divided by

(x + 5) =?

To obtain the remainder when P(x) is divided by (x + 5), we shall apply the reminder theorem as follow:

Let (x + 5) be equal to 0

(x + 5) = 0

x + 5 = 0

Subtract 5 from both side

x + 5 – 5 = 0 – 5

x = –5

Replace x in P(x) with –5 as shown below:

P(x) = polynomial

x = – 5

P(–5)

From the question given above,

P(–5) = – 2

Therefore, when P(x) is divided by

(x + 5), the remainder is – 2.

What number is greater than 271,680 but less than 276,108

Answers

Answer:

276,108 < x < 271,680

Step-by-step explanation:

*Hope this helped*

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