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
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]
Related Questions
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
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!!! 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!
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
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
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
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.
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
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.
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.
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
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
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.
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
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
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.
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 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
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]
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*
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:
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)
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
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
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
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:
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
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
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!
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
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: