evaluate the given integral by making an appropriate change of variables. 7 x − 7y 3x − y da, r where r is the parallelogram enclosed by the lines x − 7y = 0, x − 7y = 5, 3x − y = 2, and 3x − y = 7

Answers

Answer 1

Answer: The value of the integral is 49/4 ln(2).

Step-by-step explanation:

We begin by finding a suitable change of variables that simplifies the integrand and makes it easier to integrate over the region R. In this case, we can use the transformation:

u = x - 7y

v = 3x - y

To obtain the Jacobian of this transformation, we take the partial derivatives of u and v with respect to x and y:

∂u/∂x = 1, ∂u/∂y = -7

∂v/∂x = 3, ∂v/∂y = -1

So, the Jacobian is given by: J = ∂(u,v)/∂(x,y) = (1)(-1) - (-7)(3) = 20

Now we can rewrite the integral in terms of u and v:

∬R 7x - 7y/(3x - y) da = ∬R (7u + 7v)/(20v) |J| du dv

where R is the region enclosed by the lines u = 0, u = 5, v = 2, and v = 7.

The limits of integration for u and v are determined by the intersection points of the lines that form the boundary of the parallelogram R. To obtain these points, we solve the following system of equations:

u = 0 and u = 5 - 7v/3

v = 2 and v = 7 - 3u/2

Solving for u and v, we get the following limits of integration:

0 ≤ u ≤ 5 - 7v/3

2 ≤ v ≤ 7 - 3u/2

Substituting these limits of integration into the integral expression, we have:

∬R 7x - 7y/(3x - y) da = ∫2^7 ∫0^(5-7v/3) (7u + 7v)/(20v) |J| du dv

Evaluating this double integral gives:∬R 7x - 7y/(3x - y) da = 49/4 ln(2)

Therefore, the value of the integral is 49/4 ln(2).

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Related Questions

The Hiking Club is on a trip to hike up a mountain. The members increased their elevation 290 feet during their hike
this morning. Now they are at an elevation of 450 feet.

a. Explain how to find their elevation before the hike.

b. Han says the equation e + 290 = 450 describes the situation.
What does the variable e represent?

C. Han says that he can rewrite his equation as
e = 450 + -290 to solve for e. Compare Han's strategy to your
strategy for finding the beginning elevation.

Answers

Answer:

Step-by-step explanation:

A. Subtract 290 from 450, 450-290= 160

B. The variable e represents the elevation before they started the hike

C. 450+-290= 450-290

The requried elevation before the hike is given as 160 feet and the required equation model of the situation is e + 290 = 450 where e represents the elevation before the hike.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

a. To find the members' elevation before the hike, we can subtract the increase in elevation from their current elevation. So, their elevation before the hike would be 450 - 290 = 160 feet.

b. In the equation e + 290 = 450, the variable "e" represents the members' elevation before the hike.

c. Han's strategy for finding the beginning elevation involves adding -290 to both sides of the equation e + 290 = 450 to get e = 450 + -290. This is equivalent to subtracting 290 from both sides of the equation e + 290 = 450. Both strategies result in the same equation, e = 160, which tells us that the members' elevation before the hike was 160 feet.

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‼️ PLEASEE HELPPP ‼️

Answers

Answer:

30

Step-by-step explanation:

3x - 27 = x +11

3x -27 +27 = 11 + 27

3x - x = x -x + 38

2x = 38

2x ÷ 2 = 38

X = 19

19 × 3 -27 = 30

HELP PLEASE!

The initial population of Rochester is 17,500 and is
projected to grow at a rate of 4.5% perdecade.
Write an expression for the projected population
of Rochester after “n” decades.

Answers

Answer:

Step-by-step explanation:

I still...really don't know

Write the number 7.8 x 10^3 in standard form.

Answers

Answer = 7,800

Since 10 is raised to the third power, there are 3 digits after the decimal, which would be 8 and two zeroes since no other digits are given, so 7,800.

Can anyone help me with this question?

Answers

It is the top left option
Top left option is the answer you’re looking for

Calculate the amount of work done if you use a 150N force to push a 50kg box 5m across the kitchen floor.

Answers

Answer:

750 J

Step-by-step explanation:

Brian is tiling a patio and ran out of tiles. The width of the remaining area of ⅔ yard. The length of the remaining area is 4 yards. What is the area Brian has left to tile?

Answers

Answer:

Area of the remaining patio = 2.67 square yards

Step-by-step explanation:

Width of the remaining area of the patio = [tex]\frac{2}{3}[/tex] yards

Length of the remaining area of the patio = 4 yards

Since, area of the remaining area of the rectangular patio

= Length × Width

= [tex]\frac{2}{3}\times 4[/tex]

= [tex]\frac{8}{3}[/tex]

= 2.67 square yards

Therefore, area of the remaining area of the patio = 2.67 square yards

The ministry of health was interested in the relationship between the office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire. After 5 years they gathered and analyzed the entire data.
A) Sample study
B)Experiment
C) Observational Study

The researchers found that those workers who reported taking regular 10-minute breaks during the workday were 41% percent more likely to develop cancer over the next five years than workers who didn't leave their offices during the workday

A)The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
B) The result suggests that starting to take 10-minute breaks during the workday will increase the risk of developing cancer for a teacher.
C)The result suggests that if a public worker takes 10-minute breaks during the workday, he has a 41% chance of developing cancer.
D)The result suggests that starting to take 10-minute breaks during the workday will increase the risk of developing cancer for a public worker.

Answers

Answer:

Step-by-step explanation:

The answer for the second part of the question would be.

C)The result suggests that there's a positive correlation between taking 10-minutes breaks during the say and developing cancer in public workers.

The correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.

What is correlation?

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.

The health ministry only distributes forms to workers every five years to collect information on office jobs and worker health concerns. They are just monitoring the workers, and the survey allows them to assess and establish a link between office employment and worker health concerns. Therefore, it is an observational study.

The conclusion that can be concluded from this study is that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.

Hence, the correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.

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The product of two numbers is 4 2/9, if one of the number is 38, find the number

Answers

Answer:

let x and y be the two number then according to question ,

xy=4 2/9

or, xy= 38/9

if one of the number is 38 then,

38x=38/9

or, x= 1/9 is the correct ans.

Cual es el 5% de 80?

Answers

4 porque...
.05*80=4

33 1/3 % of what number is21?

Answers

Answer:

33 1/3% of 21 is 63.64$ or rounded to the nearest whole number it is 64%

Step-by-step explanation:

I just solved

Find the distance between (2, 8) and (−6, 2).

The distance is ( ) units.

Answers

Answer:

✓100 = 10

Step-by-step explanation:

2= x1

8= x2

-6= y1

2= y2

Then you apply your distance formula to solve.

Hope it helps

Factor completely
x^2 - 8x + 16

Answers

Answer:

(x - 4)^2

Step-by-step explanation:

PLS helpp
ill give brainliest

Answers

the answer is c. if u make a number line, -2.5 would be less than -2.

Work out, giving your answer in its simplest form:
4/7 divided by 2 1 / 3

Answers

Step-by-step explanation:

4/7÷21/3

=4/7*3/21

=12/147

Answer:

[tex]\frac{12}{49}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{7}[/tex] ÷ 2 [tex]\frac{1}{3}[/tex] ← change mixed number to improper fraction

= [tex]\frac{4}{7}[/tex] ÷ [tex]\frac{7}{3}[/tex]

To perform the division

Leave the first fraction. change division to multiplication and turn the second fraction upside down.

= [tex]\frac{4}{7}[/tex] × [tex]\frac{3}{7}[/tex] ← multiply numerators/ denominators together

= [tex]\frac{4(3)}{7(7)}[/tex]

= [tex]\frac{12}{49}[/tex]

If three points are coplanar, they must be collinear. Since the answer is false, state a counterexample.

Answers

Answer:

Collinear points are points that lie on a line. Any two points are always collinear because you can always connect them with a straight line. Three or more points can be collinear, but they don't have to be. … Any two or three points are always coplanar

Step-by-step explanation:

Answer:

They could be on different lines or on no line, but in the same plane.

Step-by-step explanation:

Hope This Helps!!

(brainliest please, if possible)

Levi resolveu a expressão, 8×(-3)+7×5+(– 10)² ÷ 50, mas apagou o resultado. Resolva você também essa expressão e encontre o resultado. *​

Answers

Answer:

61

Step-by-step explanation:

8×(-3)+7×5+(-10)²÷50

apply the PEMDAS rule or (parenthesis, exponent, multiplication,division,addtion,subraction)

24+7×5+(-10)²÷50

24+7×5+100÷50

24+35+100÷50

24+35+2

61

hellppp fast plzzzzzz​

Answers

i cant see it that much

Answer:

49? I think

Step-by-step explanation:

Independent Practice


The equation k = 1.6d gives an approximate relationship between d miles and k kilometers. The distance between Columbus, Ohio, and Des Moines, Iowa, is 665 miles. Express the distance in kilometers.


A.
1,064 km


B.
415.6 km


C.
666.6 km


D.
663.4 km

Answers

[tex]k = 1.6d[/tex]

[tex]k = 1.6(665)[/tex]

[tex]k = 1064[/tex]

The distance is 1064 km.

Answer:

A. 1,064 km

Step-by-step explanation:

1 Mile is 1,6 Kilometers

430 Miles  = 688 Kilometers (430 * 1,6)

665 Miles = 1064 Kilometers (665 * 1,6)

1- 1.6(430)= 688 Km

2. 1.6(665)=1064 Km

Using 1.6 as the consant then 430* 1.6 = 688 Km

655 * 1.6 = 1048Km

if i understand what you need properly, all you do is multiply the miles x 1.6 and you will get k. so 430miles x 1.6 = 688k

and 665miles x 1.6 = 1064k

what's
[tex] \sqrt{36} [/tex]
chess ?​

Answers

[tex] \huge \purple{\tt{Answer:}} [/tex]

[tex] \sf{\sqrt{36}} = \sf{6} [/tex]

Answer:

√36=6

Step-by-step explanation:

it's can also be understood by 6×6=36

ANSWER QUICKKK
HELP !!!!! i

Answers

Answer:

its B

Step-by-step explanation:

CONVERTING METRIC UNITS - LENGTH WEIGHT & VOLUME 1
2)
2 kg =
B
1)
1 kg =
g
4)
2 cm =
mm
3)
1 cm =
mm
6)
2 km =
m
5)
1 km =
m
8)
2 L =
ml
7)
1 L =
mL
10)
2 m =
cm
9)
cm
1 m =
Which is the most? Circle the largest amount in each box.
1 L
1 m
560 m
2,000 cm
1 kg
1,250 mL
80 cm
300 g
980 mL
1 km
120 mm
950 g
greater than (>), less than (<) or equals (=) to compare the amounts.
2)
1 m
75 cm
590 mL
1L
1 km
250 m
2 cm
4)
20 mm
7 cm
50 mm
2 m
6)
250 cm
4 m
350 cm
8)
1 kg
-,200 g
10)
3m
2 L
20 mL
300 cm
12)
500
Om
1 km
4 kg

Answers

Answer:

2 KM 2 L 2 KG I dont know the rest i figured i could help someone but thats all i can do at the moment sorry i might come back to finish it later.

Step-by-step explanation:

what is the center of the circle?
(-5,-9)
(-4,-7)
(-6,-5)
(-5,-6)

Answers

Answer:

1000000066756355688777

Find the slope of the line passing through the points (-7, 4) & (-7, -8)

Answers

Answer:

Undefined

Step-by-step explanation:

The equation for finding the slope is:

y2 - y1

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

x2 - x1

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

4 - (-8)

----------

-7 - (-7)

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

4 + 8

--------

-7 +7

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

12

----

0

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

The slope is Undefined, so there is no answer

the original pattern for dress is 33 3/4 inches long. kimmy needs her dress to be 32 1/2 inches long how much shorter than the pattern does kimmy need to make her dress​

Answers

Answer: 1 1/4

Step-by-step explanation: 32 1/2 is the same as 32 2/4 so all you have to do is subtract 32 2/4 from 33 3/4 which leaves you with 1 1/4

Write an explicit and recursive rule for the geometric sequence -5, 10, -20, 40… and use it to find the 12th

Answers

Answer:

See solutions below

Step-by-step explanation:

Given the sequence -5, 10, -20, 40...

The nth term of the GP is expressed as;

Tn = ar^n-1

a is the first term

r is the common ratio

n is the number of terms

From the sequence, a = -5

r = 10/-5 = -20/10 = -2

Substitute

Tn = -5(-2)^n-1

This gives the explicit formula

For recursive;

a1 = -5

a2 = 10 = -2(-5) = -2a1

a3 = -20 = -2(10) = -2a2

From the shown sequence, we can see that;

an = -2an-1

This gives the recursive formula

Get the 12th term;

Using the explicit formula

T12 = -5(-2)^12-1

T12 = -5(-2)^11

T12 = -5(-2048)

T12 = 10240

Hence the 12th term is 10240

Ishi has $24 in his pocket. He pays $8 to have his car washed. Write and solve an expression to show the change in Ishi's money.

Answers

Answer:

8 - 24

Step-by-step explanation:

Answer: 24 + (-8)  

Step-by-step explanation:

He has 24$ do you take 8 out of it

1. 2x + 7 = 2x - 7

2. 3x + 8 = -2x + 8

3. 4(x + 1) = 4x + 4

Answers

1.
2x+7=2x-7
2x-2x=-7-7
0=-14
Math error.

2.
3x+8=-2x+8
3x+2x=8-8
5x=0
x=0


3.
4(x+1)=4x+4
4x+4=4x+4
4x-4x=4-4
0=0
Correct

Answer:

Consider left and right sides of the equations as linear functions.

Then:

1. The equation 1 has lines with the same slope (2) but different y-intercepts (7 and -7), therefore the lines are parallel and no solution.2. The lines have different slopes (3 and 2), therefore they intersect and there is one solution.3. After opening the parenthesis we get both sides same, meaning the lines are same and overlap. The equation has infinitely many solutions.

I didn't mean to click an answer but please help me out

Answers

Answer:

135

Step-by-step explanation:

135+45=180, and supplementary angles always equal 180

Answer:

The answer is 135

Step-by-step explanation:

Definition of supplementary angles: either of two angles whose sum is 180°, so 180 - 45 = 135!

Please mark as brainliest.

In the adjoining equilateral triangle PQR , X , Y and Z are the middle points of the sides PQ , QR and RP respectively. Prove that XYZ is also an equilateral triangle.

~Thanks in advance ! ​

Answers

Answer:

See Below

Step-by-step explanation:

Statements:                                                        Reasons:

[tex]1)\text{ } \Delta PQR\text{ is equilateral}[/tex]                                        Given

[tex]2)\text{ }PQ=QR=RP[/tex]                                               Definition of Equilateral

[tex]3)\text{ } X, Y, Z\text{ are the midpoints of } PQ, QR, RP[/tex]       Given

[tex]4)\text{ } PX=XQ[/tex]                                                        Definition of Midpoint

[tex]5)PQ=PX+XQ[/tex]                                               Segment Addition

[tex]6)\text{ } PQ=2XQ[/tex]                                                      Substitution

[tex]7)\text{ } QY=YR[/tex]                                                        Definition of Midpoint

[tex]8)\text{ }QR=QY+YR[/tex]                                               Segment Addition

[tex]9)\text{ } QR=2QY[/tex]                                                       Substitution

[tex]10)\text{ } 2XQ=2QY[/tex]                                                  Substitution

[tex]11)\text{ } XQ=QY[/tex]                                                      Division Property of Equality

[tex]12)\text{ } XQ=PX=QY=YR[/tex]                                Transitive Property

[tex]13)\text{ } RZ=ZP[/tex]                                                       Definition of Midpoint

[tex]14)\text{ } RP=RZ+ZP[/tex]                                             Segment Addition

[tex]15)\text{ } RP=2RZ[/tex]                                                     Substitution

[tex]16)\text{ } 2XQ=2RZ[/tex]                                                   Substitution

[tex]17)\text{ } XQ=RZ[/tex]                                                       Substitution

[tex]18)\text{ } XQ=PX=QY=YR=RZ=ZP[/tex]            Transitive Property

[tex]19)\text{ } \angle Q\cong \angle R\cong \angle P[/tex]                                             Definition of Equilateral

[tex]20)\text{ } \Delta XQY\cong \Delta YRQ \cong \Delta ZPX[/tex]                          SAS Congruence

[tex]21)\text{ } XY\cong YZ\cong ZX[/tex]                                           CPCTC

[tex]22)\text{ } \Delta XYZ\text{ is equilateral}[/tex]                                     Equilateral Triangle Theorem

Answer:

this is your answer. thanks, for great point

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