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Answer:

[tex]\int\limits {\int\limits_R {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]

Step-by-step explanation:

Given

[tex]x - y = 0[/tex]

[tex]x - y = 7[/tex]

[tex]x + y = 0[/tex]

[tex]x + y = 6[/tex]

Required

Evaluate [tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex]

Let:

[tex]u=x+y[/tex]

[tex]v =x - y[/tex]

Add both equations

[tex]2x = u + v[/tex]

[tex]x = \frac{u+v}{2}[/tex]

Subtract both equations

[tex]2y = u-v[/tex]

[tex]y = \frac{u-v}{2}[/tex]

So:

[tex]x = \frac{u+v}{2}[/tex]

[tex]y = \frac{u-v}{2}[/tex]

R is defined by the following boundaries:

[tex]0 \le u \le 6[/tex]  ,  [tex]0 \le v \le 7[/tex]

[tex]u=x+y[/tex]

[tex]\frac{du}{dx} = 1[/tex]

[tex]\frac{du}{dy} = 1[/tex]

[tex]v =x - y[/tex]

[tex]\frac{dv}{dx} = 1[/tex]

[tex]\frac{dv}{dy} = -1[/tex]

So, we can not set up Jacobian

[tex]j(x,y) =\left[\begin{array}{cc}{\frac{du}{dx}}&{\frac{du}{dy}}\\{\frac{dv}{dx}}&{\frac{dv}{dy}}\end{array}\right][/tex]

This gives:

[tex]j(x,y) =\left[\begin{array}{cc}{1&1\\1&-1\end{array}\right][/tex]

Calculate the determinant

[tex]det\ j = 1 * -1 - 1 * -1[/tex]

[tex]det\ j = -1-1[/tex]

[tex]det\ j = -2[/tex]

Now the integral can be evaluated:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex] becomes:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{x^2 - y^2}} \, *\frac{1}{|det\ j|} * dv\ du[/tex]

[tex]x^2 - y^2 = (x + y)(x-y)[/tex]

[tex]x^2 - y^2 = uv[/tex]

So:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{|det\ j|}\, dv\ du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *|\frac{1}{-2}|\, dv\ du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{2}\, dv\ du[/tex]

Remove constants

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 {\int\limits^7_0 {ue^{uv}} \, dv\ du[/tex]

Integrate v

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 \frac{1}{u} * {ue^{uv}} |\limits^7_0 du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 e^{uv} |\limits^7_0 du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{u*7} - e^{u*0}]du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{7u} - 1]du[/tex]

Integrate u

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7u} - u]|\limits^6_0[/tex]

Expand

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -(\frac{1}{7}e^{7*0} - 0)][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -\frac{1}{7}][/tex]

Open bracket

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} - 6 -\frac{1}{7}][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} -\frac{43}{7}][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{42} -\frac{43}{7}][/tex]

Expand

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]

Answer:

A . Isosceles

Step-by-step explanation:

An isosceles triangle has both two equal sides and two equal .

Answer:

2 miles

Step-by-step explanation:

Answer:

10,512 miles

Step-by-step explanation:

876 x 12 = d (d is distance)

Solving the multiplication above, 876 x 12 would equal 10,512 miles

Answer:

Bisector

Step-by-step explanation:

Given:

Sum of all the interior angles of a regular polygon is 1080°.

Measure of each side is 10 cm.

To find:

The perimeter.

Solution:

The sum of all interior angles of a regular polygon with n side is:

[tex]S=(n-2)180^\circ[/tex]

Sum of all the interior angles of a regular polygon is 1080°.

[tex]1080^\circ=(n-2)180^\circ[/tex]

[tex]\dfrac{1080^\circ}{180^\circ}=n-2[/tex]

[tex]6+2=n[/tex]

[tex]8=n[/tex]

Number of sides of the regular polygon is 8. The measure of each side is 10 cm. So, the perimeter of the regular polygon is:

[tex]\text{Perimeter}=\text{Number of sides}\times\text{Measure of each side}[/tex]

[tex]\text{Perimeter}=8\times 10[/tex]

[tex]\text{Perimeter}=80[/tex]

Therefore, the perimeter of the regular polygon is 80.

Answer:

6X(5 + 4)

6x(9)

54x

Answer:

the answer is 54x hope it will help full to you

Answer:

-8 is not a solution to the inequality

Step-by-step explanation:

[tex]3x + 13 \geqslant - 8 \\ 3x \geqslant - 21 \\ x \geqslant - 7 \\ [/tex]

Step-by-step explanation:

everything can be found in the picture

Answer:

1 and 2 only

Step-by-step explanation:

mark me as brainliest

Answer:

Step-by-step explanation:

Hope this helps u !!

The LCM of 2a(4a² + 10a + 13)(4a² + 13 - 10a).

Least Common Multiple, often known as the Lowest Common Multiple, is denoted by the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It can also be computed using two or more numbers.

The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.

We have,

16[tex]a^4[/tex] + 4a² + 169 and 8a³ +2a(2a + 13) + 16a²

First, 16[tex]a^4[/tex] + 4a² + 169

= (4a²)² + (2a)² + (13)²

= (4a²)² + 2 . 4a² . 13 + (13)² + 4a² + 104a²

= (4a² + 13)² - (10a)²

= (4a + 13 - 10a) (4a + 13 + 10a)

= (13 - 6a)(13 + 14a)

Second, 8a³ +2a(2a + 13) + 16a²

= 8a³ + 4a² + 26a + 16a²

= 8a³ + 20a² + 26a

= 2a(4a² + 10a + 13)

So, the LCM is

= 2a(4a² + 10a + 13)(4a² + 13 - 10a)

Learn more about LCM here:

https://brainly.com/question/20739723

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Answer:

a = -1  b=0  and c=1

Step-by-step explanation:

-x^2 +0x+1

This is in the form

ax^2 +bx+c

a = -1  b=0  and c=1

Answer: -64 Maybe

Step-by-step explanation:

It look like each term goes up by double of the last term.

Answer:

-3

Step-by-step explanation:

[tex]\frac{7-25}{-2(-3)}[/tex]

=[tex]\frac{-18}{-2*-3}[/tex]

=[tex]\frac{-18}{6}[/tex]

=-3

[tex]\quad\quad\quad\quad\huge\tt{⟹\frac{7 - 25}{ - 2( - 3)} }[/tex]

[tex]\quad\quad\quad\quad\huge\tt{ ⟹\frac{7 - 25}{ - 2( - 3)} }[/tex]

[tex]\quad\quad\quad\quad\huge\tt{ ⟹\frac{-18}{ - 2( - 3)} }[/tex]

[tex]\quad\quad\quad\quad\huge\tt{ ⟹\frac{-18}{ 6} }[/tex]

[tex]\quad\quad\quad\quad\huge\tt{ ⟹ - 3} [/tex]

[tex]\quad\quad\quad\quad\huge \boxed{\tt{ \color{green} - 3} }[/tex]

________

#LetsStudy

Answer:

11-

3 / 8 * 5 / 5 = 15 / 40

2 / 5 * 8 / 8 = 16 / 40

16 / 45 + 15 / 45 =

31 / 40

12-

5 / 6 * 9 /9 = 45 / 54

4 / 9 * 6 / 6 = 24 / 54

24 / 54 + 45 + 54 = 69 / 54

69 / 54 =

1   15 / 54

Answer:

x   -   h(x)

0   -   1

1    -   3

2   -   5

3   -   7

Step-by-step explanation:

Just substitute the x value into the function

Answer:

Step-by-step explanation:

The answer is B.

It's a line that shows every point that satisfies the equation

y = 3x + 4  which is what I think you meant (but I'm not sure). If I am correct then there are a million possible points that could be the answer to this question.

If I am not correct, leave a comment that tells me so, and I'll revise my answer.

Never mind the question has the right equation. And my answer remains as given.

Answer:

B

Step-by-step explanation:

OEMJIGOVNarioendsdmarfwsipf JUST BELIEVE, also looking is good

The true statements on comparing Jasmine’s two drawings are B and C.

The sum of a finite traingle's interior angle is equal to 180° and this is called the Angle Sum Property of a Triangle.

It is given in the question

Jasmine drew triangles on a globe and on a flat map of the world

On comparing both the triangle the conclusions are

The triangle drawn on the globe is a spherical triangle and the angle sum of the interior angle will be greater that the two right angles or 180°.

Among the option given this is also true that

The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe

Therefore option B and C are both true statement comparing Jasmine’s two drawings .

To know more about Angle Sum Property

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Answer:

5. a) 5b

   b) 3b + 2b

Step-by-step explanation:

a) b + b + b + b + b is the same as

5 * b or 5b

b) 5b = 3b + 2b

or 3 * b + 2* b = 5b

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

There for the diameter is 2(4.8 )= 9.6 ft

Given: Volume of the cone is 83.7 m³

We know that:

[tex]\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : \dfrac{\pi r^2h}{3}}}[/tex]

where r is the radius of the cone and h is the height of the cone

Given: Height of the cone = 5m

Substituting the values in the formula, we get:

[tex]\sf{\implies \dfrac{\pi r^2(5)}{3} = 83.7}[/tex]

[tex]\sf{\implies \pi r^2 = 83.7 \times \dfrac{3}{5}}[/tex]

[tex]\sf{\implies \pi r^2 = 83.7 \times 0.6}[/tex]

[tex]\sf{\implies \pi r^2 = 50.22}[/tex]

[tex]\sf{\implies r^2 = \dfrac{50.22}{\pi}}[/tex]

[tex]\sf{\implies r^2 = 16}[/tex]

[tex]\sf{\implies r = 4}[/tex]

We know that : Diameter is two times the radius

⇒  Diameter of the Cone is 8 meters

Good question. It is supposed to be both the y-intercept and the x-intercept and is the only point on a graph that can be both. Something in wrong in that thing.

Answer: 7

Step-by-step explanation:

find x

6x(6+4)=5x(1+x)

Then x=11

AB= 11-4=7

Answer:

B.) 7

Step-by-step explanation:

I got it correct on founders edtell

Answer:

CO

Step-by-step explanation:

Conditional: If p, then q.

Converse: If q, then p.

Conditional: If the measure of an angle is 90 degrees, then it is a right angle.

If p, then q.

p = the measure of an angle is 90 degrees

q = it is a right angle

Converse:

If q, then p.

If it is a right angle, then the measure of the angle is 90 degrees.

Answer: CO

Answer:

Amount spent on food  = 510

Amount spent on entertainment = 720

Step-by-step explanation:

They have 3000 for vacation.

Amount spent on food = 17% of 3000

or 17/100*3000

17*30= 510

Amount spent on entertainment = 24% of 3000

or 24/100*3000

24*30= 720

Step-by-step explanation:

A shaded right rectangular pyramid is shown. where is the shade rectangular pyramid....how do I know the answer when you did post the full

question

Answer:

Length = 35

w = 5

Step-by-step explanation:

l x w = area

7y x y = 175

7y^2 = 175

y^2 = 175/7

y^2=25

y=5

The length is 7y, so it's 5 times 7 or 35.

The width is just y, so it's 5.

Answer: 5 billion pennies

Step-by-step explanation:

Answer:

B: 112.5

Step-by-step explanation:

first, we split up the rhombus into two triangles, with the height of 15 and the length of 7.5. when you multiply these you will get 112.5, and normally if you are just getting the area of the triangle, then you would divide it by two, but seeing that we have 2 triangles here, we would multiply it by two afterwards so an easier way to do it is just to not divide.

Answer:

the distance is called the circumference