What is the answer to this problem 9/11=?/22

Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

4 0

3 years ago

Is (8,8) a solution to the equation y=x?

Nookie1986 [14]

Answer:

Yes

Step-by-step explanation:

(8,8) is a solution is y=x.

If we substitute the point into the equation, the equation is true.

(8,8) is in (x,y) format

Substitute:

y=x

8=8

LS=RS (left side equal rights side)

7 0

3 years ago

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What is not perpendicular to 7x +2y= 3

vfiekz [6]

Every line that does not have the slope of 2/7 is perpendicular to this line.

In order to find this fact, we first must find what is perpendicular. To do that, we first have to find the slope of this line. We can do this by solving for y.

7x + 2y = 3

2y = -7x + 3

y = -7/2x + 3/2

Now we can take the slope of -7/2 and flip and negate it. This will give us the perpendicular slope (2/7). Now we know any line that does not have this slope is not perpendicular to this line.

6 0

3 years ago

What’s the answer??? (SOMEONE PLEASE HELP ME) WILL MARK BRAINLIEST!

MissTica

Your answer is B, "The function g because the graphs of f and g are symmetrical about the line y=x"

4 0

3 years ago

Find x A. 22√2 B. 22 C. 11√3/3 D. 11√3

mel-nik [20]

Answer

$22\sqrt{2}$

Step-by-step explanation:

First we gave a name to the side that is common for both triangles, can be Y for example.

Using trigonometric functions we can make a relationship between the two angles that we have and the magnitud of the side.

$sin(45)=\frac{11}{Y} \\$ , Because sin(x)= op/hip

$cos(60)=\frac{Y}{x}$ , Because con(x)=ad/hip

Having this equations, we can solve the system and find x

$Y=\frac{11}{sin(45)} \\Y=cos(60)*x$

we equal Y and solve

$\frac{11}{sin(45)}=cos(60)*x\\ x=\frac{11}{sin(45)*cos(60)} \\x=\frac{11}{\frac{\sqrt{2} }{2} *\frac{1}{2} } \\x=\frac{11}{\frac{\sqrt{2} }{4} } \\x=\frac{44}{\sqrt{2} }\\$

Then we rationalize

$x=22\sqrt{2}$

Hope you like it!

7 0

3 years ago

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