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erik [133]
3 years ago
11

Evaluate the given integral by making an appropriate change of variables, where r is the rectangle enclosed by the lines x - y =

0, x - y = 7, x + y = 0, and x + y = 6.
Mathematics
1 answer:
vova2212 [387]3 years ago
6 0
\begin{cases}u=x-y\\v=x+y\end{cases}

\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial u}{\partial y}\\\\\dfrac{\partial v}{\partial x}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&-1\\1&1\end{bmatrix}
\implies\det\mathbf J=2

The area of the region is then given by

\displaystyle\iint_R\mathrm dA=\int_{u=0}^{u=7}\int_{v=0}^{v=6}2\,\mathrm dv\,\mathrm du=84
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How do I simplify −9(3−4w)−8w
laiz [17]
Multiply out the bracket so
-27 + 36w - 8w
Then collect the terms so
-27 + 28w

Answer = - 27 + 28w
3 0
3 years ago
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In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of third angle os 88 degrees
Volgvan

Answer:

Answers: 46, 23, and 111

Step-by-step explanation:

To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:

x=2y

z=y+88

x+y+z=180

Substituting, z = 1/2(x)+88, now plug z into the third equation:

x+1/2(x)+1/2(x)+88=180

this simplifies to 2x+88=180

subtracting 88 from both sides leaves 2x=92

x=46

plug this in to the first equation: 46 = 2y, so y = 23

plug this into the third one leaves z = 111

Hope this helps!

3 0
3 years ago
Someone please help me with this ASAP
Natasha_Volkova [10]

Answer:

y= -11

Step-by-step explanation:

3 0
3 years ago
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Pleasee help x.x 1. Solve the system by elimination-
patriot [66]
Q1. The answer is x = 1, y = 1, z = 0

<span>(i) -2x+2y+3z=0
</span><span>(ii) -2x-y+z=-3 
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</span><span>_________
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</span>(i) -2x+2y+3z=0
(iii) 2x+3y+3z=5
_________
5y + 6z = 5

Sum up the second and the third equation:
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2y + 4z = 2


(iv) 5y + 6z = 5
(v) 2y + 4z = 2
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Divide the fifth equation by 2
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Multiple the second equation by -3 and sum the equation
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2y = 2
y = 2/2 = 1


y + 2z = 1
1 + 2z = 1
2z = 1 - 1
2z = 0
z = 0


-2x-y+z=-3
-2x - 1 + 0 = -3
-2x = -3 + 1
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x = -2/-2 = 1



Q2. The answer is x = -37, y = -84, z = -35

<span>(i) x-y-z=-8 
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______
</span>Divide the third equation by 2 and rewrite z in the term of x:
(iii) x+z=2
z = 2 - x
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Substitute z from the third equation and express y in the term of x:
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Substitute z from the third equation and y from the first equation into the second equation:
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-4x + 8x - 40 + 10 - 5x = 7
-x -30 = 7
-x = 30 + 7
x = -37
y = 2x - 10 = 2*(-37) - 10 = -74 - 10 = -84
z = 2 - x = 2 - 37 = -35</span>
8 0
3 years ago
Enter the plan width for the rectangular room. Round your answer to the nearest tenth.
Jobisdone [24]

Answer:

350

Step-by-step explanation:

5x7x10=350

5 0
3 years ago
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