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KIM [24]
3 years ago
15

Evaluate the surface of the integral rr

Mathematics
1 answer:
rewona [7]3 years ago
4 0
The part of the plane z=18-3x-9y in the first octant is one of the faces of a tetrahedron whose vertices correspond exactly to the intercepts of the plane. These are

3x+9\cdot0+0=18\implies x=6\implies(6,0,0)
3\cdot0+9y+0=18\implies y=2\implies(0,2,0)
3\cdot0+9\cdot0+z=18\implies z=18\implies(0,0,18)

We can parameterize this surface with the vector-valued function

\mathbf s(u,v)=(6(1-u)(1-v),2u(1-v),18v)


where 0\le u\le1 and 0\le v\le1. Then the surface element is

\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|\,\mathrm du\,\mathrm dv=12\sqrt{91}(1-v)\,\mathrm du\,\mathrm dv

so the surface integral becomes

\displaystyle\iint_{\mathcal S}e^z\,\mathrm dS=12\sqrt{91}\int_{v=0}^{v=1}\int_{u=0}^{u=1}(1-v)e^{18v}\,\mathrm du\,\mathrm dv
=\displaystyle12\sqrt{91}\int_{v=0}^{v=1}(1-v)e^{18v}\,\mathrm dv
=\dfrac{12\sqrt{91}}{324}e^{18v}(19-18v)\bigg|_{v=0}^{v=1}
=\dfrac{\sqrt{91}}{27}(e^{18}-228)
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Solve my question please, I’ll mark u as brainlest if the answer is correct and if you solved my question!!!
ikadub [295]

Answer:

x = price of balcony tickets = $7

y = price of orchestra tickets = $21

Step-by-step explanation:

Let

x = price of balcony tickets

y = price of orchestra tickets

y = 3x (1)

148y + 76x = 3,640 (2)

Substitute y = 3x into (2)

148y + 76x = 3,640 (2)

148(3x) + 76x = 3,640

444x + 76x = 3,640

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x = 3,640/520

x = 7

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y = 3x (1)

y = 3(7)

y = 21

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3 0
3 years ago
Find the value of x for which WXYZ must be a parallelogram.
Alik [6]
Set angle W equal to angle Y
4x + 20 = x + 26
Solve
4x = x + 6
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4 0
4 years ago
Read 2 more answers
Long Island City is 10 Miles farther from Sam's house than Brooklyn is. Write an algebraic expression to represent the distance
weqwewe [10]

Answer:

b = long city island (l) + 10

Step-by-step explanation:

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soldier1979 [14.2K]
 it should be 1.6 hope that helps you 
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3 years ago
Solve the equation x2 – 10x – 8= 0 to the nearest tenth.
4vir4ik [10]

Answer:

x = -0.8 and 10.8

Step-by-step explanation:

Given the equation x2 – 10x – 8= 0

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x = 10±√100+32/2

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x = -0.8 and 10.8

3 0
3 years ago
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