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Nataliya [291]
3 years ago
14

Find the area of the part of the paraboloid z = 9 - x^2 - y^2 that lies above the xy-plane.

Mathematics
1 answer:
svetoff [14.1K]3 years ago
3 0

Parameterize this surface (call it S) by

\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(9-u^2)\,\vec k

with 0\le u\le3 and 0\le v\le2\pi. Take the normal vector to S to be

\vec r_u\times\vec r_v=2u^2\cos v\,\vec\imath+2u^2\sin v\,\vec\jmath+u\,\vec k

Then the area of S is

\displaystyle\iint_S\mathrm dA=\iint_S\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^3u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv

=\displaystyle2\pi\int_0^3u\sqrt{1+4u^2}\,\mathrm du=\boxed{\frac{37\sqrt{37}-1}6\pi}

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Oduvanchick [21]

Answer: y=-5x-36

Step-by-step explanation:

In order for two lines to be parallel they need to have the same slope. so the slope (m) of the new line needs to be -5.

slope(m) =-5

and the point (-8,4) is given to us. we can create a new equation for a line using the point slope formula because we have a slope (m=-5) and a point (-8,4)

                       

point slope formula: y-y1=m(x-x1)    

y-4=-5(x--8)

simplify and pay attention to negative signs

y-4=-5(x+8)

y-4=-5x-40

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5 0
2 years ago
HELP DUE SOON 20 POINTS
Mariulka [41]

Answer:

x = 10

Step-by-step explanation:

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3 years ago
Find the greatest possible error for each measurement.
exis [7]
I think it is d I am not sure but i guess it's D
7 0
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Okay, help me out here!!
luda_lava [24]

Answer:

65.8

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6.11+51.7+7.99=65.8

3 0
3 years ago
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mestny [16]

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