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natita [175]
2 years ago
10

Someone help pls!!! giving brainliest

Mathematics
1 answer:
maw [93]2 years ago
8 0

Answer:

I think you can add 9 +8 to get your finial answer.

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G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =
Svetach [21]
Presumably you should be doing this using calculus methods, namely computing the surface integral along \mathbf r(u,v).

But since \mathbf r(u,v) describes a sphere, we can simply recall that the surface area of a sphere of radius a is 4\pi a^2.

In calculus terms, we would first find an expression for the surface element, which is given by

\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k
\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j
\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k
\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u

So the area of the surface is

\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u
=-2\pi a^2(\cos\pi-\cos 0)
=-2\pi a^2(-1-1)
=4\pi a^2

as expected.
6 0
3 years ago
LMNP is roatated 90 degrees clockwise around the origin
AlexFokin [52]

It would be c, (1, 0)

7 0
2 years ago
Kindly solve ½=4/?, What's going to be the answer? Thank you
Luda [366]

Answer:

8

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
How do u get this?? I know the answer but then I don't know why they shuld divide by 2 I will mark the person who explains wit p
Greeley [361]

Answer:

10.89

Step-by-step explanation:

Circle:

C = TTD

C = TT(6.6)

C = 20.73451151

C = 20.73

Triangle:

A = bh/2

A = 6.6(3.3)/2        6.6/2=3.3

A = 21.78/2

A = 10.89

Shaded Region = 10.89

5 0
2 years ago
May someone help me out with this please.
Fed [463]
I think The answer is 22.5
5 0
3 years ago
Read 2 more answers
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