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3 years ago

What is 6% of 72,000

Mathematics

2 answers:

Ainat [17]3 years ago

8 0

72,000 x .06 = 4320................

marishachu [46]3 years ago

5 0

4320 is the 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

Thank you very much for your help!

Kobotan [32]

For a.
$x^2+y^2=25$

For b.
$(x-4)^2+(y-3)^2=25$

For c.
$(x-5)^2+(y-4)^2=9$

Hope that helps

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3 years ago

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Zielflug [23.3K]

Answer:

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35/8- 4 and 3/8

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Step-by-step explanation:

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3 years ago

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prohojiy [21]

Answer:

I hope this helps!

Step-by-step explanation:

ACB

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3 years ago

Which graph of a relation is also a function ?

Illusion [34]

Answer:

Step-by-step explanation:

A graph is only a function when there is only one y value for each x value.

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Sorry, not all the lines are straight, but you get the point. B is the only one that doesn't have more than one point on the lines I drew.

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3 years ago