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3 years ago

I will mark brainliest to whoever has the best answer

Mathematics

1 answer:

gogolik [260]3 years ago

3 0

Answer:

REPOST YOURE PICTURE

Step-by-step explanation:

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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

To mix the color “autumn purple,” a painter mixes 28 parts of blue to 48 parts of red. What is the ratio of blue to red? Express

kupik [55]

Answer:

blue : red

7 : 12

Step-by-step explanation:

blue : red

28 48

Divide each by 4

28/4 48/4

7 12

blue : red

7 : 12

7 0

2 years ago

Read 2 more answers

Li’s brother used the work shown to determine that he must grow at most 6 inches to be able to ride the roller coaster. Is this

miv72 [106K]

No, the work is correct, but the interpretation is not. “6 is less than or equal to h<span>” means that h is greater than or equal to 6. He must grow at least 6 inches, not at most 6 inches.</span>

8 0

3 years ago

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If x = 5 & y = 3 what is 3x + 5y?

notka56 [123]

Answer:

Step-by-step explanation:

If you plug in 5 for x and 3 for y then the equation would be 3(5)+5(3) or 15+15.

4 0

2 years ago

Monica is a lawyer who earns $8,322.65 every month. She spends $830.98 on rent, $210.36 on food, and $120.45 on gas every month.

dolphi86 [110]

Answer:

Money left from her earning after expenses is $ 7160.86

Step-by-step explanation:

Money earned by Monica every month = $ 8322.65

Money spend on rent = $ 830.98

Money spend on food = $ 210.36

Money spend on gas every month = $ 120.45

Money left from her earning = 8322.65 - ( 830.98 + 210.36 + 120.45 )

= 8322.65 - 1161.79

= $ 7160.86

3 0

3 years ago

Read 2 more answers