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3 years ago

a right triangle has side lengths 8, 15, and 17 as shown below. Use these lengths to find cosY, sinY, and tanY

Mathematics

1 answer:

Anit [1.1K]3 years ago

3 0

Cos Y = 8/17
sin Y = 15/17
tan Y = 15/8

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3 years ago

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1: 2 2/3 - 3/5 <br> 2: 2 1/5 + 1 1/10<br> 3: 2 5/7 - 2/3<br> 4: 1/4 + w = 6 1/3

Yanka [14]

2 2/3 - 3/5 = 2 1/15

2 1/5 + 11/10 = 3 3/10

2 5/7 - 2/3 = 2 1/21

1/4 + w = 6 1/3

w = 6 1/12

Hope this helps :)

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3 years ago

Let M be the closed surface that consists of the hemisphere

ycow [4]

Since $M$ is closed, you can use the divergence theorem: The flux of $\vec E(x,y,z)$ across $M$ is

$\displaystyle\iint_{\partial M}\vec E\cdot\mathrm d\vec S=\iiint_M(\nabla\cdot\vec E)\,\mathrm dV=54\iiint_M\mathrm dV$

which is 54 times the volume of the hemisphere centered at (0, 0, 0) with radius 1, $\boxed{36\pi}$ .

Judging by the question content, you're supposed to find this value by computing the the integral of $\vec E$ across $M_1$ and $M_2$ .

Across $M_1$ :

Parameterize the hemisphere by

$\vec r(u,v)=(\cos u\sin v,\sin u\sin v,\cos v)$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to $M_1$ to be

$\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=(\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v)$

The flux of $\vec E$ across $M_1$ is

$\displaystyle\iint_{M_1}\vec E\cdot\mathrm d\vec S=18\int_0^{\pi/2}\int_0^{2\pi}(\cos u\sin v,\sin u\sin v,\cos v)\cdot\left(\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}\right)\,\mathrm du\,\mathrm dv$

$=\displaystyle18\int_0^{\pi/2}\int_0^{2\pi}\sin v\,\mathrm du\,\mathrm dv=36\pi$

Across $M_2$ :

Parameterize the disk by

$\vec s(u,v)=(u\cos v,u\sin v,0)$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal to $M_2$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec u}{\partial v}=(0,0,-u)$

Then the flux across $M_2$ is

$\displaystyle\iint_{M_2}\vec E\cdot\mathrm d\vec S=18\int_0^{2\pi}\int_0^1(u\cos v,u\sin v,0)\cdot\left(\frac{\partial\vec s}{\partial v}\times\frac{\partial\vec s}{\partial u}\right)\,\mathrm du\,\mathrm dv=0$

Then the total flux across $M$ is $36\pi$ , as expected.

4 0

3 years ago

a right triangle has side lengths 8, 15, and 17 as shown below. Use these lengths to find cosY, sinY, and tanY​

a right triangle has side lengths 8, 15, and 17 as shown below. Use these lengths to find cosY, sinY, and tanY