Find the P coordinates

Mathematics

1 answer:

bagirrra123 [75]2 years ago

5 0

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Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 + y2.

vekshin1

$x^2+y^2+z^2=100z\iff x^2+y^2+(z-50)^2=50^2$

The surface of interest can be parameterized by

$\mathbf r(u,v)=\begin{cases}x(u,v)=50\cos u\sin v\\y(u,v)=50\sin u\sin v\\z(u,v)=50(\cos v+1)\end{cases}$

with $0\le u\le2\pi$ and $0\le v\le\arccos\dfrac{49}{50}$ .

The area of the surface $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm dA=\iint_T\left\|\mathbf r_u\times\mathbf r_v\right\|\,\mathrm du\,\mathrm dv$

We have

$\|\mathbf r_u\times\mathbf r_v\|=50^2\sin v$

so the area is given by the double integral

$\displaystyle50^2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\arccos(49/50)}\sin v\,\mathrm dv\,\mathrm du=100\pi$

6 0

3 years ago

abruzzese [7]

Answer :B 4 miles

thank me later

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2 years ago

A business bought a lot of 2,500 lamps for 50,000 dollars and wants to sell them at 15 percent profit how much should each lamp

aev [14]

50,000 / 2500 = 20....he bought them for 20 bucks a piece. So if he wants to sell them at 15% profit, he would sell them for 20 + 0.15(20) = $ 23 bucks.

A 15% profit of 50,000 dollars is 0.15(50,000) = 7500. Plus the 50 grand spent totals 57500. So they want to make a $ 7500 profit. Selling 2500 lamps at $ 23 per lamp (2500 x 23 = 57500) makes them their profit.

I should just shut up now...answer is $ 23 per lamp

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3 years ago

2x exponent of 2 divided by 27 x=18

Paha777 [63]

Answer:

Step-by-step explanation:

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2 years ago

❗❗❗PLS I NEED HELP ON THIS I DON'T UNDERSTAND PLS HELP❗❗❗❗❗❗

andrezito [222]

Where yo mamas attttt , 5-(4)= 23

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2 years ago

Find the P coordinates​

Find the P coordinates