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3 years ago

Someone can help me with it , please.

Mathematics

1 answer:

hjlf3 years ago

6 0

Answer:

hdhdjdjdjdjsjjsjsjshhdhsnkskshhdhsnskhdhbdjdjds

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Choose the best coordinate system to find the volume of the portion of the solid sphere rho <_4 that lies between the cones φ

MrRissso [65]

Answer:

So, the volume is:

$\boxed{V=\frac{128\sqrt{2}\pi}{3}}$

Step-by-step explanation:

We get the limits of integration:

$R=\left\lbrace(\rho, \varphi, \theta):\, 0\leq \rho \leq 4,\, \frac{\pi}{4}\leq \varphi\leq \frac{3\pi}{4},\, 0\leq \theta \leq 2\pi\right\rbrace$

We use the spherical coordinates and we calculate a triple integral:

$V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}\int_0^4 \rho^2 \sin \varphi \, d\rho\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \left[\frac{\rho^3}{3}\right]_0^4\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \cdot \frac{64}{3} \, d\varphi\, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} [-\cos \varphi]_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} \sqrt{2} \, d\theta\\\\$

we get:

$V=\frac{64}{3} \int_0^{2\pi} \sqrt{2} \, d\theta\\\\V=\frac{64\sqrt{2}}{3}\cdot[\theta]_0^{2\pi}\\\\V=\frac{128\sqrt{2}\pi}{3}$

So, the volume is:

$\boxed{V=\frac{128\sqrt{2}\pi}{3}}$

4 0

2 years ago

Find the midpoint between (-6, 8) and (4, 6) Midpoint is _____ ______

seropon [69]

Answer:

(-1,7) is the midpoint of these two points

Step-by-step explanation:

4 0

3 years ago

Tom works 12 hours a day at a café. He is paid $8 an hour. How much money is he paid in 10 days?

Masja [62]

Answer:

Tom will be paid $140 in 10 days

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Solve. 3(2w-7)=3 What is W?

almond37 [142]

- - Solve:

Start of by simplifying both sides of your problem.

3*2x+3*-7=32

6w+-21=3

6w-21=3

- - Now you need to add 21 to both sides to be able to finish solving.

6w-21+21=3+21

6w=34

- - Final step:

$\frac{6w}{6} = \frac{24}{6}$

Answer: w=4

8 0

3 years ago

Read 2 more answers

Amy loaned \$5$5dollar sign, 5 to each of 202020 people. She recorded each loan by writing -\$5−$5minus, dollar sign, 5 in her b

polet [3.4K]

Answer:

-$100

Step-by-step explanation:

If Amy subtracted $5 from her bank balance 20 times, it is ...

$5 × 20 = $100

less than it was.

The amount of change totaled -$100.

7 0

3 years ago