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Igoryamba
3 years ago
5

If a board 8ft is cut into three equal pieces how long are they

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
3 0
The answer is 2.667 :) .-.
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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
Negative positive or no association
Eddi Din [679]

Answer:

Positive association

Step-by-step explanation:

As the Temperature goes up the more money you have to spend because you pay for the electricity that produces the heat

positive association is when one varriable increases so does the other.

7 0
2 years ago
Solve: 7-5x= -5x - 6x +7
docker41 [41]
7=-16x+7
0=-16x
0=x

7-0=0-0+7
7=7
6 0
2 years ago
Read 2 more answers
There are 570 students at a school if each classroom holds 30 students how many classrooms are needed at the school?
Irina18 [472]

Answer: 19

Step-by-step explanation:

570 divided by 30

6 0
3 years ago
What is the value of x un the following equation: <br> -5.5x + 0.56 = -1.64
Ksenya-84 [330]
To solve this, you must subtract .56 from -1.64. Then divide that by -5.5x. So the answer is .4
8 0
3 years ago
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