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likoan [24]
3 years ago
10

Show a way to count from $82 to $512

Mathematics
1 answer:
gogolik [260]3 years ago
5 0
You could add two until you get to 512
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Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circu
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0.0221 feet per minute.

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\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h

If the Base Diameter = Height of the Cone

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Therefore,

\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}

Rate of Change of the Volume, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}

Since gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. Therefore, the Volume of the cone is increasing at a rate of 10 cubic feet per minute.

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We want to determine how fast is the height of the pile is increasing when the pile is 24 feet high.

We have:

\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10\\\\$When h=24$ feet$\\\dfrac{3\pi *24^2}{12}\dfrac{dh}{dt}=10\\144\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{144\pi}\\ \dfrac{dh}{dt}=0.0221$ feet per minute

When the pile is 24 feet high, the height of the pile is increasing at a rate of 0.0221 feet per minute.

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