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3 years ago

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A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of

the circle formed by a ripple increases at the rate of 5 feet per minute. Find the rate at which the area is changing at the instant the radius is 12 feet.

1 answer:

zalisa [80]3 years ago

3 0

Answer:

376.9911ft²/minute

Explanation:

In the given question the rate of chage of radius in given as

$\frac{\mathrm{d}r }{\mathrm{d} t}$ =5ft per minute

we know ares of circle A=pi r^{2}

differentiating w.r.t. t we get

$\frac{\mathrm{d} A}{\mathrm{d} t}=2\pi r\frac{\mathrm{d}r }{\mathrm{d} t}$

Now, we have find $\frac{\mathrm{d}A }{\mathrm{d} t} at r=12 feet$

$\frac{\mathrm{d} A}{\mathrm{d} t}=2\times\pi\times12\times5=120\pi=376.9911ft^{2}/minute$

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Explanation:

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Answer:

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Explanation:

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A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.6 m/s at ground level.

galina1969 [7]

Answer:

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<u>Time taken to reach 1180 m is 11.29 seconds</u>

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<u>Time the rocket will keep going up after the engines shut off is 13.06 seconds.</u>

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The distance the rocket will keep going up after the engines shut off is 836.05 m

Total distance traveled by the rocket in the upward direction is 1180+836.05 = 2016.05 m

The rocket will fall from this height

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<u>Time taken by the rocket to fall from maximum height is 20.29 seconds</u>

Time the rocket will stay in the air is 11.29+13.06+20.29 = 44.64 seconds

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