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3 years ago

Related Rates

Mathematics

1 answer:

Whitepunk [10]3 years ago

4 0

Answer:

0.382 m/min
8 1/3 ft/s

Step-by-step explanation:

1. The rate of change of volume is ...

V = πr^2h

V' = πr^2h'

h' = V'/(πr^2) = (3 m^3/min)/(π(5 m)^2) = 0.12/π m/min

h' ≈ 0.382 m/min

2. In the attached, ∆PCM ~ ∆MXS, so we can write the proportion ...

x/9 = s/15 . . . . where x = BX and s = BS in the diagram

Multiplying by 15 gives ...

s = (15/9)x = (5/3)x

Then the rate of change is ...

s' = (5/3)x' = (5/3)(5 ft/s)

s' = 8 1/3 ft/s

The tip of the shadow is moving at 8 1/3 feet per second.

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