Question

Related Rates

Answer 1

Answer:

1. 0.382 m/min
2. 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

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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.