1. The speed of sound, v, in air is a function of the temperature, T, of the air

Question

1. The speed of sound, v, in air is a function of the temperature, T, of the air:

V = 331.4 + 0.6(T-273)

with v in meters per second and K in kelvins. Suppose the rate of change of air temperature is -0.11 K/min.

1. Find the rate of change of the speed of sound with respect to time.

2. Find the rate of change of the speed of sound with respect to temperature.

2. Water is poured into a conical tank at a constant rate of 9 cubic feet per minute. The tank is 12 feet deep and has a radius of 4 feet at the top as shown. The shaded region is the water. Its volume is

V =1/27 pi*h^3

the instant when h = 8.0 feet, how quickly is the height of the water increasing? Round your answer to two decimal places.

Explanation / Answer

dV/dt = 0.6 dT/dt = 0.6 * -0.11/60 = -0.001 m/sec^2

dV/dT = 0.6 m/sec/K

for second question i am not able to see the diagram

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