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slega [8]
3 years ago
8

Air escapes from a balloon at a rate of 2 60 ( ) 1 R t t   3 ft / min , where t is measured in minutes. How much air (in 3 ft

) escapes during the first minute?
Physics
1 answer:
kotykmax [81]3 years ago
4 0

Answer:

Given R (t) = 60/(1+t²), ft /min

To find the amount of air in ft³, during the first min,

R (t) = 60/(1+t²

at t=1min, R is the air amount in ft³/min

Take the integral, and evaluate over [0,1]

Integral Of R (t) = 60/(1+t²) = 60 tan⁻¹(t),

60(Tan⁻¹(1) - Tan⁻¹(0)) = 60(pi/2) = 30 π

Therefore, it means that in the first minute, 30π ft³ of air escaped.

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