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?

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Physics

4 May, 11:44

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?

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Miley · Answer 1

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.