b) What is that greatest mass? c) In kilograms per minute, what is the rate of m

Question

b)What is that greatest mass?

c) In kilograms per minute, what is the rate of mass change at t = 2.00 s?

d)In kilograms per minute, what is the rate of mass change at t = 5.00 s?

Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by m = 5.50t 0.8 - 2.85t + 18.00, with t 0, m in grams, and t in seconds. At what time is the water mass greatest? What is that greatest mass? In kilograms per minute, what is the rate of mass change at t = 2.00 s? In kilograms per minute, what is the rate of mass change at t = 5.00 s?

Explanation / Answer

a) dm/dt = 4.4t^-0.2 - 2.85 = 0

t = 8.77 s

b) m = 5.50 x 8.77^0.8 - 2.85 x 8.77 + 18   = 24.25 gram

c) rate of mass change = dm/dt = 4.4t^-0.2 - 2.85 = 0

dm/dt (2)   = 0.98 gm/s   = 0.98 x 60 / 1000 = 0.0588 kg/min

d) dm/dt(5) = 0.339 gm/s = 0.0203 kg/min

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