Also the reservoir is full after how many hours? Reservoir with a capacity 2500

Question

Also the reservoir is full after how many hours? Reservoir with a capacity 2500 m^3 is filled with a single inflow pipe. The reservoir is empty when the inflow pipe is opened at t = 0. Setting Q(t) be the amount of water in the reservoir at time t the How rate of water into the reservoir (In m^3/hr) oscillates on a 24-hr cycle (see figure) and is given by the following equation Complete parts a through c. Q'(t) = 15[1 + cos[pi/12] a. How much water flows into the reservoir in the first 6 hr. The amount of water that flows into the reservoir is m^3. b. Find and graph the function that gives the amount of water in the reservoir over the interval (0, t) where t lessthanorequalto 0. What is the function that gives the amount of water in the reservoir? Q(t) =

Explanation / Answer

Solution:

Q'(t)= 15(1+cos((pi*t)/12)).

Q(t) = Q'(t) dt

= 15(1+cos((pi*t)/12)) dt

= 15 {t + (12sin(pi*t/12))/pi}

After 6 hours,

Q(6) = 15 {t + (12sin(pi*t/12))/pi} = 15 { 6 + (12/pi) (sinpi/2)} = 15 { 6 + 12/pi} = 147.30 m^3

Q(6) =147.30 m^3

when reserboir is full;

Q(t) = 2500 = 15 {t + (12sin(pi*t/12))/pi}

=> 2500/15 = {t + (12sin(pi*t/12))/pi}

=> 166.67 - (12/pi)(sin(pi*t/12)) = t

take sin(pi*t/12) = 1 approx.

=> 166.67 - 3.82 = t

=> t = 162.85 hours

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