Question

A tank holds 65 gal of water, which drains from a leak at the bottom, causing the tank to empty in 20 min. The tank drains faster when it is nearly full because the pressure on the leak is greater. Taricelli's Law gives the volume of water remaining in the tank after t minutes as WI) - 65(1- Osts 20. (a) Find viu) and Vf20). VID) - gal (20) - (b) What do your answers to part (a) represent VO) represents the initial rate at which the water is leaking, and V{20) represents the rate at which it is leaking when 20 gallons have drained. (20) represents the the time when the tank is empty, and V[0) represents the time when it is full. MO) represents the initial volume, and 1(20) represents the final volume. MO) represents the time when the tank is empty, and 720) represents the time when it is full. 120) represents the initial volume, and VID) represents the final volume. Ich Maker table of values of efort = 0, 5, 10, 15, 20. Round your answer to three decimal places.) (in minutes) V(c) (in gallons) (d) Find the net change in the volume Vase changes from o min to 20 min.

Answer 1

Vol 65 (1 ) at Vco) 2 65 65 Cin ? GSC -65 gallon a t=20 I 1(207 65 (1. 20) 2 - 2 65 (1-1) 65x0 0 gallon V6 is initial volume where e V (207 represent final volume a att v (in gallon) Nco 20 ) 65(1-5) = 23.5 65(1-10) ² 16.25 65 (1-15): 4.0625 her change 65.0 = 65 gallon