The depth (in metres) of water in a cylindrical overhead tank minutes after a drain…

MATHEMATICS · Subjective · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

5. The depth

d

(in metres) of water in a cylindrical overhead tank

t

minutes after a drain valve is opened is given by

d(t) = -0.2t^{2} + 2t + 8\qquad (0 \le t \le T),

where

T

is the time when the tank becomes empty. (a) Determine the value of

T

. (b) During the first 5 minutes, for how many minutes is the depth of water at least 9 m? Show working clearly. (c) Does the second zero of

d(t)

(if any) have any physical significance in this situation? Explain your answer.