SOLUTION: A container is being filled with water. After t seconds the depth of water, x cm, in the container is increasing at the rate of 1.44tcm/s. Given that the container is empty when

Algebra ->  Test -> SOLUTION: A container is being filled with water. After t seconds the depth of water, x cm, in the container is increasing at the rate of 1.44tcm/s. Given that the container is empty when      Log On


   

Question 1045490: A container is being filled with water. After t seconds the depth of water, x cm, in the container is increasing at the rate of 1.44tcm/s.
Given that the container is empty when t=0, use calculus to find
the value of t when x=18.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
dx%2Fdt+=+1.44t ===> x+=+1.44%28t%5E2%2F2%29+%2B+c+=+0.72t%5E2%2Bc.
When t = 0, x = 0, as given.
===> x+=+0.72t%5E2.
When x = 18 cm, 18+=+0.72t%5E2 ===> t%5E2+=+25 ===> t = 5 seconds.