Question

I'm not sure about b,c,d. Is there anyone can help with this question?

A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0)4 metres. The volume of water is given by Vt)(t) Over time, the sides of the base are decreasing ata ateof0.05 m/s and the water is leaking from a hole in the base of the box at a rate of 2 m3/s (a) Calculate the time T that it takes for the box to empty? (b) Use the Chain Rule to find a general expression for the rate of change of the dV dt dh n terms of and dt volume of water- i dt c) Find the rate of change of the height of the water at time t- 0. dt dh (d) What is the rate of change of the height of the water (i.e. at time T where T is calculated in Part (a)?

Answer 1

太 -4.大 ご。 (o- 14)-2T 0 d大 at

大 +2X 2XYX(-o.os) Yx4h at ー: At 了大 すよ

1-28 2.