Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the rate of 2 cm3/min. at what rate is the depth of the water changing at the instant when the water in the tank is 8 cm deep? show all work and include units in your answer. give an exact answer showing all work and include units in your answer

Step-by-step explanation:

From similar triangles, see diagram in attachment

We solve for to obtain,

The formula for calculating the volume of a cone is

We substitute the value of to obtain,

This implies that,

We now differentiate both sides with respect to to get,

We were given that water is drained out of the tank at a rate of

This implies that .

Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means .

We substitute this values to obtain,

can i get the link to the assignment?

step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18