Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 16cm and a height of 8cm, at the rate of 4 cm3/min. at what rate is the depth of the water changing at the instant when the water in the tank is 6 cm deep? show all work and include units in your answer. give an exact answer showing all work and include units in your answer.

Volume(V) of a circular cone is given by :

   ......[1] where r is the radius and h is height of the cone respectively.

Given: Radius of cone(r) = 16 cm and height of cone(h) = 8 cm

or

r =2h

Substitute in [1]; we have

                         ......[2]

It is also, given the rate i.e,

Differentiate V with respect to t in equation [2] we get;

{}

To find the rate of depth of the water when tank is 6 cm deep.

Simplify:

Substitute h = 6 cm we have;

or

    [Use ]

Simplify:

Therefore, the rate of depth of the water changing is,

the answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x