The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubic meters per minute. At the instant when the radius of the cone is 99 meters and the volume is 180 cubic meters, what is the rate of change of the height? The volume of a cone can be found with the equation V=\frac{1}{3}\pi r^2 h. V= 3 1 πr 2 h. Round your answer to three decimal places.

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

Differentiate the equation with respect to time t, such that

To differentiate the product,

Let r² = u, so that

Then, using product rule

Since

Then,

Using the Chain's rule

∴

Then,

Now,

From the question

At the instant when

and

We will determine the value of h, using

Now, Putting the parameters into the equation

Hence, the rate of change of the height is 0.021 meters per minute.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc