Consider a cylindrical object such that its diameter is always half its height. if the cylinder is shrinking in a such a way that its height is reducing at a rate of 2 cm/minute and its initial height (at time t=0) is 40 cm, find a formula for the volume of the cylinder in terms of time t measured in minutes. you may use the volume formula for a cylinder v=πr2h.

Step-by-step explanation:

Assuming that height is a function of time, we have to . Integrating and applying the first fundamental theorem of the calculation you get:

. Since , you have to and therefore, and

Now, if diameter is always half its height, or what is equal . With all this,

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204