A sculptor uses a constant volume of modeling clay to form a cylinder with a large height and a relatively small radius. The clay is molded in such a way that the height of the clay increases as the radius decreases, but it retains its cylindrical shape. At time t=c, the height of the clay is 8 inches, the radius of the clay is 3 inches, and the radius of the clay is decreasing at a rate of 1/2 inch per minute. Write an expression for the rate of change of the radius of the clay with respect to the height of the clay in terms of height h and radius r.

Step-by-step explanation:

The volume of a cylinder is given by the formula:

V = πr²h,

Where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.

We are to express the rate of change of the radius of the clay with respect to the height of the clay in terms of height h and radius r.

That means we express dr / dh in terms of height h and radius r. To do this, we have to first differentiate the volume with respect to the height, i.e. find dV / dh:

V = πr²h

:

the median here is 25. your lowest value is 14 and highest value is 48. to find the third quartile, find the medium number in between 25 and 48 which would be 42 i believe.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.