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

:

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

answer: x=60