Suppose that a dimension x and the area A of a shape are differentiable functions of t. Write an equation that relates to .

Complete question is;

Suppose that a dimension x and the area A = 2x² of a shape are differentiable functions of t. Write an equation that relates dA/dt to dx/dt.

Step-by-step explanation:

Since A = 2x²

Let's differentiate both sides with respect to x.

dA/dx = 4x

Now, we want to find the relationship between dA/dt and dx/dt

dA/dt can be expressed as;

(dA/dt) = (dA/dx) × (dx/dt)

Thus;

dA/dt = 4x(dx/dt)

Thus, the equation that relates dA/dt to dx/dt is;

dA/dt = 4x(dx/dt)

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi

here is a big fat