A ring-shaped region is shown below. Its inner radius is 8 ft, and its outer radius is 12 ft. Find the area of the shaded region. (Use 3.14 for it. Do not round your answer.)

Step-by-step explanation:

In this problem we want to find the area of a ring-shaped region.

The inner radius of the ring is

while the outer radius of the ring is

The area of the ring is equal to the area of the larger circle minus the area of the smaller circle.

The area of the larger circle is:

The area of the smaller circle is instead

Therefore, the area of the ring is:

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

what do you mean by fog

step-by-step explanation: