A circular rim 28 inches in diameter rotates the same number

To determine the number of revolutions per minute the larger rim makes in terms of x, we need to compare the linear speeds of the two rims.

The linear speed of a rotating object can be calculated by multiplying the circumference of the circle by the number of revolutions per second.

For the smaller rim with a diameter of 28 inches, the circumference is π * 28 = 28π inches.

For the larger rim with a diameter of 35 inches, the circumference is π * 35 = 35π inches.

Both rims rotate the same number of inches per second, so we can set up the following equation:

28π * x = 35π * N,

where N represents the number of revolutions per minute for the larger rim.

To find N in terms of x, we divide both sides of the equation by 28π:

x = (35π * N) / (28π).

Simplifying, we get:

x = (5/4) * N.

To express the number of revolutions per minute, we convert x revolutions per second to (x * 60) revolutions per minute:

(x * 60) = (5/4) * N.

Simplifying further, we have:

N = (4/5) * (x * 60) = 48x.

Therefore, the larger rim makes (C) 48x revolutions per minute in terms of x.