Question

The power, P, of a gear varies directly with its radius, r. If the power of a certain gear is 550 and the radius for that gear is 11 find the radius (r) of a gear whose power is 715. Identify the constant of variation, direct variation equation, and radius (r).

Answer 1

Answer/Step-by-step explanation:

Given that P varies directly with r, the equation for this direct variation would be:

`P = rk`,

Where,

P = power

r = radius

k = constant of variation.

If P = 550, when r = 11, constant of this direct variation is calculated as follows:

Plug in the values of P and r into the variation equation to find k.

`550 = 11k`

Divide both sides by 11

`(550)/(11) = {11k}{11}`

`50 = k`

Constant of variation = 50

To find the radius (r) of the gear whose power (P) = 715, substitute P = 715 and k = 50 in the variation equation.

`P = rk`

`715 = r*50`

`(715)/(50) = (50r)/(50)`

`(715)/(50) = (50r)/(50)`

`14.3 = r`

r = 14.3