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

$\frac{550}{11} = {11k}{11}$

$50 = k$

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.

$P = rk$

$715 = r*50$

$\frac{715}{50} = \frac{50r}{50}$

$\frac{715}{50} = \frac{50r}{50}$

$14.3 = r$

r = 14.3