Answer/Step-by-step explanation:
Given that P varies directly with r, the equation for this direct variation would be:
[tex] P = rk [/tex],
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.
[tex] 550 = 11k [/tex]
Divide both sides by 11
[tex] \frac{550}{11} = {11k}{11} [/tex]
[tex] 50 = k [/tex]
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.
[tex] P = rk [/tex]
[tex] 715 = r*50 [/tex]
[tex] \frac{715}{50} = \frac{50r}{50} [/tex]
[tex] \frac{715}{50} = \frac{50r}{50} [/tex]
[tex] 14.3 = r [/tex]
r = 14.3
