If P varies inversely as V and V varies directly as R2, find the relationship between P and R given that R = 7 when P = 2
A
P = 98R2
B
PR2 = 98
C
P = \(\frac{1}{98R2
D
P = \(\frac{PR2}{98}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
P = \(\frac{1}{v}\) and vR2 = P = \(\frac{k}{v}\)......(i)
and v KR2 .......(ii)
(where k is constant)
Subst. for v in equation (i) = p = \(\frac{1^2}{KR}\).....(ii)
when r = 7, p = 2
2 = \(\frac{k}{7^2}\)
k = 2 x 49
= 98
Subt. foe k in ....(iii)
P = \(\frac{98}{R^2}\)
PR2 = 98
Source: Myschool Past Questions Archive (Record #31890)