P varies directly as Q and inversely as the square of R . If P =1 when Q=8 and R = 2. Find the value of Q when P =3 and R=5
To solve this problem, we can set up the equation:
P = k(Q/R^2)
where k is the constant of proportionality. We can find the value of k using the initial conditions: P = 1 when Q = 8 and R = 2.
1 = k(8/2^2)
1 = k(8/4)
1 = 2k
k = 1/2
So, our equation becomes:
P = (1/2)(Q/R^2)
Now we can plug in the new conditions where P = 3, and R = 5 to find Q:
3 = (1/2)(Q/5^2)
3 = (1/2)(Q/25)
3 = (Q/50)
Q = 150
Therefore, the value of Q when P = 3 and R = 5 is 150.