P varie directly as Q and inversely proportional to The square of R if the value of P is 1, Q is 8 and R is 2. Find the value of Q when P is 3 and R is 5
Given that P varies directly as Q and inversely proportional to the square of R, we can write the relationship as:
P = kQ/R^2
where k is the constant of proportionality.
From the given values, when P = 1, Q = 8, and R = 2, we can plug these values into the equation to solve for k:
1 = k * 8 / 2^2
1 = 2k
k = 1/2
Now, we can use the constant of proportionality to find Q when P = 3 and R = 5:
3 = (1/2)Q / 5^2
3 = Q / 25
Q = 3 * 25
Q = 75
Therefore, when P is 3 and R is 5, the value of Q is 75.