solve variation problem.
if y varies directly as x and inversely as m^2 and r^2 and y=5/3 when x=1, m=2 and r=3, find y when x=3, m=1 and r=8
To solve this variation problem, we can use the formula for direct and inverse variation:
Direct Variation: y = kx
Inverse Variation: y = k/(m^2 * r^2)
Given that y varies directly as x and inversely as m^2 and r^2, we can combine these formulas:
y = kx/(m^2 * r^2)
We are also given that y = 5/3 when x = 1, m = 2, and r = 3. Plugging these values into the equation, we can solve for k:
5/3 = k/(2^2 * 3^2)
5/3 = k/36
k = (5/3) * 36
k = 60
Now that we have the value of k, we can substitute it back into the equation and solve for y when x = 3, m = 1, and r = 8:
y = (60 * 3)/(1^2 * 8^2)
y = 180/64
y = 45/16
Therefore, when x = 3, m = 1, and r = 8, the value of y is 45/16.