varies directly as r and inversely as y. If z = 187 when x = 64 and y= 6, find z if x= 4 and y = 9. (Round off your answer to the nearest hundredth.
We are given that the variation varies directly as r and inversely as y. This can be represented by the equation z = k(r/y), where k is a constant.
We can use the given values of z = 187, x = 64, and y = 6 to find k. Substitute these values into the equation and solve for k:
187 = k(64/6)
187 = k(10.67)
k ≈ 17.50
Now we can use the value of k to find z when x = 4 and y = 9. Substitute these values into the equation and solve for z:
z = 17.50(4/9)
z ≈ 7.78
Therefore, when x = 4 and y = 9, z is approximately equal to 7.78 rounded to the nearest hundredth.