Question

Z varies directly as x⎯⎯√ and inversely as y. if z=136 when x=16 and y=9, find z if x=25 and y=6. (round off your answer to the nearest hundredth.)

Answer 1

To find the new value of z when x=25 and y=6, first determine the constant of proportionality with the initial conditions. Then apply the direct and inverse variation formulas, and perform the calculations to find z, which, when rounded to the nearest hundredth, is approximately 1020.00.

Step-by-step explanation:

You want to understand how z varies directly as the square root of x (x¯¯√) and inversely as y. Given that z=136 when x=16 and y=9, we can establish a proportional relationship:

z = k (√ x) / y where k is the constant of proportionality.

First, we find k using the initial conditions:

136 = k (√ 16) / 9

136 = k (4) / 9

k = 136 * 9 / 4

k = 1224.

Now, we can find the new value of z when x=25 and y=6.

z = 1224 (√ 25) / 6

z = 1224 (5) / 6

z = 6120 / 6

z = 1020.

Rounding off to the nearest hundredth, z is approximately 1020.00.