Question

directly as Vi and inversely as y°. If: = 61 when = 36 and y = 9, find a if r = 64 and y = 6. (Round off your answer to the nearest hundredth.)

Answer 1

Given: z directly varies as √x and inversely varies as y³

when x = 36 and y = 9 then z = 61

To find:

when x = 64 and y = 6 then z = ?

Step-by-step explanation:

z ∝ √x / y³

z = k √x / y³

when x = 36 and y = 9 then z = 61

`z=\text{ }\frac{k\text{ }√(x)}{y^3}`
`\begin{gathered} 61=\frac{k\text{ * }√(36)}{9^3} \\ 61=(k*6)/(729) \\ k=(61*729)/(6)=(61*243)/(2)=(14823)/(2) \end{gathered}`

when x = 64 and y = 6

`z=\text{ }(14823)/(2)*(√(64))/(6^3)=(14823*8)/(2*216)=(4941*4)/(72)=(4941)/(18)=274.5`

the value of z = 274.5

final answer:

z = 274.5 ≈ 300 when rounded off to the nearest hundredth