Question

Y varies jointly as the cube of x and the square root of w, and Y = 128 when x = 2 and w = 16. Find Y when x = 1/2 and w = 64? P.S. Thank you for helping me for this problem.

Answer 1

Given that y varies jointly as the cube of x and the square root of w,

`y=ax^3xxsqrtw.....(1)`,

where `a` variation constant

Again inserting

y = 128 when x = 2 and w = 16 in equation (1)

`128=axx2^3xxsqrt16`

`=>128=axx8xx4`

`=>a=4`

Now the equation (1) becomes

`y=4x^3xxsqrtw`

Inserting x = 1/2 and w = 64 we get
`y=4(1/2)^3xxsqrt64`

`=>y=4xx1/8xx8=4`