Question

z is jointly proportional to x ^ 3 and y ^ 2. If z = 28 whenx x = 5 and y = 4 find x = 6 and y = 5 (Round off your answer to the nearest hundredth)

Answer 1

We know that z is proportional to x^3 and y^2.

We can express this with a proportionality constant k as:

`z=k\cdot x^3\cdot y^2`

We know that when x = 5 and y = 4, z = 28.

We can use this to find the value of k as:

`\begin{gathered} z=kx^3y^2 \\ 28=k(5)^3(4)^2 \\ 28=k*125*16 \\ k=(28)/(125*16) \\ k=(28)/(2000) \\ k=0.014 \end{gathered}`

We can know calculate z for x = 6 and y =5:

`\begin{gathered} z=0.014x^3y^2 \\ z=0.014*6^3*5^2 \\ z=0.014*216*25 \\ z=75.6 \end{gathered}`

Answer: 75.6