Question

Write a general formula to describe the variation:Z varies directly with the sum of the squares of x and y; z=5 when x=4 and y=3

Answer 1

The variation "Z varies directly with the sum of the squares of x and y" can be written into symbols and it looks like this: (with a constant k)

`Z=k(x^2+y^2)`

Applying when x = 4 and y = 3, we have:

`\begin{gathered} Z=k(x^2+y^2) \\ 5=k(4^2+3^2) \\ 5=k(16+9) \\ 5=25k \\ \text{Divide both sides by 25} \\ (5)/(25)=(25k)/(25) \\ (1)/(5)=k \end{gathered}`

The value of the constant k is 1/5.

The general formula is stated above and that is z = 1/5 (x² + y² ).