How do you write a general formula to describe each variation if z varies directly with the sum of the cube of x and the square of y; z=1 when x=2 and y=3?

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Answer 1 · 2016-10-08T16:37:30

General formula is $z = \frac{1}{17} (x^{3} + y^{2})$ $z=1/17(x^3+y^2)$

When a variable say $z$ $z$ varies directly with say $w$ $w$

we have $z \propto w$ $zpropw$ i.e. $z = w \times k$ $z=wxxk$ , where $k$ $k$ is a constant.

Here $w$ $w$ is the sum of the cube of $x$ $x$ and the square of $y$ $y$

Hence $z = (x^{3} + y^{2}) \times k$ $z=(x^3+y^2)xxk$ ......................(1)

When $z = 1$ $z=1$ when $x = 2$ $x=2$ and $y = 3$ $y=3$ , (1) becomes

$1 = (2^{3} + 3^{2}) \times k$ $1=(2^3+3^2)xxk$

or $1 = (8 + 9) \times k$ $1=(8+9)xxk$

or $17 k = 1$ $17k=1$ i.e. $k = \frac{1}{17}$ $k=1/17$

Hence, general formula is $z = \frac{1}{17} (x^{3} + y^{2})$ $z=1/17(x^3+y^2)$