Question

z varies directly with x2 and inversely with y. When x = 2 and y = 4, z = 3. What is the value of z when x = 4 and y = 9?

Answer 1

z = (kx^2)/y -> 3 = (k(2^2))/(4) -> k=3
z = (3*4^2)/9 = 16/3

Answer 2

Answer:

Joint variation says that:

If y varies directly to x and inversely to w then, the equation is of the form:

$y = k \cdot \frac{x}{w}$ where, k is the constant of variation.

As per the statement:

z varies directly with $x^2$ and inversely with y

By definition of joint variation:

$z = k \cdot \frac{x^2}{y}$          ......[1]

When  x = 2 and y = 4, z = 3.

Solve for k:

Substitute the given values in [1] we have;

 $3 = k \cdot \frac{2^2}{4}$

⇒$3 = k \cdot \frac{4}{4}$

Simplify:

3 = k

or

k = 3

Then, an equation we get;

$z = 3 \cdot \frac{x^2}{y}$

Substitute the value x =4 and y = 9 to solve for z:

$z = 3 \cdot \frac{4^2}{9} = 3 \cdot \frac{16}{9} = \frac{16}{3}$

⇒The value of $z = \frac{16}{3}$