Question

Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. x = 2.5 when y = 100.

Answer 1

2.5x40=100 100/40=2.5

Answer 2

Answer:

constant of variation(k) is, 250.

$y = \frac{250}{x}$

Step-by-step explanation:

The inverse variation says that:

$y \propto \frac{1}{x}$

then, the equation is in the form of :

$y = \frac{k}{x}$        ....[1] where, k is the constant of variation

As per the statement:

Suppose that y varies inversely with x.

then,

by definition of inverse variation we have;

$y = \frac{k}{x}$

When x = 2.5 and y = 100 then

Substitute these in [1] we have;

$100 = \frac{k}{2.5}$

Multiply 2.5 both sides we have;

$250 = k$

or

k = 250

⇒$y = \frac{250}{x}$

Therefore, the constant of variation is, 250 and the equation we get $y = \frac{250}{x}$