Question

Assume that y varies inversely with x. If y= 1.6 when x= 0.5, find x when y= 3.2

Answer 1

Answer:

x = 0.25

Step-by-step explanation:

If y varies inversely with x, then:

$y \propto \dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant k)}$

Given:

• y = 1.6 when x = 0.5

Substitute the given values into the found equation and solve for k:

$\implies 1.6=\dfrac{k}{0.5}$

$\implies k=1.6(0.5)$

$\implies k=0.8$

Therefore:

$y=\dfrac{0.8}{x}$

To find the value of x when y = 3.2, substitute y = 3.2 into the found equation and solve for x:

$\implies 3.2=\dfrac{0.8}{x}$

$\implies x=\dfrac{0.8}{3.2}$

$\implies x=0.25$