The height of a 0.5-liter orange juice box with a square base is a function of the width of its base, h=(500)/(w^2) where w is the width of the base in centimeters. Find the wid…

Question

The height of a 0.5-liter orange juice box with a square base is a function of the width of its base,


`h=(500)/(w^2)`


where w is the width of the base in centimeters. Find the width of the juice box if its height is 20 centimeters.


w =_____cm

Answer 1

w=5 cm

Explanation:

Functions

We know the height (h) of a box is a function of the width of its base:

`\displaystyle h=(500)/(w^2)`

We are required to find the width of the box when the height is h=20 cm

To find w in terms of h we must isolate w from the equation above

Operating

`\displaystyle w^2h=500`

`\displaystyle w^2=(500)/(h)`

Taking the square root

`\displaystyle w= \sqrt{(500)/(h)}`

Replacing the value of h=20

`\displaystyle w= \sqrt{(500)/(20)}= √(25)=\ 5cm`

`\boxed{w=5\ cm}`