Question

A rectangle that is x feet wide is inscribed in a circle of radius 25 feet. Express the area of the rectangle as a function of x. Give the function and state its domain.

Answer 1

Answer:

$A(x)=x(\sqrt{2500-x^{2} } )$ is the area expressed as function of x,

and x: >0, <50 is the domain of the function.

Step-by-step explanation:

Draw an appropriate figure and then express the area of the rectangle as a function of x.

We know that the diagonal of a rectangle inscribed in a circle, will be equal to the diameter of the circle. 50 feet

let w = the width of the rectangle

therefore

$x^2 + w^2 = 50^2\\w^2 = 2500 - x^2\\w = \sqrt{2500-x^{2} }$

recall

Area = x*w

replace w

$A(x)=x(\sqrt{2500-x^{2} } )$ is the area expressed as function of x

b)state the domain of the function

x: >0, <50