Question

A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function m(x), where x is the length of the radius of the circle in feet. The homeowner estimates that he will pay $1.50 per square foot of mulch. This cost is represented by the function g(m), where m is the area requiring mulch.

Answer 1

Answer:

The equation of cost of mulch is $1.50\times (\pi x^{2}-2\sqrt{2}x^{2})$.

Step-by-step explanation:

The equations m (x) and g (m) are as follows:

$m(x)=\pi x^{2}-2\sqrt{2}x^{2}\\g(m)=1.50m$

It is provided that the cost of mulch requires is represented by the function g(m), where m is the area requiring mulch.

To compute the equation of cost of mulch based on the radius of the circle substitute the value of m (x) in g (m).

The equation of cost of mulch is:

$g(m) = 1.50m$

        $=1.50\times m(x)\\\\=1.50\times (\pi x^{2}-2\sqrt{2}x^{2})$

Thus, the equation of cost of mulch is $1.50\times (\pi x^{2}-2\sqrt{2}x^{2})$.