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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.

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 class=

Respuesta :

Answer:   [tex]1.50(\pi x^2-2\sqrt{2}x^2)[/tex]

Step-by-step explanation:

Here the function that shows the total area of mulch,

[tex]m(x)=\pi x^2-2\sqrt{2}x^2[/tex]

Also, the function that shows the total cost mulch that requires,

[tex]g(m) = 1.50 m[/tex]

By putting the value of m,

We get,

[tex]\implies g(m) = 1.50( \pi x^2-2\sqrt{2}x^2 )[/tex]

Where x is the radius of the circle.

Thus, First option is correct.

The cost of the mulch is represented by the expression [tex]\rm g(m) = 1.5(\pi x^2 - 2\sqrt{2} x^2)[/tex] and this can be determined by using the given data.

Given :

  • The 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.
  • Cost is represented by the function g(m), where m is the area requiring mulch.
  • [tex]\rm m(x) = \pi x^2 -2\sqrt{2}x^2[/tex]
  • [tex]\rm g(m)=1.50 m[/tex]

Given data is used to determine the expression represents the cost of the mulch based on the radius of the circle.

Given that the cost of the mulch is represented by:

[tex]\rm g(m)=1.50 m[/tex]

Now, put the value of m that is, [tex]\rm m(x) = \pi x^2 -2\sqrt{2}x^2[/tex] in the above equation.

[tex]\rm g(m) = 1.5(\pi x^2 - 2\sqrt{2} x^2)[/tex]

Therefore, the correct option is A).

For more information, refer to the link given below:

https://brainly.com/question/21835898

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