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The radius of the inner circle of a tile pattern shown is x inches. Write a polynomial in standard form to represent the area of the space between the inner and outer circle.

The radius of the inner circle of a tile pattern shown is x inches Write a polynomial in standard form to represent the area of the space between the inner and class=

Respuesta :

semsee45

Answer:

Area of a circle:  

[tex]A=\pi r^2[/tex] (where r is the radius)

Area of largest (outer) circle:

[tex]\implies A=\pi (x+6)^2[/tex]

Area of inner circle:

[tex]\implies A=\pi x^2[/tex]

Area of space between the inner and outer circle:

[tex]\implies \pi (x+6)^2-\pi x^2[/tex]

[tex]\implies \pi [(x+6)^2- x^2][/tex]

[tex]\implies \pi (x^2+12x+36- x^2)[/tex]

[tex]\implies 12\pi x+36\pi[/tex]

Factored:

[tex]\implies 12\pi (x+3)[/tex]