Q:

Don works in home construction. He determined that the function t(A)=144a/9.25^2 gives the total number of 9 in. tiles needed to cover an area of A square feet, when spacing the tiles a quarter inch apart. Find t(400) and explain what it means.

Accepted Solution

A:
Answer:[tex]t(400)=673[/tex].Don required  673 of 9 inch tiles to cover an area of 400 square feet, when spacing the tiles a quarter inch apart.Step-by-step explanation:Given:The given function is:[tex]t(A)=\frac{144}{9.25^2}A[/tex]Here, [tex]A[/tex] represent the area to be covered, [tex]t[/tex] represent the number of tiles required to cover the given area.So, if [tex]A=400[/tex], it means that the area to be covered is 400 square units.Now, if we find [tex]t(400)[/tex], it means we need to find the number of 9 inch tiles to cover area of 400 units.So, we plug in 400 for [tex]A[/tex] to evaluate [tex]t(400)[/tex].[tex]t(400)=\frac{144}{9.25^2}\times 400=\frac{144\times 400}{85.5625}=\frac{57600}{85.5625}=673.19\approx673[/tex]Therefore, it means that 673 of 9 inch tiles are required to cover an area of 400 square feet, when spacing the tiles a quarter inch apart.