Question

1. john is building a circular pool with an area of 80π square feet. he will build a rectangular deck around the pool as shown. the width of the deck will be 3 feet less than the length of the deck. which equation represents the area of the deck (not including the area of the pool) given represents the length of the deck? a. f(n)=(n² - 3n)+80π b. f(n)=(n² - 3n)-80π c. f(n)=(n² - 3)+80π d. f(n)=(n² - 3)-80π

Explanation:

Step1: Calculate the area of the rectangular deck

The formula for the area of a rectangle is \(A = length\times width\). Given that the length of the deck is \(n\) and the width is \(n - 3\), the area of the deck (including the pool) is \(n(n - 3)=n^{2}-3n\).

Step2: Calculate the area of the deck (excluding the pool)

The area of the pool is \(80\pi\). To find the area of the deck (not including the pool), we subtract the area of the pool from the area of the deck (including the pool). So the area \(f(n)=(n^{2}-3n)-80\pi\).

Answer:

B. \(f(n)=(n^{2}-3n)-80\pi\)