Calculus question story problem!!?

Question

A 20- by 70-ft swimming pool is surrounded by a walk of uniform width. The distance from the outer edge of the walk to the pool is x feet on all sides.

a) write the area A of the sidewalk as a function of x.

b) draw a complete graph of y=A(x)

c) what are the domain and range of y=a (x)?

d) what values of the graph in part (b) is a graph of the problem situation?

e) determine he width of the sidewalk if its area is 500 ft squared

Answer 1

A(x) = (area of deck + pool) - (area of pool)

= (20+2x)(70+2x) - (20)(70)

= 1400 + 140x + 40x + 4x² - 1400

= 4x² + 180x

Since x refers to the width of something concrete (ha ha), negative values are discarded.  Deal with the range and domain questions as you see fit.

500 = 4x² + 180x

4x² + 180x - 500 = 0

x² + 45x - 125 = 0

x = [-45 ± √(2025 + 500)] / 2

= 2.62, -47.62

discard the negative: 2.62 feet