Ahomeowner has 200 feet of fence to enclose an area for a pet. (a) if the area is given by a(x)=x(100-x), what dimension maximize the area inside the fence? (b) what is the maximum area? (c) determine the domain and range of a in this application.

(a) x = 50 maximizes the area. We assume that means 50 ft × 50 ft(b) 2500 ft²(c) domain: 0 ≤ x ≤ 100; range: 0 ≤ A ≤ 2500Step-by-step explanation:

(a) The function describes a parabola that opens downward. The value of A(x) is zero when x=0 and when x=100. The vertex (maximum) is halfway between those zeros, at x=50. The dimensions are 50 and 100-50 = 50. The maximum area pen will be 50 ft square.

(b) A(50) = (50 ft)² = 2500 ft² . . . the maximum area

(c) A(x) will be negative if x < 0 or x > 100, so the domain is 0 ≤ x ≤ 100.

The value of A(x) ranges from 0 to its maximum, 2500. Hence the range is 0 ≤ A(x) ≤ 2500.

Answer: the correct answer is 10step-by-step explanation: let the number be n, then the expression becomes,then“twelve more than the quotient of a number and two, decreased by four” iswhen n=4,we substitute 4 whetever we see n to get,we simplify to obtain,we further simplify to get,therefore the correct answer is c.

There would be 36.35 pounds