Question

Select all the correct answers.

Answer 1

Answer:

The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.

⇒The water level in the pool cannot exceed 14 feet.

Step-by-step explanation:

The question is on inequalities

Given;

Length= x ft

depth= x-6  ft

Width= x-8 ft

volume ≤ 1680 ft³

Forming the inequality to find length x of the pool

Volume= base area × depth

base area × depth ≤ volume

x(x-8) × (x-6) = 1680

(x²-8x )(x-6) = 1680

x(x²-8x) -6 (x²-8x)=1680

x³-8x²-6x²+48x=1680

x³-14x²+48x=1680

x³-14x²+48x-1680 ≤ 0

⇒The water level in the pool cannot exceed 14 feet...why?

taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;

d=x-6 = 17-6=11 ft

⇒11 ft is less than 14ft