The manager at a daycare facility wants to put a fence around a rectangular play yard just outside of the building. she will use a wall of the building as one side of this rectangle, so that fencing is only needed on the other three sides. if there are 96 feet of fencing available, and x represents the length of one of the sides of the rectangle that is perpendicular to the building's wall, then find the value of x that will maximize the area of this play yard. (see the picture below)

24

Step-by-step explanation:

If x is the length of the perpendicular sides, then the length of the parallel side must by 96−2x.

The total area is:

A = x (96 − 2x)

A = 96x − 2x²

This is a parabola, so we know the maximum is at the vertex (at x = -b/(2a)).

x = -96 / (2 · -2)

x = 24

Or, we can optimize using calculus.  Find dA/dx and set to 0:

dA/dx = 96 − 4x

0 = 96 − 4x

x = 24

The value of x that maximizes the area is x = 24 ft.

b

step-by-step explanation:

b

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.