A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 21 feet long, 14 feet wide, and 9 inches deep.
a) Determine the volume, in cubic feet, of mulch the contractor will need.
b) If mulch costs $11 per cubic foot, what will the cost of mulch be?

Step-by-step explanation:

a) The volume of a rectangular prism can be calculated by multiplying its dimensions.

In this case, you know the rectangular solid has 21 feet long, 14 feet wide, and 9 inches deep.

Since , then its depth in feet is:

 Therefore, its volume is:

b) Knowing that each cubic foot of mulch costs $11, you can calculate the total cost of the mulch the contractor needs to buy, multiplying the volume by the $11.

Then, you get:

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)