Answer:
The dimensions are 50 and 100 square foot
Step-by-step explanation:
Let x = length of fenced side parallel to the side that borders the playground
y = length of each of the other two fenced sides
Then, x + 2y = 200
<=> x = 200-2y
The Area = xy = y(200-2y)
The dimensions of the playground that will minimize the homeowner's total cost for materials when the area of the playground is maximum. He can cover more area but with the same cost.
The graph of the area function is a parabola opening downward.
The maximum area occurs when y = -200/[2(-2)] = 50
=> x = 100
So the dimensions are 50 and 100 square foot
Recall that

. So we can add twice the first equation to the second one to get

Since

, we have

so

If

, then

If

, then

So the solution set is
Answer to number 16 is 27 and 17 is 2
Answer:
2141.76 cubic inches
Step-by-step explanation:
Given that it measures 8.8 inches across a properly inflated basketball i.e. the diameter of each basketball is 8.8 inches.
So, the radius of the spherical ball is
inches.
Now, a spherical solid has a volume given by
.
Hence, volume of air in side each basketball is =
cubic inches.
Therefore, the total volume of air inside six balls will be = 6 × 356.96 = 2141.76 cubic inches. (Answer)