Suppose you want to make a cylindrical pen for your cat to play in (with open top) and you want the volume to be 100 cubic feet. Suppose the material for the side costs $3 per square foot, and the material for the bottom costs $7 per square foot. What are the dimensions of the pen that minimize the cost of building it

Step-by-step explanation:

GIVEN: Suppose you want to make a cylindrical pen for your cat to play in (with open top) and you want the volume to be cubic feet. Suppose the material for the side costs per square foot, and the material for the bottom costs per square foot.

TO FIND: What are the dimensions of the pen that minimize the cost of building it.

SOLUTION:

Let height and radius of pen be

Volume

total cost of building cylindrical pen

for minimizing cost , putting

Hence the radius and height of cylindrical pen are and respectively.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

the answer is the third / last answer

step-by-step explanation: