A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Six hundred feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?

the smallest dimension = 100 ft

the largest dimension = 150 ft

Maximum Area = 15000 ft²

Step-by-step explanation:

let x represent length of one side and L represent length of adjacent side

so from the question

3x + 2L = 600

2L = 600 - 3x

L = (600 - 3x)/2

L = (600/2) - (3x/2)

L  = 300 - (3x/2)

now Area of rectangle = L × x

Area = (300 - (3x/2)) × x

Area = 300x - 3x²/2

now we differentiate with respect to x  and equate to 0 in other to find critical point

dA/dx ⇒ 300x/x - 3x²/x = 0

300 - 3x = 0

3x = 300

x = 300/3

x = 100

so we input value of x into our previous equation

Area = 300x - 3x²/2

= 300(100) - (3(100)²)/2

= 30000 - 15000

Area = 15000

also we input value of x in L = 300 - (3x/2)

L  = 300 - (3(100))/2)

L = 300 - 150

L = 150

Therefore

the smallest dimension = 100 ft

the largest dimension = 150 ft

Maximum Area = 15000 ft²

the answer is 844

step-by-step explanation:

it is 844 because if you add 836.50 + 7.5 you will get 844

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it