Mathematics, 04.04.2020 05:21 tylorroundy

Using the side of a building as one side and fencing for the other three sides, a rectangular garden will be constructed. Given that there are 60 feet of fencing available, determine the dimensions that would create the garden of maximum area and identify the maximum area. Enter only the maximum area. Do not include units in your answer.

Answers: 3

Show answers

Answers

Answer from: granniejo

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

The maximum area is 450 feet²

Step-by-step explanation:

The garden is fencing for three sides only, That means the length of the fencing is equal to the sum of the length of the three sides

Assume that garden is y feet long and x feet wide and the fencing will cover on side of y feet and two sides of x feet

∵ The sum of the length of the 3 sides = y + x + x

∴ The sum of the length of the 3 sides = y + 2x

- The length of the fencing is equal to the sum of the sides

∵ The fencing is 60 feet

- Equate y + 2x by 60

∴ y + 2x = 60

- Find y in terms of x by subtracting 2x from both sides

∴ y = 60 - 2x

To find the dimensions which make the maximum area, find the area of the garden, then substitute y by x, and differentiate it with respect to x, then equate the differentiation by 0 to find the value of x, and substitute this value in the equation of y to find y and in the equation of the area to find the maximum area

∵ The formula of the area of a rectangle is A = l × w

∵ l = y and w = x

∴ A = x y

- Substitute the value of y above in A

∵ A = x(60 - 2x)

- Multiply bracket by x

∴ A = 60x - 2x²

Now differentiate x with respect to x

∵ A' = 60(1) - 2(2)x

∴ A' = 60 - 4x

- Equate A' by 0 to find x

∴ 0 = 60 - 4x

- Add 4x to both sides

∴ 4x = 60

- Divide both sides by 4

∴ x = 15

- Substitute the value of x in the equation of y to find it

∵ y = 60 - 2(15)

∴ y = 30

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

To find the maximum area substitute x by 15 in the equation of the area

∵ A = 60(15) - 2(15)²

∴ A = 900 - 450

∴ A = 450

The maximum area is 450 feet²

Answer from: Quest

15.5

step-by-step explanation:

∑ $2^{n-2}$

n = 1

substitute n = 1, 2, 3, 4, 5 and sum the terms

= $2^{-1}$ + $2^{0}$ + $2^{1}$ + 2² + 2³

= 0.5 + 1 + 2 + 4 + 8

= 15.5

Which of the following is the result of expanding

Answer from: Quest

auto insurance

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Whats the name of the vertical axis

Answers: 2

Answer

Mathematics, 21.06.2019 18:00

Saline iv fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. a new supplier sells 500 ml bags for $2 each. the hospital uses about 10,000, 1000 ml bags each month. nurses report that about half of the bags are more than half full when they are discarded. if you are going to use only one supplier, which size bag provides the best deal, and how much will you save each month? compare the cost of the new supplier to the current one.

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Is the power produced directly proportional to the wind speed, give reasons for your answer?

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Someone answer this asap for gabriella uses the current exchange rate to write the function, h(x), where x is the number of u.s. dollars and h(x) is the number of euros, the european union currency. she checks the rate and finds that h(100) = 7.5. which statement best describes what h(100) = 75 signifies? a. gabriella averages 7.5 u.s. dollars for every 100 euros. b. gabriella averages 100 u.s. dollars for every 25 euros. c. gabriella can exchange 75 u.s. dollars for 100 euros. d. gabriella can exchange 100 u.s. dollars for 75 euros.

Answers: 1

Answer

You know the right answer?

Using the side of a building as one side and fencing for the other three sides, a rectangular garden...

Questions