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lesya692 [45]
2 years ago
11

You have 100 feet of fencing and decide to make a rectangular garden. What is the largest area enclosed

Mathematics
1 answer:
k0ka [10]2 years ago
3 0

Answer:

625 ft^2

Step-by-step explanation:

Given

P = 100 --- perimeter

Required

The largest area

The perimeter is calculated as:

P = 2 * ( L + W)

So, we have:

2 * ( L + W) = 100

Divide both sides by 2

L + W  = 50

Make  L the subject

L = 50 - W

The area is calculated as:

A= L * W

Substitute L = 50 - W

A= (50 - W) * W

Open bracket

A = 50W - W^2

Differentiate with respect to W

A' = 50 -2W

Set to 0; to get the maximum value of W

50 - 2W = 0

Collect like terms

-2W = -50

Divide by -2

W = 25

So, the maximum area is:

A = 50W - W^2

A = 50 * 25 - 25^2

A = 1250 - 625

A = 625

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Step-by-step explanation:

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3 0
2 years ago
Mrs. Chen's students are making and decorating gift boxes for a nursing home. If the boxes are 7 inches wide, 7 inches long, and
pishuonlain [190]

Answer:

84\text{ in}^2.

Step-by-step explanation:

We have been given that  Mrs. Chen's students are making and decorating gift boxes for a nursing home. The boxes are 7 inches wide, 7 inches long, and 7 inches high. We are asked to find the amount of cardboard that is needed for each box.

We will use surface area of cuboid formula to solve our given problem.

SA=2(lw+lh+hw), where,

l = Length,

w = Width,

h = Height

SA=2(7\text{ in}\cdot7\text{ in} +7\text{ in}\cdot7\text{ in}+7\text{ in}\cdot7\text{ in})

SA=2(14\text{ in}^2+14\text{ in}^2+14\text{ in}^2)

SA=2(42\text{ in}^2)

SA=84\text{ in}^2

Therefore, Mrs Chen needs 84 square inches of cardboard.

3 0
3 years ago
Pls help i’m failing rn
Valentin [98]

Answer:

The answer is letter D.

Step-by-step explanation:

-2(4x+8)+3(5x-1)

=-8x-16+15x-3

=-8x+15x-16-3

=7x-19

4 0
3 years ago
What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?
11111nata11111 [884]
Since the sequence is arithmetic, we have an expression of the form:
 an = a1 + d (n-1)&#10;
 Where,
 a1: first term of the sequence
 d: common difference
 n: number of terms
 We look for the common difference:
 d = 22-15 = 15-8 = 7&#10;&#10;d = 7
 Then, setting values we have:
 a26 = 8 + 7 * (26-1)&#10;&#10;a26 = 183&#10;
 Then, the sum of the terms is:
 Sn = ((a1 + an) / (2)) * n&#10;
 Substituting values:
 Sn = ((8 + 183) / (2)) * 26&#10;&#10;Sn = 2483
 Answer:
 
the sum of the arithmetic sequence 8, 15, 22 is:
 
Sn = 2483
5 0
3 years ago
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