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olga nikolaevna [1]
2 years ago
14

You need to construct fence around an area of 3136 ft2. What are the dimensions of the rectangular pen that minimize the amount

of material needed
Mathematics
1 answer:
borishaifa [10]2 years ago
7 0

Answer:

Step-by-step explanation:

The the area of the rectangular pen be A = LW

L is the length

W is the width

Given

A = 3136ft²

3136 = LW..........1

Given the perimeter P = 2L+2W....... 2

From 1; L = 3136/W

Substitute into 2

P = 2(3136/W)+2W

P = 6272/W + 2W

In order to minimize the amount of material needed, then dP/dW = 0

dP/dW = -6272/W² + 2

0 = -6272/W² + 2

6272/W² = 2

cross multiply

6272 = 2W²

W² = 3136

W = √3136

W = 56ft

Since A = LW

3136 = 56L

L = 3136/56

L = 56ft

Hence the dimensions of the rectangular pen that minimize the amount of material needed is 56ft by 56ft

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Answer:

time taken to walk one mile × total distance in miles = total time

t × 4 = 40

Step-by-step explanation:

3 0
3 years ago
Find the distance between points.
SashulF [63]

Answer:

3 units

Step-by-step explanation:

Here, The distance between two points is 3 units

<u>-TheUnknownScientist</u>

4 0
3 years ago
What is the LCM of two numbers that have no common factors greater than 1?
anyanavicka [17]
This question was already answered before. I'm going to post someone else's answer with credit given of course:

"<span>The answer is their product. The least common multiple (LCM) is the smallest number which is a multiple of two numbers. If two numbers have no common factors greater than 1, then their LCM will be their product. For example, take numbers 7 and 9. They have none common factor greater than 1. So, LCM will be 7 * 9 = 63." - @W0lf93

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5 0
2 years ago
Read 2 more answers
The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 25 meters. Around the pe
erik [133]
<h3>Answer:   4w^2+190w</h3>

================================================

Explanation:

Check out the attached image below. Specifically, take a look at figure 1. We start with a rectangle which is 70 meters by 25 meters. Then we extend this rectangle out by adding two copies of w to each dimension having the larger rectangle be (70+2w) meters by (25+2w) meters.

The original smaller rectangle has area of 70*25 = 1750 square meters.

The new larger rectangle area is a bit more tricky to figure out, though its not too bad once you get the hang of it. You could use the FOIL rule to get

(70+2w)(25+2w) = 70*25+70*2w+2w*25+2w*2w

(70+2w)(25+2w) = 1750+140w+50w+4w^2

(70+2w)(25+2w) = 1750+190w+4w^2

(70+2w)(25+2w) = 4w^2+190w+1750

Or you could use the box method shown in figure 2.

The idea is to write the terms of (70+2w) and (25+2w) along the edges of the box. Then filling out the 4 inner boxes involves multiplying the outer terms. Example: row1,column2 has 50w inside it because we multiply the outer terms 25 and 2w to get 25*2w = 50w. The other boxes are filled out in a similar fashion.

Although the FOIL rule is handy and taught in a lot of math books/classes, I prefer the box method because the box method can be extended to other cases (not just multiplying two binomials).

Whichever method you use, the larger rectangle has area 4w^2+190w+1750 square meters.

-------------------------------

So,

A = area of larger rectangle = 4w^2+190w+1750

B = area of smaller rectangle = 1750

C = difference in areas of A and B

C = A - B

C = ( A ) - ( B )

C = ( 4w^2+190w+1750 ) - ( 1750 )

C = 4w^2+190w+1750-1750

C = 4w^2+190w

This represents the area of just the tile border alone. We started with the larger rectangle and took out the smaller rectangle inside to only have the border left over.

-------------------------------

If you want, you can factor out a 'w' to get

4w^2+190w = w(4w+190)

Though this may be optional.

8 0
3 years ago
Ashley is packing her bags for her vacation. She has 7 unique socks, but only 3 fit in her bag.
IrinaVladis [17]

Answer:

There are 35 possible group of 3 socks from a total of 7

Step-by-step explanation:

Given

Number of unique socks = 7

Number of possible selection = 3

Required

Number of ways she can make her selection.

The question can be categorised as combination; reason being that words like "take" as used in the question points to combination or selection.

To solve this, we make use of combination formula.

nCr = nPr/r!

Where n = 7 and r = 3

By substitution, we have

7C3 = 7P3÷3!

Taking it one at a time

7P3 = 7!÷(7-3)!

7P3 = 7! ÷ 4!

7P3 = 7 * 6 * 5 * 4! ÷ 4!

7P3 = 7 * 6 * 5

7P3 = 210

3! = 3 * 2 * 1

3! = 6.

So,

7C3 = 210 ÷ 6

7C3 = 35.

Hence, there are 35 possible group of 3 socks from a total of 7

5 0
3 years ago
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