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AfilCa [17]
3 years ago
10

Geoff wants to purchase a circular area rug for his room, but he can't decide between the small size and the large size. A small

rug covers an area of approximately 67 square feet. If a large size rug has twice the dimensions of a small rug, how many times larger is the large rug?
Mathematics
1 answer:
salantis [7]3 years ago
7 0

Answer: The larger rug is 4 times larger

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

The small circular rug covers an area of approximately 67 square feet. This means that

67 = πr²

r² = 67/π = 67/3.14 = 21.34

r = √21.34 = 4.62

If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be

2 × 4.62 = 9.24

The area of the larger rug would be

3.14 × 9.24² = 268.06ft²

Therefore

268.06/67 = 4

The larger rug is 4 times larger

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490 divided by 35 equals 14. It would take Jack 14 minutes to write a 490 word essay.
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3 years ago
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1. The difference of two numbers is 3, and the sum of three times the larger one and
vlada-n [284]

Answer: 25 and 22

Step-by-step explanation:

Since one number is 3 bigger than the other, we can call them x, and x-3.

Then we know that the sum of 3 times x and 2 times (x-3) is equal to 19, so we can make the equation

3x+2(x-3)=19

Simplifying would get you

3x+2x-6=19

adding the x's and adding six to both sides of the equations gets you

5x = 25

divide by 5 and

x=5

Put those numbers back into your previous labels for them, x and x-3, and you get 5 and 2

Hope this helps

5 0
3 years ago
There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).
hjlf

Answer:

The maximum area is therefore is 93750 ft²

Step-by-step explanation:

The given parameter are;

The a]length of fencing available = 1500 ft.

The perimeter of the figure = 9·x + 4·y

Therefore, 9·x + 4·y = 1500 ft.

The area of the figure = 6 × (x × y) = 3·x × 2·y

From the equation for the perimeter, we have;

9·x + 4·y = 1500

y = 1500/4 - 9/4·x = 375 - 9/4·x

y = 375 - 9/4·x

Substituting the value of y in the equation for the area gives;

Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²

Area = 2250·x - 27/2·x²

The maximum area is found by taking the derivative and equating to zero as follows;

d(2250·x - 27/2·x²)/dx = 0

2250 - 27·x = 0

x = 2250/27 = 250/3

x = 250/3

y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5

The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²

The maximum area is therefore = 93750 ft.²

4 0
3 years ago
If the radius of a circle is 11 cm, what is the area of the circle?
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4 0
3 years ago
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One year, Mr James travels 8 x 10^3 miles for his job. The next year he traveled 1 x 10^4 miles. How many more miles did he trav
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Answer:

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Step-by-step explanation:

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Let's assume that Mr James conveys himself to his place of work all through the first year in his private car. But in the second year, there were some days in which the car was not available. So he had to go for his job by public transportation. This itch during those days, could cause an increase in the distance covered from his home to his place of work for the second year.

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3 years ago
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