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gizmo_the_mogwai [7]
2 years ago
15

A circular garden is enlarged so that the new diameter is twice the old diameter. What is the ratio of the original area to the

enlarged area? Express your answer as a common fraction.
I do not understand WHY the answer is 1/4 I do not understand why it is k^2 and all that. HELP I am giving LOTS of points
Mathematics
2 answers:
Amanda [17]2 years ago
7 0

Answer:

  • Explained briefly below.

Step-by-step explanation:

<u>For old circular garden:</u>

take the radius as r.

then use the formula to find area of circle: πr² ......this is old garden area.

<u>For new enlarged garden:</u>

the radius is twice the old radius so, radius = 2 * r = 2r ......enlarged radius

now find area for this new garden:  π(2r)² → 4πr²

In common fractions: (old garden)/(new garden)

                                : ( πr² ) / ( 4πr² )

                                 :    1/4

bonufazy [111]2 years ago
4 0

Answer:

  • 1/4

Step-by-step explanation:

<u>Original diameter is d and new diameter is D and:</u>

  • D = 2d

<u>Area of original circle:</u>

  • A₁ = πd²/4

<u>Area of enlarged circle:</u>

  • A₂ = πD²/4 = π(2d)²/4 = πd²

<u>The ratio of areas:</u>

  • A₁ / A₂ =
  • πd²/4 ÷ πd² =
  • 1/4 ÷ 1 =
  • 1/4
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Step-by-step explanation:

We use

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Now we have

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Hope that useful for you

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7 0
3 years ago
18 and 19 please ;D!!
frosja888 [35]

Answer:

18.

∠2 = 40

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∠4 =140

19.

∠1 = 134

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Step-by-step explanation:

18. Using vertical angle theorem, 1 is equal to 2 and 3 is equal to 4. Therefore 2 is equal to 40 degrees. Then since 2 and 3 are supplementary adjacent angles or a linear pair, they equal 180 when combined. 180-40 equals 140. 3 and 4 are also vertical angles so 3 = 4 and they are both 140.

19. Angles 1 & 3 and 2 & 4 are vertical angles because they are directly across from each other and share the same bisectors. You can use what you know about special angle pairs to find the measure of each angle because since 1 & 3 are vertical angles and 2 & 4 are also vertical angles, 1 is equal to 3 and 2 is equal to 4. So, since the angle formed at the right is angle 2, we can confirm that angle 4 is equal to it and therefore angles 2 and 4  are 46 degrees. Then since angles 1 & 2 and 3 & 4 are linear pairs, we can say that angle 1 + angle 2 is equal to 180 and the same for angles 3 & 4. So subtract 180 - 46 and you get 134. Therefore angles 1 and 3 are equal to 134 degrees.

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3 years ago
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