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Katen [24]
2 years ago
6

An interior design working with a computer program decreases the radius of a circular rug by 10%. By what percent does the area

of the circular rug decrease?
Please give an explanation on how to solve this problem, thanks!
Mathematics
1 answer:
Akimi4 [234]2 years ago
6 0

Answer:

The decrease is 21%

Step-by-step explanation:

So lets say the Original area is Pi X (Radius^2)

Lets call Radius as R

For the new radius, it would be: R + 0.1R which is 1.1R

The new area is: Pi X 1.1R^2, which going further is 1.21 after squaring 1.1.

The Original area is: Pi X Radius^2

To find the percent decrease, subtract the new area by the original, cross out Pi X Radius squared and you are only left with 21%

I am in middle school so I don't know if it is going to be incorrect, but I ask you to give it a try and tell me if it was right or not. I have barely done this topic but recently I had a bonus homework question on a question almost exactly like this and this is the way I did it and I was correct. Thanks! Hope it helped! :)

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Answer:

x = ±25

General Formulas and Concepts:

<u>Pre-Algebra</u>

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Equality Properties

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Step-by-step explanation:

<u>Step 1: Define</u>

x² = 625

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Square root both sides:                    x = ±25

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

x = -25

  1. Substitute in <em>x</em>:                    (-25)² = 625
  2. Exponents:                          625 = 625

Here we see that 625 does indeed equal 625.

∴ x = -25 is a solution to the equation.

x = 25

  1. Substitute in <em>x</em>:                    25² = 625
  2. Exponents:                          625 = 625

Here we see that 625 does indeed equal 625.

∴ x = 25 is a solution to the equation.

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