Please help me with this problem, 35 points!
The four small circles are identical. The total area of the small circles is 16 pi square inches. What is area of the larger circle? Write your answer in terms of pi .
Answers
Answer:
64[tex]\pi[/tex] in²
Step-by-step explanation:
I did not ever do a problem like this, however this is the beauty of math, you can easily reverse engineer it.
Remember,
A = [tex]\pi r^2[/tex]
And if we have 4 circles that means the area of one circle is 1/4th the total
So,
[tex]A = \frac{\pi r^2}{4}[/tex]
Assuming that 16 is the radius squared times 4 lets ignore that squared for now because when going backwards we would get rid of the squared last as that was the first step.
[tex]A = \frac{16\pi}{4} = \frac{4\pi}{1}= 4\pi[/tex]
Now lets get it back to [tex]r^2[/tex] by square rooting the 4
[tex]A = \sqrt{4}\pi = 2\pi[/tex]
The radius of one small circle is 2. Therefore; the diameter would be 4 for each. This in mind we know that two small circles diameters make up the radius of the larger circle we will multiply it by two again.
This gives us a final radius of the bigger circle of 8
Therefore, the area of the bigger circle is 8²[tex]\pi[/tex] which simplifies to 64[tex]\pi[/tex]
And a final answer of
64[tex]\pi[/tex] in²
Hope this helps :)
The area of the larger circle is 64π in²
What is a circle?A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.
Given that, there are 4 identical circles inside a big circle, the total area of the small circles is 16π in²
We know that,
Area = π × radius²
16π = 4π × radius²
Therefore, the radius of each circle = 2 in
Now, according to the arrangement we can say that the adding the diameter of two small circles will give the radius of the big circle,
Therefore, the radius of the big circle = 4 + 4 = 8 in
Therefore, the area of the big circle = π × 8² = 64π
Hence, the area of the larger circle is 64π in²
Learn more about circles, click;
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
At an angle of elevation 610
captain on a ship noticed a person on the top of a cliff waiving towards the ship. To see him better, the captain moved his ship 92m closer to the cliff. The angle of elevation at that
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Answers
Answer:
The height of the cliff CD is approximately 539.76 m
Step-by-step explanation:
The given parameters are;
The first angle of elevation with which the captain sees the person on the cliff = 61°
The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°
The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°
∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Explanation:
Answer:
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Answers
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Answers
Answer:
18 gallons from container [tex]a[/tex] and 22 gallons from the container [tex]b[/tex] to be mixed to get the required mixture.
Step-by-step explanation:
Given that the container [tex]a[/tex] has 20% concentrated cleaner
and container [tex]b[/tex] has pure water which has 0% cleaner.
Let x gallons from container a and y gallons from the container b are mixed to get a 9% concentrated solution.
So,
[tex]9\%\; \text{of}\; (x+y) = (20\% \; \text{of}\; x )+(0\% \; \text{of}\; y)\cdots(i)[/tex]
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Using the value of equation (ii) in equation (i), we have
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[tex]\Rightarrow 0.09\times 40=0.2 \times x[/tex]
[tex]\Rightarrow x=\frac{0.09\times 40}{0.2}[/tex]
[tex]\Rightarrow x=18[/tex] gallons.
From equation (ii),
18+y=40
[tex]\Rightarrow y=40-18=22[/tex] gallons.
Hence, 18 gallons from container [tex]a[/tex] and 22 gallons from the container [tex]b[/tex] to be mixed to get the required mixture.
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2.257 x 9.111 = 20.563527 or 20
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Answer:
Pretty sure it is A.
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
sorry if wrong
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Answer:
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Step-by-step explanation:
At a baseball game, the stadium gave T-shirts to the first 100 fans to arrive. Each T-shirt cost $15.00. How much did the stadium pay for the T-shirts it gave away?
