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Zolol [24]
3 years ago
5

Find the area created by the overlapping circles given the following information.

Mathematics
2 answers:
vampirchik [111]3 years ago
7 0

Answer:

<u><em>16.10 in2</em></u>

Step-by-step explanation:

Find the area created by the overlapping circles given the following information.

Circle A: radius = 6in and m∠CAD = 90°

Circle B: radius = 8in and m∠CBD = 60°

Round your answer to the nearest hundredth if necessary.

5.83 in2

10.27 in2

<u><em>16.10 in2</em></u>

27.68 in2

Odyssey

lara31 [8.8K]3 years ago
5 0

The area of a circular sector of central angle α (in radians) in a circle of radius r is given by

... A = (1/2)r²×(α - sin(α))


Your area is expected to be computed as the sum of the areas of a sector with angle π/3 in a circle of radius 8 and a sector with angle π/2 in a circle of radius 6.


... A = (1/2)8²×(π/3 - sin(π/3)) + (1/2)6²×(π/2 - sin(π/2))

... A ≈ 16.07


Radii are in inches so the units of area will be in². The appropriate choice is

... 16.10 in²


_____

It should be noted that the geometry described is impossible. Chord CD of circle A will have length 6√2 ≈ 8.4853 inches. Chord CD of circle B will have length 8 inches. They cannot both be the same chord.

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weqwewe [10]
Take x-2 and insert it into 2x^2 + 3x-2 where the x is located 
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2(x-2)^2 + 3(x-2)-2

Now work out 2(x-2)^2 + 3(x-2)-2 also follow PEMDAS
2(x-2)^2 + 3(x-2)-2 
Since (x-2)^2 is an Exponent, lets work with that first and expand (x-2)^2.
(x-2)^2
(x -2)(x-2)
x^2 -4x + 4
Now Multiply that by 2 because we have that in 2(x-2)^2
(x-2)^2  =  x^2 -4x + 4
2(x-2)^2  =  2(x^2 -4x + 4)
2(x^2 -4x + 4) = 2x^2 - 8x + 8
2x^2 - 8x + 8

Now that 2(x-2)^2 is done lets move on to 3(x-2).

Use the distributive property and distribute the 3
3(x-2) = 3x - 6

All that is left is the -2 

Now lets put it all together 
2(x-2)^2 + 3(x-2)-2

2x^2 - 8x + 8 + 3x - 6 - 2

Now combine all our like terms 
2x^2 - 8x + 8 + 3x - 6 - 2
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5 0
3 years ago
Solve for c: c - 12 = 3
vlabodo [156]

Steps to solve:

c - 12 = 3

~Add 12 to both sides

c = 15

Best of Luck!

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3 years ago
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The sum of three consecutive even integers is 126. Let x represent the first integer, x + 2 represent the second integer, and x
LekaFEV [45]
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3x + 6 = 126
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3 years ago
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Ben consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Ben's body decr
Airida [17]

Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

A(t) = A(0)e^{-kt}

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, A(10) = 0.7278A(0). We use this to find k.

A(t) = A(0)e^{-kt}

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e^{-10k} = 0.7278

\ln{e^{-10k}} = \ln{0.7278}

-10k = \ln{0.7278}

k = -\frac{\ln{0.7278}}{10}

k = 0.03177289938&#10;

Then

A(t) = A(0)e^{-0.03177289938t}

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

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1 - 0.8531 = 0.1469

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7 0
3 years ago
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