All categories

3 years ago

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

Mathematics

2 answers:

vampirchik [111]3 years ago

7 0

Answer:

16.10 in2

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

16.10 in2

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.

You might be interested in

If you triple 4 and subtract 2 everyday

storchak [24]

It would be 6 days because if you triple 4 that s 12 and 2 goes into 12, 6 times

5 0

3 years ago

Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Wr

Y_Kistochka [10]

727.29 - 248.50 = 478.79

500-478.79 = 21.21

$21.21 is the least amount of money he needs to deposit

7 0

3 years ago

Read 2 more answers

The map shows the location of the mall, library, and school in the city; Brittany travels from the school to the mall and then f

Shkiper50 [21]

Answer:A) 8 miles

Step-by-step explanation:

8 miles

7 0

2 years ago

WILL MARK BRAINLIEST what is the domain of (f/g) (x)?

tatyana61 [14]

Given that $f(x) = \sqrt{7-x}$ and $g(x) = \sqrt{x + 2}$ , we can say the following:

$\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).

Thus, let's set what is under both square roots to be greater than 0:

$\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7$

$\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2$

Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

$x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}$

Now, let's look back at the function entirely, which is:

$\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Since $\sqrt{x + 2}$ is on the bottom of the fraction, we must say that $\sqrt{x + 2} \neq 0$ , since the denominator can't equal 0. Thus, we must exclude $\sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2$ from the domain.