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Brilliant_brown [7]
3 years ago
11

Find area of the shaded region.

Mathematics
1 answer:
Monica [59]3 years ago
6 0

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}

Now, we can find the area of the triangle. We can use an alternative formula:

\displaystyle A=\frac{1}{2}ab\sin(C)

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)

The area of the shaded region is equivalent to the sector minus the triangle:

A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}

Therefore:

A_{\text{shaded}}=15\pi -18\sin(150)

Use a calculator:

A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2

The area of the shaded region is about 38.1 square centimeters.

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we have given that the incident cases of MI diagnosed in the emergency rooms of several hospitals is 500 and compared to 1,000 other subjects who visited the same emergency rooms for reasons other than cardiovascular and respiratory diseases.

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So, The option B is a correct option. The Study design is used is a Case control study.

Learn more about Case control study here

brainly.com/question/24087096

Disclaimer: This question was incomplete. Please find the full content below.

Question:

The effect of exposure to high-density automobile traffic either as a bicyclist or pedestrian was compared to minimal or no exposure to automobile traffic. It is hypothesized that direct exposure to automobile traffic has an effect on acute myocardial infarction (MI). This association was studied with 500 incident cases of MI diagnosed in the emergency rooms of several hospitals and compared to 1,000 other subjects who visited the same emergency rooms for reasons other than cardiovascular and respiratory diseases. All subjects were asked to report the amount of time that they spent exposed to high-density traffic over the past month prior to their hospital visit.

What type of study design is this?

A) Cross-sectional

B) Case-control

C) Retrospective cohort

D) Prospective cohort

E) Randomized clinical trial

#SPJ4

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