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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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Anika [276]

Answer:

<u><em>1: "An equilateral triangle is never an obtuse triangle" & "An equilateral triangle is never an isosceles triangle." </em></u>

<u><em> </em></u>

<u><em>2: Acute Isosceles Triangle </em></u>

<u><em> </em></u>

<u><em>3: False! Option B. </em></u>

<u><em> </em></u>

<u><em>4: D</em></u>

Step-by-step explanation:

2: Isosceles Triangles have two equal sides. An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles.

3: An <u>equilateral triangle</u> is a triangle in which all the sides and all the angles are equal.

4: In order for a triangle to be <u>isosceles</u>, it has to have two same sides. For a triangle to be <u>equilateral</u>, all sides and angles need to be the same. Refer to reasoning in Question 2 for next explanation.

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2 years ago
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Answer:

Height of shuttle at that instant  = 1.17 miles

Step-by-step explanation:

Refer the given figure.

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Step-by-step explanation:

Let the angle near point A be A.

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Answer: 1.645

Step-by-step explanation:

Given : The quality control manager of a soda manufacturing company wishes to use a significant level of 0.05 to test whether the variabilities in the amount of soda in the company's 16 OZ bottles is more than the variabilities in the company's 12 OZ bottles.

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