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suter [353]
3 years ago
8

Find the distance between the two points. (−2, −5), (3, 5)

Mathematics
1 answer:
IrinaVladis [17]3 years ago
8 0
The distance between the points is 5.
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Find area of the shaded region.
Monica [59]

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.

6 0
2 years ago
Find the perpendicular distance from the pointp(6, 4, 2)to the xy-plane.
Stells [14]

, 4, 2)to the xy............................................

7 0
2 years ago
Polly decides to cut the extra-large pizza into 12 equal slices, how much of the pizza is 2 slices in decimal form?
svlad2 [7]

Answer: 0.5

Step-by-step explanation:

5 0
2 years ago
This is hard i need help
taurus [48]

Answer:

a. 6  b. -2

Step-by-step explanation:

a. x^3 = 216

x = ³√216

x = 6

b. -n^3/4 = 2

-n^3 = 8

-n = ³√8

- n = 2

n = -2

3 0
2 years ago
Read 2 more answers
What is the surface area of the figure shown above
gtnhenbr [62]

Answer:

  230 cm^2

Step-by-step explanation:

The area of each parallelogram face is ...

  A = bh = (8 cm)(3 cm) = 24 cm^2

The area of the two rectangular faces shown is ...

  A = (area of top face) + (area of right side face)

  A = (8 cm)(7 cm) +(5 cm)(7 cm) = 91 cm^2

The three faces we have figured the area of are half the total area, since there are three more faces exactly the same size. Then the total area of the figure is ...

  total surface area = 2(24 cm^2 +91 cm^2) = 230 cm^2

_____

Of course, the area of a rectangle is given by A=L·W, where L and W represent the length and width of the rectangle.

7 0
3 years ago
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