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Svetlanka [38]
3 years ago
6

Find the area of the shaded part of the figure. Will mark brainliest! 15 pts

Mathematics
2 answers:
Leona [35]3 years ago
8 0

Answer:25sqrt3-25pi/3

Step-by-step explanation:

Assuming the triangle is equilateral, we clearly need to find the radius of the circle, and subtract from the entire area of the triangle.

First, the area of an equilaterail triangle is given by the formula s^2 *sqrt3/4.

Next, the connect the center of the radius to points of tangency. Note this bisects the angle of the equilateral triangle into a 30 degree angle, and connecting radii to points of tangency forms a 90 degree angle, so this is a 30-60-90 triangle. This bisects the side length of the triangle, and the ratio of sides of a 30-60-90. Set this length as x. Thus, we have 4x^2=x^2+25, so 3x^2 =25. Dividing both sides by 3, we get x^2=25/3. Note that we only need x^2, as the formula is x^2 * pi. Hence, the area of the shaded region is 25sqrt3-25pi/3.

Luba_88 [7]3 years ago
8 0

Answer:

39.13 units²

Step-by-step explanation:

Height of the triangle:

10cos(30) = 5sqrt(3)

Radius = ⅓(5sqrt(3)) = 5sqrt(3)/3

Triangle - circle

[½(10)(10)sin60] - [(3.14)(5sqrt(3)/3)²]

43.30127019 - 4.166667

39.13460352 unitsw

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9. Write the equation in standard form: 25x2 –16y2 = 400
mafiozo [28]

Answer:

25x^2 - 16y^2 - 400 = 0

Step-by-step explanation:

8 0
2 years ago
What is the y-value of sin(x) when x= -180°?
Andreyy89

In trigonometry, we start from the point (1,0), so this is the 0-degree point. Then, we start rotating counter clockwise along the unit circle.

Note that rotating 180 or -180 degrees is actually the same, because you travel half the circumference clockwise or counter clockwise. In both cases, you start from the rightmost point of the circle, (1,0), and arrive at the leftmost point, (-1,0).

Now, for every point (x,y) on the unit circle, given by a certain angle \alpha, we have

\cos(\alpha)=x,\quad \sin(\alpha)=y

So, in this case, the angle of -180 is associated with the point (-1,0), and thus we have

\sin(-180)=0

8 0
3 years ago
What is the graph of 3x + 5y = –15? Image for option 1 Image for option 2 Image for option 3 Image for option 4
saveliy_v [14]
Move x
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y = - 3 - 3/5x
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6 0
2 years ago
(x/16)-(x+2)/8))=2<br><br><br><br> PLS HELP ME BRAINLIEST TO THE FIRST CORRECT ANSWER
ArbitrLikvidat [17]

Simplify both sides of the equation

x/16−(x+2/8) = 2x/16 + −1/8x + −1/4 = 2

Distribute

1/16x + −1/8x + −1/4 = 2

(1/16x + −1/8x)+(−1/4) = 2

Combine Like Terms

−1/16x + −1/4 = 2

Add 1/4 to both sides.

−1/16x + −1/4 + 1/4 = 2 + 1/4

−1/16x = 9/4

Multiply both sides by 16/(-1).

(16/−1)*(−1/16x)=(16/−1)*(9/4)

x=−36

3 0
2 years ago
Evaluate f(x) = -4x - 5 for x = -1. <br><br> A. -9<br> B. -1<br> C. 1<br> D. 4
Nadusha1986 [10]
F(x) = -4x - 5

Subtitute the value of x to the equation:

f(-1) = -4 · (-1) - 5 = 4 - 5 = -1
7 0
3 years ago
Read 2 more answers
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