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lions [1.4K]
3 years ago
12

Find the area of the shaded region. Round to the nearest tenth if necessary.

Mathematics
1 answer:
Ket [755]3 years ago
7 0
Find the area of the large circle, and subtract the areas of the three smaller circles.

Large circle: diameter = 22 cm; radius = 11 cm

A = pi r^2 = pi * (11 cm)^2 = 121pi cm^2

Circle with 7 cm radius:

A = pi r^2 = pi * (7 cm)^2 = 49pi cm^2

Two small circles:
The largest circle has diameter = 22 cm.
The next larger circle has radius = 7 cm, so diameter = 14 cm
22 cm - 14 cm = 8 cm
The two smallest circles have a sum of diameters = 8 cm
Each smallest diameter = 4 cm, so each smallest radius = 2 cm
A = pi r^2 = pi * (2 cm)^2 = 4pi cm^2 (for each of the smallest circles)

Shaded area = 121pi cm^2 - 49pi cm^2 - 4pi cm^2 - 4 pi cm^2

Shaded area = 64pi cm^2 = 64 * 3.14159... cm^2 = 201.0619... cm^2

Answer: The shaded area is 201.1 cm^2
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Cos(-170°) = _____<br><br> -cos10°<br> cos10°<br> cos(-10°)
ikadub [295]

<em>The right answer for:</em>

<em>cos(-170°) = _____</em>

<em>is:</em>

<em>-cos10°</em>

<h2>Explanation:</h2>

The cosine function is an even function, which means that for every point (x,y) on the graph of y=cos(x) then the point (-x,y) also lies on the graph of the function. In other words, we can write:

cos(-170^{\circ})=cos(170^{\circ})

But:

170^{\circ}=180^{\circ}-10^{\circ}

So:

cos(170^{\circ})=cos(180^{\circ}-10^{\circ})

By property:

cos(a-b)=cosacosb+sinasinb \\ \\ a=180^{\circ} \\ \\ b=10^{\circ} \\ \\ cos(170^{\circ} )=cos(180^{\circ} -10^{\circ})=cos180^{\circ} cos10^{\circ} +sin180^{\circ} sin10^{\circ} \\ \\  cos(170^{\circ})=-cos(10^{\circ})+0 \\ \\ \boxed{cos(170^{\circ})=-cos(10^{\circ})}

<h2>Learn more:</h2>

Trigonometric functions: brainly.com/question/2680050

#LearnWithBrainly

4 0
3 years ago
Solve 18n - 7p-15n = 5p for n.<br> A n = 1<br> B. n=2p<br> C. n = 1/2<br> D. n=4p
andrey2020 [161]

Answer:

<h3>The answer is option D</h3>

Step-by-step explanation:

18n - 7p-15n = 5p

To solve for n first make n the subject

Group like terms

That's

18n - 15n = 5p + 7p

Simplify

3n = 12p

Divide both sides by 3 to make n stand alone

That's

3n/3 = 12p/3

We have the final answer as

<h2>n = 4p</h2>

Hope this helps you

5 0
3 years ago
Read 2 more answers
4. Asia is designing a triangular-shaped window with a height of 15 inches and
Anni [7]

Answer:

18in

Step-by-step explanation:

Given data

Height h= 15 in

Area= 135 in^2

The expression for the area is given as

Area= 1/2 Base * Height

substitute

135= 1/2* Base*15

135= 7.5 Base

Base= 135/7.5

Base=  18 in

Hence the base is 18in

3 0
2 years ago
3x-2y=6<br><br> y=3/2x-3<br><br> Find the slope, x-intercept, and y-intercept for both equations.
lys-0071 [83]

The slope-intercept form: y = mx + b

m - slope

b - y-intercept

We have 3x - 2y = 6       <em>subtract 3x from both sides</em>

-2y = -3x + 6      <em>divide both sides by -2</em>

y = 3/2 x - 3

slope: m = 3/2

y-intercept: b = -3

x-intercept for y = 0. Substitute:

3/2 x - 3 = 0      <em>add 3 to both sides</em>

3/2 x = 3       <em>multiply both sides by 2/3</em>

x = 2

<h3>Answer:</h3><h3>slope = 3/2</h3><h3>y-intercept = -3</h3><h3>x-intercept = 2</h3>

----------------------------------------------------------------

y = 3/2 x - 3 it's the same function like first function.

8 0
3 years ago
An actúe triangle has sides that are 14 mm and 97 mm long, respectively the third side of the triangle must be greater than what
marshall27 [118]
It has to be greater than the difference between the two sides, so 97-14=83
8 0
3 years ago
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