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kondaur [170]
3 years ago
12

Given two central angles in any two circles, the ratio of the arc length to the radius of each corresponding circle is equal if

and only if each central angle is equal. That is, given central angle θ1 degrees with arc length s1 in a circle of radius r1 and central angle θ2 degrees with arc length s2 in a circle of radius r2, then s1/r1=s2/r2 if and only if θ1 = θ2. Prove the above theorem using the fact that the ratio of an arc length over the circumference of a circle is the same as the ratio of its central angle (in degrees) over 360 degrees. Hint: First write the above proportion for each circle. Then apply it to s1/r1=s2/r2 and conclude that θ1 = θ2.
Mathematics
1 answer:
krok68 [10]3 years ago
6 0
First, we have
s1/r1 = s2/r2

The question also states the fact that
s/2πr = θ/360°

Rearranging the second equation, we have 
s/r = 2πθ/360°

Then we substitute it to the first equation
s1/r1 = 2πθ1/360°
s2/r2 = 2πθ2/360°

which is now 
2πθ1/360° = 2πθ2/360°

By equating both sides, 2π and 360° will be cancelled, therefore leaving 
θ1 = θ2
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Rina8888 [55]
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combine like terms
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This can be factored/simplified by dividing everything by 7
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6 0
3 years ago
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tekilochka [14]

Answer:

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Step-by-step explanation:

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=> 5x + y + 48 = 0

4 0
3 years ago
What is the result of adding these two equations?
timofeeve [1]

Answer:

the result of adding these two equations is

3x = 14

Step-by-step explanation:

We are given two equations

5x − y  = 6          eq. 1

−2x + y = 8        eq. 2

Add the like terms together

5x - 2x = 3x

− y + y = 0

6 + 8 = 14

So the result of adding these equations is

3x + 0 = 14

3x = 14

Bonus:

The value of x is

3x = 14

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6 0
3 years ago
Line j passes through points 1,6 and 7,1 line k is parallel to line j. What is the slope of line k?
Mashutka [201]
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m = -5 / 6

Slope or parallel lines are the same
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6 0
2 years ago
IN
ycow [4]

Answer:

45 pages in 1 hour

Step-by-step explanation:

Find the unit rate by dividing the number of pages by the number of hours

135/3

= 45

This means he can read 45 pages in 1 hour.

The unit rate is 45 pages in 1 hour.

8 0
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