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navik [9.2K]
3 years ago
6

The value of the 4 in 34,258 and 47,163

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
7 0
The value of 4 in 34,258 is 10 times the value of the 4 in 47,163.
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Step-by-step explanation:

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In circle o, the length of radius OL is 6 cm and the length
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Answer:

14.2cm

Step-by-step explanation:

The diagram representing the circle and its attributes has been attached to this response.

<em>As shown in the diagram;</em>

The circle is centered at o,

The length of radius OL = 6cm

The length of the arc LM = 6.3cm

The angle MON = 75°

The angle LOM = θ

<em>Remember that;</em>

The length, L, of an arc is given by;

L = (θ / 360) x (2πr)         -------------(i)

Where;

θ is the angle subtended by the arc

r = radius of the circle.

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L = (θ / 360) x (2πr)  

Where;

L = length of arc LM = 6.3cm

r = radius of the circle = length of radius OL = 6cm

<em>Substitute these values into the equation to get;</em>

6.3 = (θ / 360) x (2 x π x 6)

6.3 = (θ / 360) x (12 x π)

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6.3 = (θ / 30) x (22 / 7)

θ = \frac{6.3*30*7}{22}

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Therefore, the angle subtended by arc LM is 60.14°

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The angle subtended by arc LMN is;

θ + 75° = 60.14° + 75° =  135.14°

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L = (θ / 360) x (2πr)  

Where;

L = length of arc LMN

θ = angle subtended by LMN = 135.14°

r = radius of the circle = length of radius OL = 6cm

<em>Substitute these values into the equation;</em>

L = (135.14° / 360°) x (2 x π x 6)             [Take π = 22/7]

L = 14.15cm

Therefore, the length of arc LMN is 14.2cm to the nearest tenth.

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