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3 years ago

Divide 42 in a ratio of 1:2:3?

1 answer:

6 0

Ratio 1:2:3 means we have x, 2x and 3x as the three parts

x+2x+3x = 42
6x = 42
6x/6 = 42/6
x = 7

Since x = 7, this means 2x = 2*7 = 14 and 3x = 3*7 = 21

Dividing 42 into the ratio of 1:2:3 means we have 7:14:21 as the answer

If we divide all three parts of 7:14:21 by the GCF 7, we reduce it down to 1:2:3

As a check,
7+14+21 = 21+21 = 42
so it works out

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How to prove this???

swat32

$\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
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go to right side now

$4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)$

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$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A) \\
\Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A)$

so $\sin^2 A + \cos^2 A = 1$

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