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suter [353]
3 years ago
6

One number is four times another number and their difference is 24. find the number.

Mathematics
1 answer:
Flura [38]3 years ago
3 0
8 and 32.

8 times 4 = 32
32 - 8 = 24

4x - x = 24.
 ^    ^
1     2
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I don't need you to work it out, just theorem(s) i need to reach the answer :)
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Not sure why such an old question is showing up on my feed...

Anyway, let x=\tan^{-1}\dfrac43 and y=\sin^{-1}\dfrac35. Then we want to find the exact value of \cos(x-y).

Use the angle difference identity:

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Meanwhile, if \tan x=\dfrac43, then (by Pythagorean theorem) \sec x=\dfrac53, so \cos x=\dfrac35. And from this, \sin x=\dfrac45.

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