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Alchen [17]
3 years ago
7

llean works as a welder in web designer as a welder she earns $18 per hour last week she works x hours as a wlder and her Fran p

aid her $75 to design a webpage.write an expression to represent the total amount llean earned last week
Mathematics
1 answer:
melamori03 [73]3 years ago
5 0
18 times x = $75

I wasn’t able to find the multiplication sign on my keyboard and didn’t want to confuse you so I replaced x with times
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I don't need you to work it out, just theorem(s) i need to reach the answer :)
VikaD [51]
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:

\cos(x-y)=\cos x\cos y+\sin x\sin y

and right away we find \sin y=\dfrac35. By the Pythagorean theorem, we also find \cos y=\dfrac45. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

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

So,

\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}
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