Not sure why such an old question is showing up on my feed...
Anyway, let
![x=\tan^{-1}\dfrac43](https://tex.z-dn.net/?f=x%3D%5Ctan%5E%7B-1%7D%5Cdfrac43)
and
![y=\sin^{-1}\dfrac35](https://tex.z-dn.net/?f=y%3D%5Csin%5E%7B-1%7D%5Cdfrac35)
. Then we want to find the exact value of
![\cos(x-y)](https://tex.z-dn.net/?f=%5Ccos%28x-y%29)
.
Use the angle difference identity:
![\cos(x-y)=\cos x\cos y+\sin x\sin y](https://tex.z-dn.net/?f=%5Ccos%28x-y%29%3D%5Ccos%20x%5Ccos%20y%2B%5Csin%20x%5Csin%20y)
and right away we find
![\sin y=\dfrac35](https://tex.z-dn.net/?f=%5Csin%20y%3D%5Cdfrac35)
. By the Pythagorean theorem, we also find
![\cos y=\dfrac45](https://tex.z-dn.net/?f=%5Ccos%20y%3D%5Cdfrac45)
. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
Meanwhile, if
![\tan x=\dfrac43](https://tex.z-dn.net/?f=%5Ctan%20x%3D%5Cdfrac43)
, then (by Pythagorean theorem)
![\sec x=\dfrac53](https://tex.z-dn.net/?f=%5Csec%20x%3D%5Cdfrac53)
, so
![\cos x=\dfrac35](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cdfrac35)
. And from this,
![\sin x=\dfrac45](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cdfrac45)
.
So,
Answer:
216
Step-by-step explanation:
A=2(wl+hl+hw)=2·(12·2+6·2+6·12)=216
I’m sorry if I’m wrong but I do think your answer is X=22y^-1
If we add 8 oz of glycol to the 40 oz mixture we have 48 oz of mixture and 4+8 = 12 oz glycol
12 / 48 = 1/4 = 25 % glycol
the answer is 8 oz