Answer:
The answer to your question is a) C + J + S = 80
b) C = J + 5
c) S = 45 hours
Step-by-step explanation:
a) To represent the number of hours that they work together, just add the variables and equal them to 80.
Carlito + Juan + Sara = 80
C + J + S = 80 Equation l
b) Juan worked 5 hours more than Carlito
Juan = Carlito + 5
J = C + 5 Equation ll
c) Hours worked by Sara
S = 3J Equation lll
C = J - 5
Substitute equation ll and lll in equation l to find J
J - 5 + J + 3J = 80
5J = 80 - 5
5J = 75
J = 75/5
J = 15
-Find S
S = 3(15)
S = 45 hours
Tan 2 x-2 tan x=0
Tan x (tan x-2 ) =0
A tan x=0 —> x=0 and x =K π
B tan x=2 —> x=63.43 +k180 deg
Answer:
Step by step Explanation:
![\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BPerpendicular%7D%20%7D%7B%5Ctext%7BHypotenuse%7D%7D%20%3D%20%5Cdfrac%7B12%7D%7B15%7D%5C%5C%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BBase%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%20%5Cdfrac%7B9%7D%7B15%7D%5C%5C%5C%5C%5Ctext%7BNow%2C%7D%5C%5C%5C%5C%5Ctan%20%5Cdfrac%7B%5Ctheta%7D2%20%3D%20%5Cdfrac%7B%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%7D%7B%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%7D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cdfrac%7B2%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%20%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%20%7D%7B2%5Ccos%5E2%20%5Ctfrac%7B%5Ctheta%7D2%7D~~~~~~%3B%5Cleft%5B%5Ctext%7BMultiply%20by%7D~%202%5Ccos%5Ctfrac%7B%5Ctheta%7D2%20%5Cright%5D)
![=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Csin%20%5Ctheta%7D%7B1%2B%20%5Ccos%20%5Ctheta%7D~~~~~~~~~~~~%3B%5B2%20%5Csin%20x%20%5Ccos%20x%20%3D%20%5Csin%202x%20~%20%5Ctext%7Band%7D~%202%5Ccos%5E2%20x%20%3D1%2B%5Ccos%202x%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B1%2B%20%5Ctfrac%7B9%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B%5Ctfrac%7B24%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B15%7D%5Ctimes%20%5Cdfrac%7B15%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D2)
The answer should be
x = 7 or just 7
Hope it helped !!
