3 days they with both have 4 dollars
Answer:
.14
Step-by-step explanation:
Answer:
unclear man, u cant add them together sorry
Step-by-step explanation:
Double angle (or half angle, depending how you look at it) identities:
![\cos^2\dfrac x2=\dfrac{1+\cos x}2](https://tex.z-dn.net/?f=%5Ccos%5E2%5Cdfrac%20x2%3D%5Cdfrac%7B1%2B%5Ccos%20x%7D2)
![\sin^2\dfrac x2=\dfrac{1-\cos x}2](https://tex.z-dn.net/?f=%5Csin%5E2%5Cdfrac%20x2%3D%5Cdfrac%7B1-%5Ccos%20x%7D2)
![\implies\cot^2\dfrac x2=\dfrac{\cos^2\frac x2}{\sin^2\frac x2}=\dfrac{1+\cos x}{1-\cos x}](https://tex.z-dn.net/?f=%5Cimplies%5Ccot%5E2%5Cdfrac%20x2%3D%5Cdfrac%7B%5Ccos%5E2%5Cfrac%20x2%7D%7B%5Csin%5E2%5Cfrac%20x2%7D%3D%5Cdfrac%7B1%2B%5Ccos%20x%7D%7B1-%5Ccos%20x%7D)
So we have
![\cot^215^\circ=\dfrac{1+\cos30^\circ}{1-\cos30^\circ}=\dfrac{1+\frac{\sqrt3}2}{1-\frac{\sqrt3}2}](https://tex.z-dn.net/?f=%5Ccot%5E215%5E%5Ccirc%3D%5Cdfrac%7B1%2B%5Ccos30%5E%5Ccirc%7D%7B1-%5Ccos30%5E%5Ccirc%7D%3D%5Cdfrac%7B1%2B%5Cfrac%7B%5Csqrt3%7D2%7D%7B1-%5Cfrac%7B%5Csqrt3%7D2%7D)
![\implies\cot^215^\circ=7+4\sqrt3](https://tex.z-dn.net/?f=%5Cimplies%5Ccot%5E215%5E%5Ccirc%3D7%2B4%5Csqrt3)
![\implies\cot15^\circ=\sqrt{7+4\sqrt3}=2+\sqrt3](https://tex.z-dn.net/?f=%5Cimplies%5Ccot15%5E%5Ccirc%3D%5Csqrt%7B7%2B4%5Csqrt3%7D%3D2%2B%5Csqrt3)
Note that when taking the square root, we should take into account that that could yield two possible solutions, but we know
and
, so it's also the case that
.
Also, the reason we have equality in the last step can be explained like so:
![7+4\sqrt3=4+4\sqrt3+3=4+4\sqrt3+(\sqrt3)^2=(2+\sqrt3)^2](https://tex.z-dn.net/?f=7%2B4%5Csqrt3%3D4%2B4%5Csqrt3%2B3%3D4%2B4%5Csqrt3%2B%28%5Csqrt3%29%5E2%3D%282%2B%5Csqrt3%29%5E2)
(not unlike the process used to complete the square)
Answer:
44, 58, 74
Step-by-step explanation:
you add up by 2´s.
Which means, 4+4=8, 8+6=14, 14+8=22, 22+10=32
4,6,8,10,12,14,16