Answer:B
Step-by-step explanation: a factor of a number that is multiplied by itself
There is not enough information to answer :(
If she did not reach her goal then
miles she drove must be less than 385
or
miles she drove<385
so rate=55 miles per hour
so
miles driven=h times 55
subsitute
55 times h<385
divide both sides by 55
h<7
she drove less than 7 hours
inequality=55h<385
h<7
Answer: ![\frac{\sqrt{6}-\sqrt{2}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B6%7D-%5Csqrt%7B2%7D%7D%7B2%7D%20)
Step-by-step explanation:
We apply the formula
.
Note that
. Take
and
in the formula above to get
![\cos(\frac{41}{12}\pi)=\cos(3\pi)\cos(\frac{7}{12}\pi)-\sin(3\pi)\sin(\frac{7}{12}\pi)=(-1)\cdot \cos(\frac{7}{12}\pi)-0\cdot\sin(\frac{7}{12}\pi)=-\cos(\frac{7}{12}\pi)](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B41%7D%7B12%7D%5Cpi%29%3D%5Ccos%283%5Cpi%29%5Ccos%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29-%5Csin%283%5Cpi%29%5Csin%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29%3D%28-1%29%5Ccdot%20%5Ccos%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29-0%5Ccdot%5Csin%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29%3D-%5Ccos%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29)
Then the value of this expression is ![-\cos(\frac{7}{12}\pi)](https://tex.z-dn.net/?f=-%5Ccos%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29%20)
We can use the cosine addition formula again to simplify further. Decompose the fraction in the argument as:
![\cos(\frac{7}{12}\pi)=\cos((\frac{3}{12}+\frac{4}{12})\pi)=\cos((\frac{1}{4}\pi + \frac{1}{3})\pi)](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29%3D%5Ccos%28%28%5Cfrac%7B3%7D%7B12%7D%2B%5Cfrac%7B4%7D%7B12%7D%29%5Cpi%29%3D%5Ccos%28%28%5Cfrac%7B1%7D%7B4%7D%5Cpi%20%2B%20%5Cfrac%7B1%7D%7B3%7D%29%5Cpi%29%20)
Applying the formula with
and
we obtain
![\cos(\frac{7}{12}\pi)=\cos(\frac{1}{4}\pi)\cos(\frac{1}{3}\pi)-\sin(\frac{1}{4}\pi)\sin(\frac{1}{3}\pi)=\frac{\sqrt{2}}{2}\cdot\frac{1}{2} -\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2}=\frac{\sqrt{2}-\sqrt{6}}{2}](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B7%7D%7B12%7D%5Cpi%29%3D%5Ccos%28%5Cfrac%7B1%7D%7B4%7D%5Cpi%29%5Ccos%28%5Cfrac%7B1%7D%7B3%7D%5Cpi%29-%5Csin%28%5Cfrac%7B1%7D%7B4%7D%5Cpi%29%5Csin%28%5Cfrac%7B1%7D%7B3%7D%5Cpi%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Ccdot%5Cfrac%7B1%7D%7B2%7D%20-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Ccdot%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3D%5Cfrac%7B%5Csqrt%7B2%7D-%5Csqrt%7B6%7D%7D%7B2%7D%20)
We conclude that this expression has the value ![-\frac{\sqrt{2}-\sqrt{6}}{2}=\frac{\sqrt{6}-\sqrt{2}}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%7B2%7D-%5Csqrt%7B6%7D%7D%7B2%7D%3D%5Cfrac%7B%5Csqrt%7B6%7D-%5Csqrt%7B2%7D%7D%7B2%7D%20)