Answer:
Step-by-step explanation:
P(less than 6) = 2/5
For the first one, we have
![\dfrac1{1-\cos x}+\dfrac1{1+\cos x}=\dfrac{1+\cos x}{(1-\cos x)(1+\cos x)}+\dfrac{1-\cos x}{(1-\cos x)(1+\cos x)}](https://tex.z-dn.net/?f=%5Cdfrac1%7B1-%5Ccos%20x%7D%2B%5Cdfrac1%7B1%2B%5Ccos%20x%7D%3D%5Cdfrac%7B1%2B%5Ccos%20x%7D%7B%281-%5Ccos%20x%29%281%2B%5Ccos%20x%29%7D%2B%5Cdfrac%7B1-%5Ccos%20x%7D%7B%281-%5Ccos%20x%29%281%2B%5Ccos%20x%29%7D)
![=\dfrac{1+\cos x+1-\cos x}{1-\cos^2x}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%2B%5Ccos%20x%2B1-%5Ccos%20x%7D%7B1-%5Ccos%5E2x%7D)
![=\dfrac2{\sin^2x}](https://tex.z-dn.net/?f=%3D%5Cdfrac2%7B%5Csin%5E2x%7D)
Multiply this by
and you end up with
![=\dfrac{2\sin x}{\sin^2x}=\dfrac2{\sin x}=2\csc x](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2%5Csin%20x%7D%7B%5Csin%5E2x%7D%3D%5Cdfrac2%7B%5Csin%20x%7D%3D2%5Ccsc%20x)
For the second one,
![-\tan^2x+\sec^2x=-\dfrac{\sin^2x}{\cos^2x}+\dfrac1{\cos^2x}=\dfrac{1-\sin^2x}{\cos^2x}=\dfrac{\cos^2x}{\cos^2x}=1](https://tex.z-dn.net/?f=-%5Ctan%5E2x%2B%5Csec%5E2x%3D-%5Cdfrac%7B%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%2B%5Cdfrac1%7B%5Ccos%5E2x%7D%3D%5Cdfrac%7B1-%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%3D%5Cdfrac%7B%5Ccos%5E2x%7D%7B%5Ccos%5E2x%7D%3D1)
Answer:
D. ![y=-0.927x+13.634](https://tex.z-dn.net/?f=y%3D-0.927x%2B13.634)
Step-by-step explanation:
We graph the points on the graph. The graph is attached.
Let us take two points (1, 14) and (15, 1), and calculate the slope
between them <em>(we choose these points because the line passing through them will be the best fit for all points) </em>
![m=\frac{14-1}{1-15} =\frac{13}{-14} =-0.9286](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B14-1%7D%7B1-15%7D%20%3D%5Cfrac%7B13%7D%7B-14%7D%20%3D-0.9286)
Thus we have the equation
![y=-0.9286x+b](https://tex.z-dn.net/?f=y%3D-0.9286x%2Bb)
Let us now calculate
from the point ![(1,14)](https://tex.z-dn.net/?f=%281%2C14%29)
![14=-0.9286(1)+b](https://tex.z-dn.net/?f=14%3D-0.9286%281%29%2Bb)
![b=14.9286](https://tex.z-dn.net/?f=b%3D14.9286)
So the equation we get is
![y=-0.9286x+14.9286](https://tex.z-dn.net/?f=y%3D-0.9286x%2B14.9286)
Let us now turn to the choices given and see which choice is closest to our equation: we see that choice D.
is the closest one, so we pick it.
Answer:
Letter A. (0,-6)
Step-by-step explanation:
(0,-6) is where the line crosses the x-intercept.
Hope this helps