17+75=x
or it could be written x-17=75
since he PAID $17 for gas, that makes it negative
if he has $75 left over AFTER subtracting $17, 17+75 is the total he had before.
Answer:
n=6
Step-by-step explanation:
Answer:
θ
![1.75\pi](https://tex.z-dn.net/?f=1.75%5Cpi)
r 10.551 244.151
Step-by-step explanation:
The maximum value for
is:
![\theta_{max} = \ln r](https://tex.z-dn.net/?f=%5Ctheta_%7Bmax%7D%20%3D%20%5Cln%20r)
![\theta_{max} = 2.199\pi\,rad](https://tex.z-dn.net/?f=%5Ctheta_%7Bmax%7D%20%3D%202.199%5Cpi%5C%2Crad)
The formula for the slope of the tangent line in polar coordinates is:
![m = \frac{r'\cdot \sin \theta + r \cdot \cos \theta}{r' \cdot \cos \theta - r \cdot \cos \theta}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Br%27%5Ccdot%20%5Csin%20%5Ctheta%20%2B%20r%20%5Ccdot%20%5Ccos%20%5Ctheta%7D%7Br%27%20%5Ccdot%20%5Ccos%20%5Ctheta%20-%20r%20%5Ccdot%20%5Ccos%20%5Ctheta%7D)
Horizontal tangent lines have a slope of zero. So, the following relation must be satisfied:
![r'\cdot \sin \theta + r \cdot \cos \theta = 0](https://tex.z-dn.net/?f=r%27%5Ccdot%20%5Csin%20%5Ctheta%20%2B%20r%20%5Ccdot%20%5Ccos%20%5Ctheta%20%3D%200)
![r'\cdot \sin \theta = - r \cdot \cos \theta](https://tex.z-dn.net/?f=r%27%5Ccdot%20%5Csin%20%5Ctheta%20%3D%20-%20r%20%5Ccdot%20%5Ccos%20%5Ctheta)
![\tan \theta = - \frac{r}{r'}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20-%20%5Cfrac%7Br%7D%7Br%27%7D)
![\tan \theta = -\frac{e^{\theta}}{e^{\theta}}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20-%5Cfrac%7Be%5E%7B%5Ctheta%7D%7D%7Be%5E%7B%5Ctheta%7D%7D)
![\tan \theta = -1](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20-1)
![\theta = \tan^{-1}(-1)](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ctan%5E%7B-1%7D%28-1%29)
, for all
.
The maximum value of i is:
![i = \frac{\theta_{max}-\frac{3}{4}\pi }{\pi}](https://tex.z-dn.net/?f=i%20%3D%20%5Cfrac%7B%5Ctheta_%7Bmax%7D-%5Cfrac%7B3%7D%7B4%7D%5Cpi%20%7D%7B%5Cpi%7D)
![i = \frac{2.199-0.75}{1}](https://tex.z-dn.net/?f=i%20%3D%20%5Cfrac%7B2.199-0.75%7D%7B1%7D)
(
).
Then, values are listed below:
θ
![1.75\pi](https://tex.z-dn.net/?f=1.75%5Cpi)
r 10.551 244.151
Answer:
Step-by-step explanation:
If the ratio of the interior angle to the exterior angle for a regular polygon is 5:1, find:a. the size of each exterior angle, b. the number of sides of the polygon, c. the sum of the interior angles
hope that help
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