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
234 / 18 = 13 So she gets thirteen dollars an hour.
I did 13 x 8 and got 104 so the answer is 8 hours.
Fractions can be simplified by making sure that the numerator and the denominator cannot be divided by any number.
The given 12/60 is very obvious that it is divisible by 2.
After dividing by 2, you will get 6/30.
It seems it is not in simplest form. It is divisible by 3.
Dividing the numerator and denominator by 3 then you will get
2/15.
So the lowest term is 2/15.
Answer:
value of x = 3.
Step-by-step explanation:
according to the question ;
- 11x + 4 = 37
- 11x = 37 - 4
- 11x = 33
- x = 33/11
- x = 3
Because base angles on an isosceles trapezoid are equal you set up this equation
7x - 12 = 5x + 6
-5x+12 -5x +12
2x = 18
/2 /2
x = 9