Answer:
−13.35
Step-by-step explanation:
i took the quiz
![\bf \stackrel{\textit{testing for the x-axis symmetry, }\theta =-\theta }{r=8cos(3\theta )\implies r=8cos[3(-\theta)]}\implies r=8cos(-3\theta) \\\\\\ r=8cos(3\theta)~~\boxed{\checkmark}~~\impliedby \stackrel{\textit{trigonometry symmetry identities}}{cos(\theta)=cos(-\theta)}\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Btesting%20for%20the%20x-axis%20symmetry%2C%20%7D%5Ctheta%20%3D-%5Ctheta%20%7D%7Br%3D8cos%283%5Ctheta%20%29%5Cimplies%20r%3D8cos%5B3%28-%5Ctheta%29%5D%7D%5Cimplies%20r%3D8cos%28-3%5Ctheta%29%0A%5C%5C%5C%5C%5C%5C%0Ar%3D8cos%283%5Ctheta%29~~%5Cboxed%7B%5Ccheckmark%7D~~%5Cimpliedby%20%5Cstackrel%7B%5Ctextit%7Btrigonometry%20symmetry%20identities%7D%7D%7Bcos%28%5Ctheta%29%3Dcos%28-%5Ctheta%29%7D%5C%5C%5C%5C%0A-------------------------------)
![\bf \stackrel{\textit{testing for the y-axis symmetry, }\theta =\pi -\theta }{r=8cos(3\theta )\implies r=8cos[3(\pi -\theta)]}\implies r=8cos(3\pi -3\theta)\boxed{\otimes}\\\\ -------------------------------\\\\ \stackrel{\textit{testing for the origin symmetry, }\theta =\pi +\theta }{r=8cos(3\theta )\implies r=8cos[3(\pi +\theta)]}\implies r=8cos(3\pi +3\theta)\boxed{\otimes}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Btesting%20for%20the%20y-axis%20symmetry%2C%20%7D%5Ctheta%20%3D%5Cpi%20-%5Ctheta%20%7D%7Br%3D8cos%283%5Ctheta%20%29%5Cimplies%20r%3D8cos%5B3%28%5Cpi%20-%5Ctheta%29%5D%7D%5Cimplies%20r%3D8cos%283%5Cpi%20-3%5Ctheta%29%5Cboxed%7B%5Cotimes%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Cstackrel%7B%5Ctextit%7Btesting%20for%20the%20origin%20symmetry%2C%20%7D%5Ctheta%20%3D%5Cpi%20%2B%5Ctheta%20%7D%7Br%3D8cos%283%5Ctheta%20%29%5Cimplies%20r%3D8cos%5B3%28%5Cpi%20%2B%5Ctheta%29%5D%7D%5Cimplies%20r%3D8cos%283%5Cpi%20%2B3%5Ctheta%29%5Cboxed%7B%5Cotimes%7D)
so as you can see, since the x-axis test yielded the same original expression, it has symmetry with the x-axis, or namely the "polar axis".
Answer:
3/13
Step-by-step explanation:
First you need to know what a reciprocal is. Is the fraction flipped.
Steps:
1. turn 4 1/3 into an improper fraction
4x3 +1 = 13
13/3
2. Flip it
13/3 ---> 3/13
Hope that helped!
Answer:
210
Step-by-step explanation:
Answer:
radius is 16
diameter is 32
Step-by-step explanation:
Your radius is the line starting from the point in the middle to any part of the edge of the circle. A diameter is when there is a long straight line from both ends reaching the edges of the circle crossing the point.
A diameter is just the radius doubled but except it all has to be straight coming reaching both edges.
A radius is half of a diameter.
