To do this you first have to find the measure of the angle that is inside that pie-shaped part of the circle. The measure around the circle is 360 which is the same as 2pi. Subtract 5pi/3 from 2pi and you get pi/3, which happens to be a 60 degree angle. What you are looking for is arc length (not arc measure which is measured in degrees, not inches, feet, etc.) The formula for that is this:
![\frac{ \beta }{360}* \pi d](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cbeta%20%7D%7B360%7D%2A%20%5Cpi%20d%20)
, where beta is the arc measure in question and d is the diameter of the circle. If the central angle we found measured 60 degrees, then the arc it intercepts also measures 60 degrees, therefore s measures 300 (360-60). So now our formula looks like this:
![\frac{300}{360} * \pi 18](https://tex.z-dn.net/?f=%20%5Cfrac%7B300%7D%7B360%7D%20%2A%20%5Cpi%2018)
. When you do all that math, multiplying pi in, you get an arc length of 47.1, the first choice.
Answer:
the function is -3 i think
Answer:
![(a)\ y = 4\ or\ y = -\frac{1}{2}](https://tex.z-dn.net/?f=%28a%29%5C%20y%20%3D%204%5C%20or%5C%20y%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
![(b)\ x = 2 \ or\ x = -\frac{1}{4}](https://tex.z-dn.net/?f=%28b%29%5C%20x%20%3D%202%20%5C%20or%5C%20x%20%3D%20-%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
Solving (a)
![2y^2 - 7y - 4 = 0](https://tex.z-dn.net/?f=2y%5E2%20-%207y%20%20-%204%20%3D%200)
Expand
![2y^2 +y - 8y - 4 = 0](https://tex.z-dn.net/?f=2y%5E2%20%20%2By%20-%208y%20%20-%204%20%3D%200)
Expand
![y(2y + 1) -4(2y + 1) = 0](https://tex.z-dn.net/?f=y%282y%20%2B%201%29%20%20-4%282y%20%2B%201%29%20%3D%200)
Factor out 2y + 1
![(y -4)(2y + 1) = 0](https://tex.z-dn.net/?f=%28y%20-4%29%282y%20%2B%201%29%20%3D%200)
Split
![y - 4 =0\ or\ 2y + 1 = 0](https://tex.z-dn.net/?f=y%20-%204%20%3D0%5C%20or%5C%202y%20%2B%201%20%3D%200)
Solve:
![y = 4\ or\ y = -\frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%204%5C%20or%5C%20y%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
Solving (b):
![2(2x)^2 - 7(2x) - 4 = 0](https://tex.z-dn.net/?f=2%282x%29%5E2%20-%207%282x%29%20-%204%20%3D%200)
Compare the above with the equation in (a)
![2y^2 - 7y - 4 = 0](https://tex.z-dn.net/?f=2y%5E2%20-%207y%20%20-%204%20%3D%200)
We have:
![2x = y](https://tex.z-dn.net/?f=2x%20%3D%20y)
So:
![2x = 4 \ or\ 2x = -\frac{1}{2}](https://tex.z-dn.net/?f=2x%20%3D%204%20%5C%20or%5C%20%202x%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
Solve for x in both cases
![x = 2 \ or\ x = -\frac{1}{4}](https://tex.z-dn.net/?f=x%20%3D%202%20%5C%20or%5C%20x%20%3D%20-%5Cfrac%7B1%7D%7B4%7D)
Answer:
50%
Step-by-step explanation:
the percent of decrease from 10 to 5 is 50%
When 10 is decreased to 5:
10-5= 5
5 is half of 10.
1/2 as a percent is 50%