Answer: 17.8 yds
<u>Step-by-step explanation:</u>
The length of the arc of the ENTIRE circle is the circumference (C = 2πr).
We only want a 60° section of that circumference <em>which is 60°/360° = 1/6 of the circumference.</em>
The formula for length of an arc is: ![s=2\pi r\bigg(\dfrac{\theta}{360^o}\bigg)](https://tex.z-dn.net/?f=s%3D2%5Cpi%20r%5Cbigg%28%5Cdfrac%7B%5Ctheta%7D%7B360%5Eo%7D%5Cbigg%29)
Given r = 17, θ = 60°
![s=2\pi (17)\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =2\pi(17) \bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =\dfrac{17 \pi}{3}\\\\\\.\quad =\large\boxed{17.8}](https://tex.z-dn.net/?f=s%3D2%5Cpi%20%2817%29%5Cbigg%28%5Cdfrac%7B60%5Eo%7D%7B360%5Eo%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D2%5Cpi%2817%29%20%5Cbigg%28%5Cdfrac%7B1%7D%7B6%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B17%20%5Cpi%7D%7B3%7D%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Clarge%5Cboxed%7B17.8%7D)
Answer:
200
Step-by-step explanation:
20% of the 1,000 people, which is 200 people.
1/2abSinC
1/2*8*5*sin(140)=12.9cm
* means multiply
Suppose that the point A(x,y) belongs to this parabola. The defining point of the parabola is that the distance between a point F and the directrix. Suppose that the chosen point F is at (a,b). Then, the distance from A to the directrix is |b+4| while the distance from A to the focus is given by the pythagorean theorem:
![d= \sqrt{(x-a)^2+(y-b)^2}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%28x-a%29%5E2%2B%28y-b%29%5E2%7D%20)
.
We have that these two have to be equal. Squaring both sides we get:
![b^2+8b+16=(x-a)^2+(y-b)^2](https://tex.z-dn.net/?f=b%5E2%2B8b%2B16%3D%28x-a%29%5E2%2B%28y-b%29%5E2)
.
This is the equation that describes all equations of parabolas with that directrix; you just need to choose the focus and substituting a and b will yield the equation.