Check the picture below.
since chords NQ and MP cross the center of the circle at R, that means that those two chords are diametrical chords and the angles made by both are vertical angles and thus twin angles, namely both are 18° as you see in the picture, so the angle NMP in magenta is really 162° + 18° + 18° = 198°, and we know the radius NR is 8.
![\textit{arc's length}\\\\ s=\cfrac{r\pi \theta }{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =198 \end{cases}\implies s=\cfrac{(8)\pi (198)}{180}\implies s\approx 27.6](https://tex.z-dn.net/?f=%5Ctextit%7Barc%27s%20length%7D%5C%5C%5C%5C%20s%3D%5Ccfrac%7Br%5Cpi%20%5Ctheta%20%7D%7B180%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20%5Ctheta%20%3D%5Cstackrel%7Bdegrees%7D%7Bangle%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D8%5C%5C%20%5Ctheta%20%3D198%20%5Cend%7Bcases%7D%5Cimplies%20s%3D%5Ccfrac%7B%288%29%5Cpi%20%28198%29%7D%7B180%7D%5Cimplies%20s%5Capprox%2027.6)
For the first question it is (3x-5) degrees second question is (x-5)
Interest I = PRT /100
P = $ 1000
R = 5.5% per annum
T = 18 months = 18 /12 = 1.5 years.
I = 1000 * 5.5 * 1.5 /100
I = $ 82.5
Amount = P + I = 1000 + 82.5 = 1082.5.
Hence the it would have grown to $1082.5
Well , i took a while to understand the question , lol . I guess the answer is. 7 students
Answer:
The distance each bus travels is given as d=tr where
- d is distance bus travels
- t is a time bus travels
- r is the speed of the bus
:
Distance first bus travels for 4 hours is d1=4r.
Distance other bus travels for 4 hours is d2=4(r+12).
:
The total distance between them is 480 miles and since they go in opposite directions this distance is the sum of distances each bus travels.
:
d1+d2=480
4r+4(r+12)=480
4r+4r+48=480
8r+48=480
8r=432
r=432/8
r=54 mph, this is a speed of the first bus
:
r+12=66 mph, this is the speed of the second bus
Hope this helps you!!!! :D
