Answer:
See below.
Step-by-step explanation:
![\frac{1+cos(\theta)}{sin(\theta)} +\frac{sin(\theta)}{1+cos(\theta)}=2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B1%2Bcos%28%5Ctheta%29%7D%7Bsin%28%5Ctheta%29%7D%20%2B%5Cfrac%7Bsin%28%5Ctheta%29%7D%7B1%2Bcos%28%5Ctheta%29%7D%3D2csc%28%5Ctheta%29)
![\frac{(1+cos(\theta))(1+cos(\theta))}{sin(\theta)((1+cos(\theta))} +\frac{(sin(\theta))(sin(\theta))}{(1+cos(\theta))(sin(\theta))}=2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B%281%2Bcos%28%5Ctheta%29%29%281%2Bcos%28%5Ctheta%29%29%7D%7Bsin%28%5Ctheta%29%28%281%2Bcos%28%5Ctheta%29%29%7D%20%2B%5Cfrac%7B%28sin%28%5Ctheta%29%29%28sin%28%5Ctheta%29%29%7D%7B%281%2Bcos%28%5Ctheta%29%29%28sin%28%5Ctheta%29%29%7D%3D2csc%28%5Ctheta%29)
![\frac{(1+cos(\theta))(1+cos(\theta))+(sin(\theta))(sin(\theta))}{sin(\theta)((1+cos(\theta))}=2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B%281%2Bcos%28%5Ctheta%29%29%281%2Bcos%28%5Ctheta%29%29%2B%28sin%28%5Ctheta%29%29%28sin%28%5Ctheta%29%29%7D%7Bsin%28%5Ctheta%29%28%281%2Bcos%28%5Ctheta%29%29%7D%3D2csc%28%5Ctheta%29)
![\frac{(1+2cos(\theta)+cos^2(\theta)+sin^2(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B%281%2B2cos%28%5Ctheta%29%2Bcos%5E2%28%5Ctheta%29%2Bsin%5E2%28%5Ctheta%29%29%7D%7Bsin%28%5Ctheta%29%281%2Bcos%28%5Ctheta%29%29%7D%20%3D2csc%28%5Ctheta%29)
Recall the identities:
![\frac{1+2cos(\theta)+1}{sin(\theta)(1+cos(\theta))} =2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B2cos%28%5Ctheta%29%2B1%7D%7Bsin%28%5Ctheta%29%281%2Bcos%28%5Ctheta%29%29%7D%20%3D2csc%28%5Ctheta%29)
![\frac{2+2cos(\theta)}{sin(\theta)(1+cos(\theta)}=2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B2cos%28%5Ctheta%29%7D%7Bsin%28%5Ctheta%29%281%2Bcos%28%5Ctheta%29%7D%3D2csc%28%5Ctheta%29)
![\frac{2(1+cos(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B2%281%2Bcos%28%5Ctheta%29%29%7D%7Bsin%28%5Ctheta%29%281%2Bcos%28%5Ctheta%29%29%7D%20%3D2csc%28%5Ctheta%29)
![\frac{2}{sin(\theta)} =2csc(\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bsin%28%5Ctheta%29%7D%20%3D2csc%28%5Ctheta%29)
![2csc(\theta)=2csc(\theta)](https://tex.z-dn.net/?f=2csc%28%5Ctheta%29%3D2csc%28%5Ctheta%29)
Ans: 1.1 miles more
Speed = distance/time
Time is 1/5 of an hour
1/5 of 1hr = 1/5 or 0.2 hrs
Speed = 16 mph
So, we're after distance.
Distance = speed x time
= 16mph x 0.2
= 3.2 miles
Walks for 3/7 hour at 5 miles per hour :
Time & speed given, distance is what we're after.
(3/7 of 1hr is 3/7)
Distance = speed x time
= 5mph x 3/7
= 15/7 miles or 2.14285...miles
So, distance is about 2.1 miles to 1 d.p
Thus, 3.2 - 2.142... (the full ans) = 1.057... miles
Well, he biked 1.06 miles or 1.1 miles (depending on how you want to round it) more than walking.
Hope this helps!
Answer:
h= 12.3
Step-by-step explanation: