Keeping in mind that "R" and "r" are constants whilst "s" is a variable and θ is a function in terms of "s", thus
![\bf s^2=R^2+r^2-2Rrcos(\theta )\implies 2s^1=0+0-2Rr\left[ \stackrel{chain~rule}{-sin(\theta )\cfrac{d\theta }{ds}} \right] \\\\\\ 2s=2Rrsin(\theta )\cfrac{d\theta }{ds}\implies 2s=\cfrac{2Rrsin(\theta )d\theta }{ds}\implies \cfrac{2s\cdot ds}{2Rr}=sin(\theta )d\theta \\\\\\ \cfrac{s\cdot ds}{Rr}=sin(\theta )d\theta](https://tex.z-dn.net/?f=%5Cbf%20s%5E2%3DR%5E2%2Br%5E2-2Rrcos%28%5Ctheta%20%29%5Cimplies%202s%5E1%3D0%2B0-2Rr%5Cleft%5B%20%5Cstackrel%7Bchain~rule%7D%7B-sin%28%5Ctheta%20%29%5Ccfrac%7Bd%5Ctheta%20%7D%7Bds%7D%7D%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0A2s%3D2Rrsin%28%5Ctheta%20%29%5Ccfrac%7Bd%5Ctheta%20%7D%7Bds%7D%5Cimplies%202s%3D%5Ccfrac%7B2Rrsin%28%5Ctheta%20%29d%5Ctheta%20%7D%7Bds%7D%5Cimplies%20%5Ccfrac%7B2s%5Ccdot%20ds%7D%7B2Rr%7D%3Dsin%28%5Ctheta%20%29d%5Ctheta%20%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bs%5Ccdot%20ds%7D%7BRr%7D%3Dsin%28%5Ctheta%20%29d%5Ctheta)
Which of these is incorrect? A) 41,792 < 42,699 B) 42,699 > 43,595 Eliminate C) 42,699 < 44,792 D) 43,595 > 41,792
2 answers:
You might be interested in
