Answer:
20%
Step-by-step explanation:
Answer:
Step-by-step explanation:
![1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}](https://tex.z-dn.net/?f=1-2%5Csin%5E2x%3D%5Csin%20x%5C%5C%5C%5C%5Ctext%7Bsubstitute%7D%5C%20t%3D%5Csin%20x%2C%5C%20t%5Cin%5B-1%2C%5C%201%5D%5C%5C%5C%5C1-2t%5E2%3Dt%5Cqquad%5Ctext%7Bsubtract%20t%20from%20both%20sides%7D%5C%5C%5C%5C-2t%5E2-t%2B1%3D0%5Cqquad%5Ctext%7Bchange%20the%20signs%7D%5C%5C%5C%5C2t%5E2%2Bt-1%3D0%5C%5C%5C%5C2t%5E2%2B2t-t-1%3D0%5C%5C%5C%5C2t%28t%2B1%29-1%28t%2B1%29%3D0%5C%5C%5C%5C%28t%2B1%29%282t-1%29%3D0%5Ciff%20t%2B1%3D0%5C%20%5Cvee%5C%202t-1%3D0%5C%5C%5C%5Ct%2B1%3D0%5Cqquad%5Ctext%7Bsubtract%201%20from%20both%20sides%7D%5C%5C%5Cboxed%7Bt%3D-1%7D%5C%5C%5C%5C2t-1%3D0%5Cqquad%5Ctext%7Badd%201%20to%20both%20sides%7D%5C%5C2t%3D1%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5Cboxed%7Bt%3D%5Cdfrac%7B1%7D%7B2%7D%7D)
Given that the time taken to get to campus is inversely proportional to driving rate, let the time be t and rate be r, thus the function will be written as:'
t=k/r
where
k is the constant of proportionality given by:
k=tr
when r=20 mph, t=1.25 hrs
thus
k=20×1.25
k=25 miles
thus the formula is:
t=25/r
when r=55 mph, the value of t will be:
t=25/55
t=5/11 hours
