Whiteboy781
Answered

he temperature of a chemical reaction ranges between 30 degrees Celsius and 70 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 10-hour period. What is a cosine function that models this reaction?

f(t) = 20 cos 10t + 50

f(t) = 50 cos 10t + 20

f(t) = −50 cos pi over 5 t + 20

f(t) = −20 cos pi over 5 t + 50

Verified Answer :

Since3122015

\(f(t)=-20\cos\left(\frac{\pi}{5}t\right)+50\\f'(t)=20\sin(\frac{\pi}{5}t)*(\frac{\pi}{5})=0\\\sin(\frac{\pi}{5}t)=0\\\frac{\pi}{5}t=0,\pi\\t=0,5\\\\f(0)=-20\cos(\frac{\pi}{5}(0))+50\\f(0)=-20+50\\f(0)=30\\f(5)=-20\cos(\frac{\pi}{5}(5))+50\\f(5)=-20(-1)+50\\f(5)=20+50\\f(5)=70\)

f(t) = -20 * cos(pi / 5) + 50

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