The temperature of a chemical reaction ranges between 40 degrees celsius and 180 degrees celsius. the temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 12-hour period. what is a cosine function that models this reaction?
f(t) = 70 cos 12t + 110
f(t) = 110 cos 12t + 70
f(t) = −70 cos pi over 6t + 110
f(t) = −110 cos pi over 6t + 70

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.