Select the correct answer. The formula below, Newton's law of cooling, allows us to calculate the temperature of an object as it cools. T = R + (T0 − R)e-kt T = temperature of the object after t minutes T0 = initial temperature R = temperature of the surroundings k = cooling rate (depends on the object and conditions) Suppose the temperature in Denver, Colorado was 55°F when a 5°F arctic cold front moved over the state. Using k = 0.012, how long would it take a puddle of water to freeze? (Recall that water freezes at 32°F.) A. just over 51 minutes B. just over 55 minutes C. just over 61 minutes D. just over 65 minutes

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?