The velocity V of sound in air at temperature T is given by V = 20.04 √T, where T is measured in kelvins (K) and V is in m/s. Assume that T = 300 ± 0.4K. Estimate V, and find the uncertainty in the estimate.

A buoy bobs up and down on ocean waves. It’s heigh is measured by the function h(t)= 3 cos (t) where h(t) is measured in feet and t is measured in seconds. What is the rate of change (in ft/s) of the heights of the buoy at t= 3pi/2

Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. Suppose that the length of the ladder is 7.7 meters and the top is sliding down the wall at a rate of 0.2 m/s. dx Calculate when h = 2.9. dt (Use decimal notation. Give your answer to three decimal places.) dx dt h=2.9 h X a m/s

For many species of fish, the allometric relationship between the weight W and the length L is approximately  W = kL3,  where k is a constant. Find the rate of change of the weight as a corresponding rate of change of the length. (dL/dt)