An exploration submarine should be able to descend 1200 m down in the ocean. If the ocean density is 1020 kg/m3, what is the maximum pressure on the submarine hull?

A barometer to measure absolute pressure shows a mercury column height of 725 mm. The temperature is such that the density of the mercury is 13 550 kg/m3. Find the ambient pressure.

Suppose that a quantity y=y(t) increases at a rate that is proportional to the square of the amount present, and suppose that at time t=0, the amount present is

$$y_0$$

. Find an initial-value problem whose solution is y(t).

Solve the given differential equation by finding an appropriate integrating factor.

$$\left( 10 - 6 y + e ^ { - 3 x } \right) d x - 2 d y = 0$$

A piston, mp=5 kg, is fitted in a cylinder, A=15 cm2, that contains a gas. The setup is in a centrifuge that creates an acceleration of 25 m/s2 in the direction of piston motion toward the gas. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.