Near a buoy, the depth of a lake at the point with coordinates $(x, y)$ is $z = 200 + 0.02x^2 - 0.001y^3,$ where $x, y,$ and $z$ are measured in meters. A fisherman in a small boat starts at the point (80, 60) and moves toward the buoy, which is located at (0, 0). Is the water under the boat getting deeper or shallower when he departs? Explain.

The spring of the pressure gauge shown in Figure has a force constant of $1000 \mathrm{~N} / \mathrm{m}$, and the piston has a diameter of $2.00 \mathrm{~cm}$. As the gauge is lowered into water, what change in depth causes the piston to move in by $0.500 \mathrm{~cm}$ ?

Create a list of equations for the following problem. Calculate the mass in kilograms of gravel stored in a rectangular bin $18.5$ feet by $25.0$ feet. The depth of the gravel bin is 15 feet, and the density of the gravel is 97 pound-mass per cubic foot.

Give the first five terms of the following:

$\bold{i}$. The arithmetic sequence whose first two terms are $1, 7$ $\bold{ii}$. The geometric sequence whose first two terms are $2, 8$

Determine the common difference and common ratio for the sequences

Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 28 inches and a depth of 14 inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

The parabolic mirror in the Hale Telescope at the Palomar Observatory in Southern California has a diameter of 200 inches and a concave depth of 3.75375 inches. Determine the location of its focus (to the nearest inch).

The volume of a bubble that starts at the bottom of a lake at 4.55 °C increases by a factor of 10 as it rises to the surface where the temperature is 18.45 °C and the air pressure is 0.965 atm. Assuming that the density of the lake water is $1.00\;\mathrm{g/cm^3}$, determine the depth of the lake. (Hint: You will need to use Equation 10.1.)

Solve the problem.

The pressure exerted by a certain liquid at a given point is directly proportional to the depth of the point beneath the surface of the liquid. If the pressure exerted at 30 feet is 13 pounds per square inch, what is the pressure exerted at 70 feet?

You respond to a local lake where a diver complains of difficulty breathing that occurred immediately after rapidly ascending from a depth of approximately 30 feet. On assessment, you note that he has cyanosis around his lips and has pink froth coming from his nose and mouth. You should:

***Depth *** The cross section of a five-meter trough is an isosceles trapezoid with a two-meter lower base, a three-meter upper base, and an altitude of $2$ meters. Water is running into the trough at a rate of $1$ cubic meter per minute. How fast is the water level rising when the water is $1$ meter deep?

For the pressure vessel of a spherical pressure vessel has an inside diameter of $0.8 \mathrm{~m}$. Determine $(a)$ the volume of liquefied propane required to fill the vessel to a depth of $0.6 \mathrm{~m},(b)$ the corresponding mass of the liquefied propane. (Density of liquefied propane $=580 \mathrm{~kg} / \mathrm{m}^{3}$.), determine the area of the surface in contact with the liquefied propane.

Brenna completes $65\%$ of her first serves. If she attempted $80$ first serves last match, how many did she complete?

a) Pressure $=\ldots \ldots$. Its units are $\ldots$. per square .... (or .... ).

b) In fluids (liquids and gases), pressure acts in .... directions, and pressure .... as the depth increases.

c) In a hydraulic machine, the $\ldots$. is the same throughout. The larger piston exerts the .... force.

d) Air pressure can be measured by a mercury ..... The... height of the mercury is usually about .. mm.

Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction , form, and strength. Scuba diving: depth, visibility