Sometimes it is difficult to open an exterior door of a building because the air distribution system maintains a pressure difference between the inside and outside of the building. Estimate how big this pressure difference can be if it is “not too difficult” for an average person to open the door.

When asked the question "What is time? ", the fourthcentury Christian phi losopher St. Augustine replied, "If you don't ask me, I know, but if you ask me, I don 't know." Construct a truth table for St. Au gustine 's statement and determine whether or not it is a tautology.

A homogeneous, 4-ft-wide, 8-ft-long rectangular gate weighing $800 \mathrm{lb}$ is held in place by a horizontal flexible cable as shown in the figure. Water acts against the gate which is hinged at point $A$. Friction in the hinge is negligible. Determine the tension in the cable.

A pump supplies water under pressure to a large tank as shown . The circular-plate valve fitted in the short discharge pipe on the tank pivots about its diameter $A-A$ and is held shut against the water pressure by a latch at B. Show that the force on the latch is independent of the supply pressure, p, and the height of the tank, h.

A long, vertical wall separates seawater from freshwater. If the seawater stands at a depth of $7 \mathrm{~m}$, what depth of freshwater is required to give a zero resultant force on the wall? When the resultant force is zero will the momentum due to the fluid forces be zero? Explain.

A structure is attached to the ocean floor as shown . A 2 -m-diameter hatch is located in an inclined wall and hinged on one edge. Determine the minimum air pressure, $p_1$, within the container that will open the hatch. Neglect the weight of the hatch and friction in the hinge.

Write a rule for g. Let the graph of g be horizontal shrink by a factor of 2/3, followed by a translation 5 units left and 2 units down of the graph of

$$f(x) = x^2.$$

A cell phone provider offers a plan that costs $40 per month plus$.20 per text message sent or received. A comparable plan costs $60 per month but offers unlimited text messaging. a. How many text messages would you have to send or receive in order for the plans to cost the same each month? b. If you send or receive an average of 50 text messages each month, which plan would you choose? Why?

Find the zeros of the polynomial function.

$$g ( x ) = 2 x ^ { 2 } + x - 1$$

A television sports commentator wants to estimate the proportion of Americans who follow professional football. What sample size should be obtained if he wants to be within 3 percentage points with 95% confidence if

he uses a 2010 estimate of 53% obtained from a Harris poll?

Use a calculator to find the value of each expression rounded to two decimal places. $\tan ^{-1} 0.2$

Forms used to make a concrete basement wall are shown. Each 4-ft-long form is held together by four ties-two at the top and two at the bottom as indicated. Determine the tension in the upper and lower ties. Assume concrete acts as a fluid with a weigh: of $150 \mathrm{lb} / \mathrm{ft}^3$.

Solve the equation. Check your solution. -10 = 2(7 - 2x)

Solve the given differential equation by using an appropriate substitution.

$$\frac { d y } { d x } = \sin ( x + y )$$