Is the statement true or false for a function f whose domain is all real numbers? If a statement is true, explain how you know. If a statement is false, give a counterexample. If $f ^ { \prime } ( x ) \geq 0$ for all x, then $f ( a ) \leq f ( b )$ whenever $a \leq b.$

A $110 \mathrm{~kg}$ ice hockey player skates at $3.00 \mathrm{~m} / \mathrm{s}$ toward a railing at the edge of the ice and then stops himself by grasping the railing with outstretched arms. During this stopping process, the player's torso moves $30.0 \mathrm{~cm}$ toward the railing. What is the change in the kinetic energy of the center of mass during the stop?

The P215/65R 15 Cobra Radial G/T tire has a diameter of exactly 26 inches. Suppose that a car's wheel is making 2 revolutions per second (the car is traveling a little less than 5 miles per hour). Then $h(t)=13 \sin \left(4 \pi t-\frac{\pi}{2}\right)+13$ represents the height $h$ (in inches) of a point on the tire as a function of time $t$ (in seconds). The car starts to move when $t=0$.

During the first second that the car is moving, at what time $t$ is the point on the tire exactly 13 inches above the ground?

If y = ln (e^(-t^2)+10), then dy/dx =

(A) -2t

(B) 1/(e^(-t^2) + 10)

(C) (-2te^(t^2))/(e^(-t^2) + 10)

(D) (-2t)/(e^(-t^2) + 10)

(E) -2t + 1/10

Show that $\cos \theta=\frac{e^{i \theta}+e^{-i \theta}}{2} \text { and } \sin \theta=\frac{e^{i \theta}-e^{-i \theta}}{2 i}.$

Under certain conditions, wind blowing past a rectangular speed limit sign can cause the sign to oscillate with a frequency $\omega$. Assume that $\omega$ is a function of the sign width, b, sign height, h, wind velocity, V, air density, $\rho$, and an elastic constant, k, for the supporting pole. The constant, k, has dimensions of FL. Develop a suitable set of pi terms for this problem.

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word.

When the wind blows just the right way, the putrid stench of ..

Let A be an n x n matrix. (a) Suppose that the matrix B is obtained from A by multiplying the j-th row of A by k, which is nonzero. Find an elementary row operation that, when applied to B, gives A. (b) Suppose that the matrix C is obtained from A by interchanging the i-th and j-th rows of A. Find an elementary row operation that, when applied to C, gives A. (c) Suppose that the matrix D is obtained from A by adding k times the j-th row of A to its i-th row. Find an elementary row operation that, when applied to D, gives A.

Using the vocabulary list for this lesson, supply the correct word to complete the sentence.

He had a[n] ___ expression, but a dark secret lurked deep within.

Three painters, Beth, Bill, and Edie, working together, can paint the exterior of a home in 10 hours (hr). Bill and Edie together have painted a similar house in 15 hr. One day, all three worked on this same kind of house for 4 hr, after which Edie left. Beth and Bill required 8 more hr to finish. Assuming no gain or loss in efficiency, how long should it take each person to complete such a job alone?

Complete the sentence by writing the correct form of the word shown in parentheses. You may not need to change the form that is given.

This........... of my constitutional rights is an outrage! (abrogate)

Underline the adjective clause, and circle the noun or pronoun it modifies.
Luke remembered the day when he nearly fell through the ice.

Use your answer from the last question to explain why the cold packs are made with this type of gel rather than with ice.

The table shows the coefficient of friction $\mu$ of ice as a function of temperature. The lower $\mu$ is, the more “slippery” the ice is. Estimate $\mu^{\prime}(C)$ at (a) C=-10 and (b) C=-6. If skating warms the ice, does it get easier or harder to skate? Briefly explain.

$$\begin{matrix} \text{}{^{\circ} \mathrm{C}} & \text{-12} & \text{-10} & \text{-8} & \text{-6} & \text{-4} & \text{-2}\\ \text{}{\mu} & \text{0.0048} & \text{0.0045} & \text{0.0043} & \text{0.0045} & \text{0.0048} & \text{0.0055}\\ & \text{ }\\ \end{matrix}$$