Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. Round to the nearest second or the nearest thousandth of a degree, as appropriate. Use a calculator as necessary. $119^{\circ} 8^{ \prime} 3^{\prime \prime}$

Investigate the one-parameter family of functions. Assume that a is positive. (a) Graph f(x) using three different values for a. (b) Using your graph in part (a), describe the critical points of f and how they appear to move as a increases. (c) Find a formula for the x-coordinates of the critical point(s) of f in terms of a. $f ( x ) = ( x - a ) ^ { 2 }$

A cat's crinkle ball toy of mass 15 g is thrown straight up with an initial speed of 3 m/s. Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) How much work is done by the gravitational force during the ball's rise to its peak? (c) What is the change in the gravitational potential energy of the ball during the rise to its peak? (d) If the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy when it reaches the maximum height? (e) What if the gravitational potential energy is taken to be zero at the maximum height the ball reaches, what would the gravitational potential energy be when it leaves the hand? (f) What is the maximum height the ball reaches?

Think of a student behavior that exists at your school and that a teacher or the principal might want to change. Then devise a way to change that behavior by using behavior modification techniques. Write out your plan in a short paper.

Solve the equation.

$$6 ^ { x - 2 } = 36$$

Solve each equation. $\log _{4} x=\frac{3}{2}$

Each of exercises refers to the Euler phi function denoted

$$\phi$$

, which is defined as follows: For each integer

$$n \geq 1 , \phi ( n )$$

is the number of positive integers less than or equal to n that have no common factors with n except

$$\pm 1$$

. For example,

$$\phi ( 10 ) = 4$$

because there are four positive integers less than because there are four positive integers less than

$$\pm 1$$

; namely, 1, 3, 7, and 9. Prove that there are infinitely many integers n for which

$$\phi ( n )$$

is a perfect square.

Consider the two forces acting on the person who stands still-namely, the downward pull of gravity and the upward support of the floor. Are these forces equal and opposite? Do they form an action-reaction pair? Why or why not?

A spinner is divided into 12 congruent regions, colored red, blue, and green. Landing on red is twice as likely as landing on blue. Landing on blue and landing on green are equally likely. a. What is the probability of landing on green? Show your work or explain in words how you got your answer. b. How many regions of the spinner are colored green? Explain your reasoning.

One side of a regular pentagon measures 0.8 meter. What is the perimeter of the regular pentagon?

Solve each triangle using either the Law of Sines or the Law of Cosines. $a=4, c=5, B=55^{\circ}$

Solve the following differential equations by using integrating factors. $x y^{\prime}=3 y+x^{2}$

A store posted a sign to entice shoppers that read: "Our prices are rising slower than anyplace else in town." Restate the sign using calculus terminology.

Write expressions for K and $K_P$ for the following reactions.

$$\mathrm { CuO } ( s ) + \mathrm { H } _ { 2 } ( g ) \rightleftharpoons \mathrm { Cu } ( l ) + \mathrm { H } _ { 2 } \mathrm { O } ( g )$$