If those occasions won't work for you, there are other ways of finding topics for poems: a. Look through a newspaper for items that catch your imagination. b. Pretend you are Cinderella, a rock star, the last dinosaur (or any other figure from a story or a movie or real life). c. Begin with a question:

• "What kind of house would I have lived in in 1600?"
• "How would I be remembered if I disappeared this very moment?"
• "Twenty years from now, who will I be?" d. Choose an object or a creature and speak to it as though it were capable of understanding what you say. You might call your poem "A Conversation with a House" or "To a Pizza Pie" or "Words for an Old Dog." e. Write a poem consisting of a series of images. Its title might be "A Catalog of Sounds" or "A List of Memories." Or its first line might be "I see _-" (or "I smell," "I taste," "I touch," "I hear"). f. Write a poem consisting of a series of contrasting metaphors.
• "A cat seems to be _________ , but it really is_________ "
• "Fog seems to be_________ but it really is_________ "
• "An onion seems to be _________ but it really is_________ .

For each polynomial function f, (i) Determine the end behavior of f. (ii) Determine the zeros of f. State the multiplicity of each zero. Determine whether the graph of f crosses or only touches the axis at each x-intercept. (iii) Find the x- and y-intercepts of the graph of f. (iv) Use test numbers to find the intervals over which the graph of f is above or below the x-axis. (v) Sketch the graph of y = f(x). $f ( x ) = - x ^ { 2 } \left( x ^ { 2 } - 1 \right)$

For each polynomial function f, (i) Determine the end behavior of f. (ii) Determine the zeros of f. State the multiplicity of each zero. Determine whether the graph of f crosses or only touches the axis at each x-intercept. (iii) Find the x- and y-intercepts of the graph of f. (iv) Use test numbers to find the intervals over which the graph of f is above or below the x-axis. (v) Sketch the graph of y = f(x). $f ( x ) = - x ^ { 2 } ( x - 1 ) ^ { 2 }$

One measurement of the quality of a quarterback in the National Football League is known as the quarterback passer rating. The rating formula is $R(c, t, i, y)=\frac{50+20 c+80 t-100 i+100 y}{24}$, where c% of a quarterback's passes were completed, t% of his passes were thrown for touchdowns, i% of his passes were intercepted, and an average of $y$ yards were gained per attempted pass. If $c, t$, and $y$ remain fixed, what happens to the quarterback passer rating as $i$ increases? Explain your answer with and without mathematics.

The solenoid of an MRI machine produces a magnetic field of 1.5 T. The solenoid is 2.5 m long and 1.0 min diameter, and is wrapped with a single layer of tightly wound (touching one another) insulated wires 2.2 mm in diameter. Find the current that flows in the solenoid. (Your answer should be rather large. A typical MRI solenoid uses niobium-titanium wire kept at a temperature where helium is liquid and where the wire is superconducting.)

Two spheres, each of mass $M=2.33 \mathrm{~g}$, are attached by pieces of string of length $L=45.0 \mathrm{~cm}$ to a common point. The strings initially hang straight down, with the spheres just touching one another. An equal amount of charge, $q$, is placed on each sphere. The resulting forces on the spheres cause each string to hang at an angle of $\theta=10.0^{\circ}$ from the vertical. Determine $q$, the amount of charge on each sphere.

Solve using one or more problem-solving strategies.

In how many different ways can you arrange the shapes in each set so that at least one side of each shape is completely touching one side of another shape, and all shapes are adjacent? Sketch each arrangement. (Arrangements you can turn or flip to match each other count as one arrangement.)

$3$ equilateral triangles

In a volleyball game, a player on one team spikes the ball over the net when the ball is 10 feet above the court. The spike drives the ball downward with an initial vertical velocity of -55 feet per second. Players on the opposing team must hit the ball back over the net before the ball touches the court. How much time do the opposing players have to hit the spiked ball?

Suppose that $f(x)=\frac{x^{2}}{1+x^{2}}, x \geq 0$ (a) Use a graphing calculator to graph f(x) for $x \geq 0.$ Note that the graph is S shaped. (b) Find a line through the origin that touches the graph of f(x) at some point (c, f (c)) with c > 0. This is the tangent line at (c, f (c)) that goes through the origin. Graph the tangent line in the same coordinate system that you used in (a).

For each polynomial function: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|. $f(x)=3\left(x^{2}+8\right)\left(x^{2}+9\right)^{2}$

Let $\left(x_1, y_1\right)$ be the coordinates of a point on the parabola $x^2=4 p y$. The equation of the line that just touches the parabola at the point $\left(x_1, y_1\right)$, called a tangent line, is given by

$$y-y_1=\frac{x_1}{2 p}\left(x-x_1\right) \text {. }$$

For each parabola in Exercise 8, find the equations of the tangent lines at the endpoints of the chord. Use a graphing utility to graph the parabola and tangent lines.

Movable center section. Figure $25.41$ shows two capacitors in series, with a rigid center section that can be moved vertically, either upward or downward. (a) The plate area $A$ is the same for the capacitors. In terms of $A, a, b$, and $\varepsilon_0$, what is the equivalent capacitance $C ?$ (b) Evaluate $C$ for $A=2.0 \mathrm{~cm}^2, a=7.0 \mathrm{~mm}$, and $b=4.0 \mathrm{~mm}$. (c) If the center section is moved downward (without touching the bottom plate), does $C$ increase, decrease, or stay the same?

You notice your neighbor has installed a large coil of wire in close proximity to the power line coming into your house (underground cables are not available in your neighborhood). (a) What is the likely intention of your neighbor? (b) Is the plan likely to succeed? Explain. (c) When confronted, your neighbor simply shrugs and claims there’s no way it can cost you anything, anyway, since nothing of his is touching anything on your property. True or not? Explain.

You hang four pendulum bobs from strings connected to a wooden dowel. The strings are different lengths. How can you get the second longest pendulum bob to vibrate while the other three do not—without touching the pendulums? (a) Shake the dowel back and forth. (b) Shake the dowel back and forth at the resonant frequency of that pendulum. (c) Move the dowel sideways at any frequency. (d) Blow air on that bob.