The uniform slender rod of mass m and length L is released from rest in the inverted vertical position. Neglect friction and the mass of the small end roller and find the initial acceleration of A. Evaluate your result for $\theta=30^{\circ}$.

Lucia walks $2 \frac{3}{4}$ miles on Monday. On Tuesday, she walks $1 \frac{1}{2}$ times farther. How far did Lucia walk on Tuesday?

If you must do positive work to bring a charged balloon toward a negatively charged sphere, is the charge on the balloon positive or negative?

Handel flips a fair coin seven times and it comes up heads seven times. What is the probability his next flip will be heads? Why?

Calculate the area of each rectangle. Width = 15 inches Length = $\frac{2}{3}$ inch

Suppose that in Exercise 1.6 you decide to flip the coin 100 times. What conclusion would you be likely to draw if you observed 95 heads?

Express using a positive exponent: $8^{-6}$ .

Determine intervals of increase and decrease and intervals of concavity for the given function. Then sketch the graph of the function. Be sure to show all key features such as intercepts, asymptotes, high and low points, points of inflection, cusps, and vertical tangents. $f(t)=3 t^{5}-20 t^{3}$

Let f(x)=x$^2$ and let g(x)=(x-3)$^2$+2.

(a) Give the formula for $g$ in terms of $f$, and describe the relationship between $f$ and $g$ in words.

(b) Is g a quadratic function? If so, find its standard form and the parameters a, b, and c.

(c) Graph g, labeling all important features.

The distance from a point P to a line L is the length of the line segment connecting P to L at a right angle. Show that the distance from $\left(x_{1}, y_{1}\right)$ to the line ax+by+c=0 equals $\frac{\left|a x_{1}+b y_{1}+c\right|}{\sqrt{a^{2}+b^{2}}}$.

Two uniform cylinders, each of mass $m=6 \mathrm{~kg}$ and radius $r=125 \mathrm{~mm}$, are connected by a belt as shown. If the system is released from rest when $t=$ 0 , determine $(a)$ the velocity of the center of cylinder $B$ at $t=3 \mathrm{~s},(b)$ the tension in the portion of belt connecting the two cylinders.

Indicate whether the following are fission or fusion reactions.

$$\begin{array}{l}{\text { a. } ^{1}_{1} H+^{2}_{1} H \longrightarrow ^{3}_{2} H e+\gamma} \\ {\text { b. } ^{1}_{0} n+^{235}_{92} U \longrightarrow ^{146}_{57} L a+^{87}_{35} B r+3_{0}^{1} n}\end{array}$$

$$\begin{array}{l}{\text { c. } ^{21}_{10} \mathrm{Ne}+^{4}_{2} \mathrm{He} \longrightarrow_{12}^{24} \mathrm{Mg}+^{1}_{0} n} \\ {\text { d. } ^{208}_{82} \mathrm{Pb}+^{58}_{26} \mathrm{Fe} \longrightarrow_{108}^{265} \mathrm{Hs}+_{0}^{1} n}\end{array}$$

Why do you think businesses offer discounts if the invoice is paid early? Do you think it is always to the purchaser's advantage to pay early?

• Explain your reasoning.
• Show your understanding of mathematics in an organized manner.
• Use charts, graphs, and diagrams in your explanation.
• Show the solution in more than one way or relate it to other situations.
• Investigate beyond the requirements of the problem.

The uniform slender bar of length 2r and mass m rests against the circular surface as shown. Determine the normal force at the small roller A and the magnitude of the ideal pivot reaction at O.