A block with mass m = 5.00 kg slides down a surface inclined $36.9 ^ { \circ }$ to the horizontal. The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has mass 25.0 kg and moment of inertia $0.500 \mathrm { kg } \cdot \mathrm { m } ^ { 2 }$ with respect to the axis of rotation. The string pulls without slipping at a perpendicular distance of 0.200 m from that axis. What is the acceleration of the block down the plane?

Substitute the units of each quantity into the equation $u_{t}=\alpha^{2} u_{x x}-v u_{x}$ where v has units of velocity to see that every term has the same units.

Solve for $x$.

$$\log _3\left(\log _3 x\right)=1$$

Explain why the Supreme Court decision in Schenck v. U.S. seemed to justify jailing radicals.

How is the term provision used differently under IFRS than under U.S. GAAP?

Collar A starts from rest at $t=0$ and moves downward with a constant acceleration of $7 \mathrm{in} . / \mathrm{s}^2$. Collar $B$ moves upward with a constant acceleration, and its initial velocity is $8 \mathrm{in}$./s. Knowing that collar $B$ moves through $20 \mathrm{in}$. between $t=0$ and $t=2 \mathrm{~s}$, determine $(a)$ the accelerations of collar $B$ and block $C,(b)$ the time at which the velocity of block $C$ is zero, $(c)$ the distance through which block $C$ will have moved at that time.

Rebecca read an article online with the headline, “Survey shows that among employed Americans, people who text frequently tend to have lower-paying jobs than those who do not.” Rebecca immediately sent a text message to her friend Sissy: “OMG cc! txting makes u have less $$ $! 2 bad 4 us!!!” While it is possible that Rebecca is correct, the statement she read didn’t say that texting caused people to have lower incomes, only that people who frequently text have lower incomes. Give another possible explanation for why those who text frequently may have lower-paying jobs. $$

Prove or disprove that $H=\left\{h \in G \mid h^{-1}=h\right\}$ is a subgroup of the group $G$ if $G$ is abelian.

Solve the inequality. Use set-builder or interval notation to write a solution set to the inequality.

$$2 x^2+3 x+1<0$$

Describe the integer values of b for which $x^{2}+b x+1=0$ has no solutions.

$$\begin{array}{|c|c|c|}\hline & {A} & {B} & {c} \\ \hline 1 & {b} & {x^{2}+b x+1=0} & {x^{ 2}+b x+2=0} \\ \hline 2 & {-3} & {\square} & {\square} \\ \hline 3 & {-2} & {\square} & {\square} \\ \hline 4 & {-1} & {\square} & {\square} \\ \hline 5 & {0} & {\square} & {\square} \\ \hline{6} & {1} & {\square} & {\square} \\ \hline 7 & {2}& {\square}& {\square} \\ \hline 8 & {3}& {\square}& {\square} \\ \hline\end{array}$$

A 42.0-cm-diameter wheel, consisting of a rim and six spokes, is constructed from a thin, rigid plastic material having a linear mass density of 25.0 g/cm. This wheel is released from rest at the top of a hill 58.0 m high. (a) How fast is it rolling when it reaches the bottom of the hill? (b) How would your answer change if the linear mass density and the diameter of the wheel were each doubled?

Solve the inequality. Graph the solution set and write it using interval notation and set-builder notation.

$$5 ( x - 2 ) \leq 5$$

A salesman drives from Ajax to Barrington, a distance of 120 mi, at a steady speed. He then increases his speed by 10 mi/h to drive the 150 mi from Barrington to Collins. If the second leg of his trip took 6 min more time than the first leg, how fast was he driving between Ajax and Barrington?

solve for y in terms of x. \

$$\log _7 y=2 \log _7 5+\log _7 x+3$$