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Diagram the sentence using what you have learned.

The jolly judges grinned playfully.

Solve the indicated system by setting $X$ equal to the appropriate matrix and reducing it using the up-arrow key and editing repeatedly the three basic commands. To avoid losing the command to interchange rows, which is seldom necessary, execute it at least once in each exercise even if it is not needed. Solve the indicated exercises listed below..

Exercise 62

Two waveforms, $v_1(t)$ and $v_2(t)$, have identical amplitudes and oscillate at the same frequency, but $v_2(t)$ lags $v_1(t)$ by a phase angle of $60^{\circ}$. If

$$v_1(t)=4 \cos \left(2 \pi \times 10^3 t+30^{\circ}\right) \mathrm{V},$$

write the expression appropriate for $v_2(t)$ and plot both waveforms over the time span from $-1 \mathrm{~ms}$ to $+1 \mathrm{~ms}$.

Make a table of values and graph each function. $y=2 \sqrt{x+3}+6$

The length of a steel rod at $5{\degree} \mathrm{C}$ is $12.500 \mathrm{~m}$. Calculate its length when heated to $154{\degree} \mathrm{C}$ .

Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of g and h relative to the graph of f.

$$\begin{array}{l}{f(x)=x^{3}-3 x^{2}+2} \\ {g(x)=-f(x)} \\ {h(x)=f(2 x)}\end{array}$$

Ms. White asked the 25 sixth graders in her class, "How many pets do typical oth graders in our class have?" Ms. White summarized the responses in the table.

$$\begin{array}{|c|c|}\hline \text { Number of } & {\text { Number of }} \\ \text { Students } & {\text { Pets }} \\ \hline 8 & {0} \\ \hline 10 & {1} \\ \hline 4 & {2} \\ \hline 2 & {3} \\ \hline 1 & {38} \\ \hline\end{array}$$

About how many pets does each sixth grader in Ms. White's class own? How did you make your decision?

The trim around a window has a total length of $\frac { r t } { w ^ { 3 } } \left( \frac { r t y } { w } + 2 t y - \frac { 8 } { w ^ { 2 } } \right)$ a. Simplify the expression. b. Identify the variables that cannot equal zero.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A wheelchair ramp must be constructed so that the slope is not more than 1 inch of rise for every 1 foot of run , so I used the tangent ratio to determin e the maximum angle that the ramp can make with the ground.

Gillian works from 20 to 30 hours per week during the summer. She earns $12.50 per hour. Her friend Emily also has a job. Her pay for t hours each week is given by the function e(t) = 13t, where$15 \leq t \leq 25$. a. Find the domain and range of each function. b. Compare their hourly wages and the amount they earn per week.

Find a solution $x \in \mathbf{Z}, 0 \leq x<n$, for each of the congruences $a x \equiv b(\bmod n)$. Note that, $a$ and $n$ are relatively prime.\

$$5 x+43 \equiv 15(\bmod 22)$$

Rod $AB$ moves over a small wheel at $C$ while end $A$ moves to the right with a constant velocity $\mathbf{v}_A$. Using the method of Sec. 15.9, derive expressions for the angular velocity and angular acceleration of the rod.

$(a)$ Find $x>>L$ limit of the potential of a finite uniformly charged rod and show that it coincides with that of a point charge formula. $(b)$ Why would you expect this result?