A 200-g block is pressed against a spring of force constant 1.40 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at $60.0^{\circ}$ to the horizontal. Using energy considerations, determine how far up the incline the block moves from its initial position before it stops (a) if the ramp exerts no friction force on the block and (b) if the coefficient of kinetic friction is 0.400.

Find all subsets of set $\{5,12,13,14\}$

Dion's long distance phone bill was $\$$ 13.80. His long-distance calls cost$\

$$0.05 per minute. Write and solve an equation to find the number of minutes he was charged for. Show that your answer is reasonable.$$

In Fig. 31–13, how much is the dc voltage across a. the output coupling capacitor, $C_\text{out}$? b. the load, $R_\text{L}$?

Sketch the graph of $f(x)=2-2 \sin x$ on the interval $[0, \pi / 2]$.

Write the distance $d$ from the origin to a point on the graph of $f$ as a function of $x$. Use a graphing utility to graph $d$ and find the minimum distance.

Solve the equation.

$$\log x^2=\log (-3 x-2)$$

Prove that if $d=(a, b), a \mid c$, and $b \mid c$, then $a b \mid c d$.

Graph the set.

$$[-4,6) \cup[0,8)$$

Six $4.8~ \mu \mathrm{F}$ capacitors are connected in parallel. What is the equivalent capacitance?

In this given problem, graph the given inequality.

$$x \geq 3(x+1)+y$$

Solve. Write the solution set in set-builder notation.

$$5 x-4<2 x+5$$

Compare the ratios.

$$\frac { 9 } { 2 } \square \frac { 10 } { 7 }$$

The designers of a water park are creating a new slide and have sketched some preliminary drawings. The length of the ladder is 30 feet, and its angle of elevation is $60^{\circ}$.

(a) Find the height h of the slide.

(b) Find the angle of depression $\theta$ from the top of the slide to the end of the slide at the ground in terms of the horizontal distance d the rider travels.

(c) The angle of depression of the ride is bounded by safety restrictions to be no less than $25^{\circ}$ and not more than $30^{\circ}$. Find an interval for how far the rider travels horizontally.

What electric potential difference exists across a $5.4-\mu \mathrm{F}$ capacitor that has a charge of $8.1 \times 10^{-4} \mathrm{C}$?