(a) Based on Tiresias' prediction, which heroic qualities will Odysseus need to rely upon as he continues his journey? Explain.

Two workers carry a uniform $15.0$-ft plank that weighs $22.0 \mathrm{lb}$. A load of blocks weighing $165\ \mathrm{lb}$ is located $7.00\ \mathrm{ft}$ from the first worker. How much force does each employee need to use to lift the board and load?

A steel control rod is 5.5 ft long and must not stretch more than 0.04 in. when a 2-kip tensile load is applied to it. Knowing that $E=29 \times 106$ psi, determine (a) the smallest diameter rod that should be used, (b) the corresponding normal stress caused by the load.

A cast-iron tube is used to support a compressive load. Knowing that $E=69 \mathrm{GPa}$ and that the maximum allowable change in length is $0.025 \%$. Actermine $(a)$ the maximum normal stress in the tube, $(b)$ the minimum wall thickness for a load of $7.2 \mathrm{kN}$ if the outside diameter of the tube is $50 \mathrm{~mm}$.

Use the theorem to show that there is at least one root of the equation in the given interval.

$$x^3-2 x-1=0 ; \quad(0,2)$$

Explain why the following statement does not need to be justified. “The midpoint of a segment is a point on the segment that divides it into two congruent segments.”

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) $g(x)=2 x^{3}+x^{2}+1$

Calculate $\frac{d y}{d x}$. You need not expand your answers. $y=\frac{3 x-1}{(x-5)(x-4)(x-1)}$

a) Determine the load impedance for the circuit shown in Fig. that will result in maximum average power being transferred to the load if $\omega=5 \mathrm{krad} / \mathrm{s}$. b) Determine the maximum average power delivered to the load from part (a) if $v_g=$ $80 \cos 5000 t \mathrm{~V}$. c) Repeat part (a) when $Z_{\mathrm{L}}$. consists of two components from Appendix $\mathrm{H}$ whose values yield a maximum average power closest to the value calculated in part (b).

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) $g(x)=\frac{x^{3}}{x^{2}-4}$

Use one of the formulas for special series to find the sum of the series.

$$\sum_{i=1}^{42} 1$$

A propped cantilever beam is subjected to uniform load $q$. The beam has flexural rigidity $E I=2000\ \mathrm{kip}-\mathrm{ft}^2$ and the length of the beam is $10 \mathrm{ft}$. Find the intensity $q$ of the distributed load if the maximum displacement of the beam is $\delta_{\max }=0.125\ \mathrm{in}$.

There are 1,012 souvenir paperweights that need to be packed in boxes. Each box will hold 12 paperweights. How many boxes will be needed?

A uniform rope of cross-sectional area 0.50 cm² breaks when the tensile stress in it reaches

$$6.00 × 10^6 N/m^2.$$

(a) What is the maximum load that can be lifted slowly at a constant speed by the rope? (b) What is the maximum load that can be lifted by the rope with an acceleration of 4.00 m/s²?