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 $50 \mathrm{~mm}$.

Find the Maclaurin series for the function. Use the table of power series for elementary functions. $g(x)=\arctan 5 x$

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

Explain why you may need less than one liter of water to prepare a molar solution of one liter.

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

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

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).

(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 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?

Use the geometric series

$$f ( x ) = \frac { 1 } { 1 - x } = \sum _ { k = 0 } ^ { \infty } x ^ { k }$$

, for |x|<1, to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.

What factor would you need to multiply by $(3d + 1)$ to get $9 d^{2}+6 d+1 ?$

How many packages of each does Loren need to buy to have 24 fish fillets and 24 buns?

A child’s electronic toy is supplied by three 1.58-V alkaline cells having internal resistances of $0.0200 \Omega$ in series with a 1.53-V carbon-zinc dry cell having a $0.100 - \Omega$ internal resistance. The load resistance is $10.0 \Omega$. (a) Draw a circuit diagram of the toy and its batteries. (b) What current flows? (c) How much power is supplied to the load? (d) What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?