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.

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

You need to find the LCM of 13 and 14. Would you rather list their multiples or use their prime factorizations? Explain.

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

A fixed-end column with circular cross section is acted on by compressive axial load $P$. The $18 -\text{ft}$-long-column has an outer diameter of $5\ \text{in.}$, a thickness of $0.5\ \text{in.}$, and is made of aluminum with a modulus of elasticity of $10,000\ \mathrm{ksi}$. Find the buckling load of the column.

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

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

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 $\delta_{\max }=0.125\ \mathrm{in}$.

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

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

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 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 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 × 10⁶ psi, determine (a) the smallest diameter rod that should be used, (b) the corresponding normal stress caused by the load.

What is the sequence of buttons you need to press to enter the number $5.8 \times 10^{-8}$ into a scientific calculator?