What is the average $Q_{10} ?$

Consider the mapping $w=z^{n}$, where n is an integer (a generalization of the mapping $w=z^{2}$). Use the polar representation of complex numbers to show that (a) Circles centred at the origin in the z plane are mapped onto circles centred at the origin in the w plane. (b) Straight lines passing through the origin intersecting with angle $\theta_{0}$ in the z plane are mapped onto straight lines passing through the origin in the w plane but intersecting at an angle $n \theta_{0}$.

Find dy/dx by implicit differentiation. $5 y^{2}-2 x^{2}=10$

Use a CAS to perform the following steps. a. Plot the equation with the implicit plotter of a CAS. Check to see that the given point P satisfies the equation. b. Using implicit differentiation, find a formula for the derivative dy/dx and evaluate it at the given point P. c. Use the slope found in part (b) to find an equation for the tangent line to the curve at P. Then plot the implicit curve and tangent line together on a single graph.

$$x \sqrt{1+2 y}+y=x^{2}, \quad P(1,0)$$

An incompressible liquid with negligible viscosity flows steadily through a horizontal pipe. The pipe diameter linearly varies from a diameter of $10 \mathrm{~cm}$ to a diameter of $2.5 \mathrm{~cm}$ over a length of $2 \mathrm{~m}$. Develop an expression for the acceleration of a fluid particle along the pipe centerline. Plot the centerline velocity and acceleration versus position along the pipe, if the inlet centerline velocity is $1 \mathrm{~m} / \mathrm{s}$.

In a laminar flow between parallel plates spaced 12 in. apart, the shear stress at the wall is 1.0 psf and the fluid viscosity 0.002 lb s/ft$^{2}$. What is the centerline velocity and the velocity gradient 1 in. from the centerline?

The number of moles of solute divided by the number of ki lograms of solvent is

(a) molarity

(b) molality.

(c) mole fraction

(d) solubility.

Define the following concentration terms and give their units: percent by mass, mole-fraction, molarity, molality. Compare their advantages and disadvantages.

Simplify. $\frac{3 e f^{2}}{2 e^{3}} \cdot \frac{4 d e^{2}}{6 e f}$

Hurricane Inc. purchased a portfolio of available-for-sale securities in 2014, its first year of operations. The cost and fair value of this portfolio on December 31, 2014, was as follows:

$$\begin{array}{lrrr} \text { Name } & \text { Number of Shares } & \text { Total Cost } & \text { Total Fair Value } \\ \hline \text { Tornado Inc. } & 800 & \$ 14,000 & \$ 15,600 \\ \text { Tsunami Corp. } & 1,250 & 31,250 & 35,000 \\ \text { Typhoon Corp. } & 2,140 & \underline{~~43,870} & \underline{~~42,800}\\ &&\underline{\underline{\$ 93,400}}&\underline{\underline{\$ 93,400}} \end{array}$$

On June 12, 2015, Hurricane purchased 1,450 shares of Rogue Wave Inc. at $45 per share plus a$100 brokerage fee.

How are unrealized gains and losses treated differently for available-for-sale securities than for trading securities?

In $1993$ and $2000$, the average prices paid for a new car were $\$ 16,871$ and $\$ 20,356$, respectively. Assume the average price increased linearly.

(a ) Find a function $f$ that models the average price paid for a new car. Graph $f$ together with the two data points. (b ) Interpret the slope of the graph of $f$. (c ) Graphically approximate the year when the average price paid would be $\$ 33,000$.

The concentration of commercially available concentrated nitric acid is 70.0 percent by mass, or 15.9 M. Calculate the density and the molality of the solution.

For the function, give the amplitude, period, vertical translation, and phase shift, as applicable.

$$y=\cot \left(\frac{x}{2}+\frac{3 \pi}{4}\right)$$

A sulfuric acid solution containing 571.6 g of

$$H_2SO_4$$

per liter of solution has a density of

$$1.329 g/ cm^3$$

Calculate the molality.