In this exercise, sketch the graph of the equation.

$$x^2+(y-8)^2=25$$

An older type of thermostat used in furnace and heat pump control is described earlier. The glass vial tilts back and forth so that electrical contacts are made via the mercury (an electrically conducting liquid metal), and the furnace or heat pump is turned off and on. Discuss why the vial tilts back and forth. (Newer thermostats are electronic.)

In this exercise, sketch the graph of the inequality.

$$y \geq 6-\ln (x+5)$$

In this exercise, factor the expression completely.

$$5 x^2+7 x-24$$

What is the maximum electrical work that can be obtained from $6.54 \mathrm{~g}$ of zinc metal that reacts in a Daniell cell, described in the chapter opening, whose cell potential is $1.10 \mathrm{~V}$ ? The overall cell reaction is

$$\mathrm{Zn}(s)+\mathrm{Cu}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Cu}(s)$$

An electrical cable consists of 125 strands of fine wire, each having $2.65-\mu \Omega$ resistance. The same potentiai difference is applied between the ends of each strand and resuits in a total current of $750 \mathrm{~mA}$. (a) What is the current in each strand? (b) What is the applied potential difference? (c) What is the resistance of the cable?

In this exercise, sketch the graph of the equation.

$$y=\dfrac{4}{1-3 x}$$

An electrical technician requires a capacitance of $2 \mu \mathrm{F}$ in a circuit across a potential difference of $1 \mathrm{kV}$. A large number of $1 \mu \mathrm{F}$ capacitors are available to him each of which can withstand a potential difference of not more than $400 \mathrm{~V}$. Suggest a possible arrangement that requires the minimum number of capacitors.

In this exercise, sketch the graph of the equation.

$$y=2 x^2-7 x-30$$

A 33% efficient power plant puts out 850 MW of electrical power. Cooling towers are used to take away the exhaust heat. If the air temperature is allowed to rise $7.0 \mathrm{C}^{\circ}$, estimate what volume of air $(\mathrm{km}^{3})$ is heated per day. Will the local climate be heated significantly?

A sound speaker is rated at a voltage of P = 120.00 V and a current of I = 10.00 A. Electrical power consumption is P = IV. To test the speaker, a signal of a sine wave is applied to the speaker. Assuming that the sound wave moves as a spherical wave and that all of the energy applied to the speaker is converted to sound energy, how far from the speaker is the intensity equal to 3.82 W/m²?

In this exercise, evaluate the expression without the aid of a calculator.

$$\arctan (-1)$$

You are given a sealed box with two electrical terminals. The box contains a $5.00~\Omega$ resistor in series with either an inductor or a capacitor. When you attach an ac generator with an rms voltage of $0.750 \mathrm{~V}$ to the terminals of the box, you find that the current increases with increasing frequency. Does the box contain an inductor or a capacitor? Explain.

If two electrical resistors with resistances $R_1$ and $R_2$ are connected in parallel (see the figure), then the total resistance in the circuit is given by the complex rational expression

$$\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}} \text {. }$$

Simplify the expression. Then find the total resistance if $R_1=10 \mathrm{ohms}$ and $R_2=20 \mathrm{ohms}$.