91Ó°ÊÓ

Except in scieptific work, temperafure is usually measured in degrees Fahrenhcit (F) or in degrees Celsius (C). The relation between \(\mathrm{F}\) and \(\mathrm{C}\) is linear. (In the equation that relates \(\mathrm{F}\) to \(\mathrm{C},\) both \(\mathrm{F}\) and \(\mathrm{C}\) appear to the first degrec.) The frcezing point of water in the Fahrenheit scale is \(32^{\circ} \mathrm{F} ;\) in the Celsius scale it is \(0^{\circ} \mathrm{C}\). The boiling point of water in the Fahrenheit. scale is \(212^{\circ} \mathrm{F} ;\) in the Celsius scale it is \(100^{\circ} \mathrm{C}\). Find an equation that gives the Fahrenheit temperature \(F\) in terms of the Celsius temperature C. Is there a temperature at which the Fahrenheit and Celsius readings are equal? If so, find it.

Evaluate. \(5 !\).

Evaluate. \(\frac{5 !}{8 !}\).

Set \(f(x)=\sin x\). (a) Using a graphing utility, graph \(g(x)=f(x-c)\) for \(c=-\frac{1}{2} \pi,-\frac{1}{4} \pi, \frac{1}{3} \pi, \frac{1}{2} \pi, \pi .2 \pi .\) Compare your graphs with the graph of \(f\). (b) Now graph \(g(x)=a f(b x-c)\) for several values of \(a\). \(b\). \(c .\) Describe the effect of \(a\), the effect of \(b\), the effect of \(c\).

Express the volume of a cube as a function of the total surface area.

Evaluate. \(\frac{8 !}{3 ! 5 !}\).

Sketch the graph of the function. $$f(x)=\sqrt{\sin ^{2} x}$$.

Express the surface area of a cube as a function of the length of the diagonal of a face.

Sketch the graph of the function. $$g(x)=-2 \cos x$$.

Express the volume of a cube as a function of one of the diagonals.