91Ó°ÊÓ

Find the domain of each function. $$ f(x)=\sqrt{x^{2}-5 x-24} $$

Write the standard form and the general form of the equation of each circle. Passing through \((-7,2)\) and \((1,2) ;\) these points are endpoints of the diameter, the line that passes through the circle's center.

In Exercises, if \(f(x)=\) int \((x),\) find each function value. $$f(1.06)$$

Find a linear equation in slope-intercept form that models the given description. Describe what each variable in your model represents. Then use the model to make a prediction. In \(1995,\) the average temperature of Earth was \(57.7^{\circ} \mathrm{F}\) and has increased at a rate of \(0.01^{\circ} \mathrm{F}\) per year since then.

Explain how to use the general form of a line's equation to find the line's slope and \(y\) -intercept.

You will be developing functions that model given conditions. You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. Write the total time, \(T,\) in hours, devoted to your outgoing and return trips as a function of your rate on the outgoing trip. Then find and interpret \(T(30) .\) Hint: Time traveled \(=\frac{\text { Distance traveled }}{\text { Rate of travel }}\)

You will be developing functions that model given conditions. A chemist working on a flu vaccine needs to mix a \(10 \%\) sodium-iodine solution with a \(60 \%\) sodium-iodine solution to obtain a 50 -milliliter mixture. Write the amount of sodium iodine in the mixture, \(S,\) in milliliters, as a function of the number of milliliters of the \(10 \%\) solution used. Then find and interpret \(S(30)\)

A cargo service charges a flat fee of \(\$ 4\) plus \(\$ 1\) for each pound or fraction of a pound to mail a package. Let \(C(x)\) represent the cost to mail a package that weighs \(x\) pounds. Graph the cost function on the interval \((0,5].\)