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Write each formula as an English phrase using the word varies or proportional. \(r=\frac{d}{t},\) where \(r\) is the speed when traveling \(d\) miles in \(t\) hours?

Provide a short answer to each question. What is the equation of the vertical asymptote of the graph of \(y=\frac{1}{x-3}+2 ?\) of the horizontal asymptote?

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the interval of the domain for which the function is increasing and (f) the interval for which the function is decreasing. See Examples \(1-4\). $$f(x)=(x-2)^{2}$$

Solve each problem.Circumference of a Circle The circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11 in.?

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. A. The \(x\) -intercept is \(-3\) B. The \(y\) -intercept is 5 C. The horizontal asymptote is \(y=4\) D. The vertical asymptote is \(x=-1\) E. There is a "hole" in its graph at \(x=-4\) F. The graph has an oblique asymptote. G. The \(x\) -axis is its horizontal asymptote, and the \(y\) -axis is not its vertical asymptote. H. The \(x\) -axis is its horizontal asymptote, and the \(y\) -axis is its vertical asymptote. $$f(x)=\frac{1}{x+4}$$

Solve each problem.The illumination produced by a light source varies inversely as the square of the distance from the source. The illumination of a light source at \(5 \mathrm{m}\) is 70 candela. What is the illumination \(12 \mathrm{m}\) from the source?

Solve each problem.The force of the wind blowing on a vertical surface varies jointly as The area of the surface and the square of the velocity. If a wind of 40 mph exerts a force of 50 lb on a surface of \(\frac{1}{2} \mathrm{ft}^{2},\) how much force will a wind of 80 mph place on a surface of \(2 \mathrm{ft}^{2} ?\)

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. A. The \(x\) -intercept is \(-3\) B. The \(y\) -intercept is 5 C. The horizontal asymptote is \(y=4\) D. The vertical asymptote is \(x=-1\) E. There is a "hole" in its graph at \(x=-4\) F. The graph has an oblique asymptote. G. The \(x\) -axis is its horizontal asymptote, and the \(y\) -axis is not its vertical asymptote. H. The \(x\) -axis is its horizontal asymptote, and the \(y\) -axis is its vertical asymptote. $$f(x)=\frac{x+3}{x-6}$$

Sports Arena Construction The roof of a new sports arena rests on round concrete pillars. The maximum load a cylindrical column of circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. The arena has 9 -m-tall columns that are \(1 \mathrm{m}\) in diameter and will support a load of 8 metric tons. How many metric tons will be supported by a column 12 m high and \(\frac{2}{3} \mathrm{m}\) in diameter?

The federal government has developed the body mass index (BMI) to determine ideal weights. A person's BMI is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches. (A BMI of 19 to 25 corresponds to a healthy weight.) A 6 -foot-tall person weighing 177 Ib has BMI \(24 .\) Find the BMI (to the nearest whole number) of a person whose weight is 130 lb and whose height is 66 in.