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Chapter 1: Problem 28
Show that the points form the vertices of the indicated polygon. $$\text { Isosceles triangle: }(2,3),(4,9),(-2,7)$$
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Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring. A force of 220 newtons stretches a spring 0.12 meter. What force is required to stretch the spring 0.16 meter?
The frequency of vibrations of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 440 vibrations per second. Find the frequency of a string that has 1.25 times as much tension and is 1.2 times as long.
The percents \(p\) of prescriptions filled with generic drugs in the United States from 2004 through 2010 (see figure) can be approximated by the model \(p(t)=\left\\{\begin{array}{ll}4.57 t+27.3, & 4 \leq t \leq 7 \\ 3.35 t+37.6, & 8 \leq t \leq 10\end{array}\right.\) where \(t\) represents the year, with \(t=4\) corresponding to \(2004 .\) Use this model to find the percent of prescriptions filled with generic drugs in each year from 2004 through \(2010 .\) (Source: National Association of Chain Drug Stores) (GRAPH CAN'T COPY)
Sketch the graph of the function. $$g(x)=\left\\{\begin{array}{ll}x+6, & x \leq-4 \\\\\frac{1}{2} x-4, & x>-4\end{array}\right.$$
Write a sentence using the variation terminology of this section to describe the formula. Area of a triangle: \(A=\frac{1}{2} b h\)
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