91Ó°ÊÓ

The loudness of sound is measured in decibels in honor of Alexander Graham Bell (1847-1922), inventor of the telephone. If the variation in pressure is \(P\) pounds per square inch, then the loudness \(L\) in decibels is $$ L=20 \log _{10}(121.3 P) $$ Find the variation in pressure caused by music at 115 decibels.

In Problems 29-34, find an equation for each line. Then write your answer in the form \(A x+B y+C=0 .\) Through \((4,1)\) and \((8,2)\)

plot the graphs of both equations on the same coordinate plane. Find and label the points of intersection of the two graphs. $$ \begin{array}{l} y=-2 x+3 \\ y=3 x^{2}-3 x+12 \end{array} $$

Let \(p\) denote the perimeter of an equilateral triangle. Find a formula for \(A(p)\), the area of such a triangle.

Verify that $$ \frac{\pi}{4}=4 \tan ^{-1}\left(\frac{1}{5}\right)-\tan ^{-1}\left(\frac{1}{239}\right) $$ a result discovered by John Machin in 1706 and used by him to calculate the first 100 decimal places of \(\pi .\)

change each rational number to a decimal by performing long division. $$ \frac{5}{17} $$

In Problems \(35-38\), find the slope and \(y\) -intercept of each line. \(3 y=-2 x+1\)

A right triangle has a fixed hypotenuse of length \(h\) and one leg that has length \(x\). Find a formula for the length \(L(x)\) of the other leg.

In the equally tempered scale to which keyed instruments have been tuned since the days of J.S. Bach \((1685-1750)\), the frequencies of successive notes \(\mathrm{C}, \mathrm{C} \\#, \mathrm{D}, \mathrm{D} \\#, \mathrm{E}, \mathrm{F}, \mathrm{F} \\#, \mathrm{G}, \mathrm{G}\|, \mathrm{A}, \mathrm{A}\|, \mathrm{B}\) C form a geometric sequence (progression), with \(\bar{C}\) having twice the frequency of \(\mathrm{C}\) (C# is read \(\mathrm{C}\) sharp and \(\overline{\mathrm{C}}\) indicates one octave above \(\mathrm{C}\) ). What is the ratio \(r\) between the frequencies of successive notes? If the frequency of \(A\) is 440 , find the frequency of \(\bar{C}\).

plot the graphs of both equations on the same coordinate plane. Find and label the points of intersection of the two graphs. $$ \begin{array}{l} y=x \\ x^{2}+y^{2}=4 \end{array} $$