91Ó°ÊÓ

The tension \(T\) on a string in a musical instrument varies jointly as the string's mass per unit length \(m,\) the square of its length \(l,\) and the square of its fundamental frequency \(f . \mathrm{A} 2-\mathrm{m}\) long string of mass \(5 \mathrm{gm} / \mathrm{m}\) with a fundamental frequency of 80 has a tension of \(100 \mathrm{N}\). How long should the same string be if its tension is going to be changed to \(72 \mathrm{N} ?\)

A peanut butter jar in the shape of a right circular cylinder is 4 in. high and 3 in. in diameter and sells for \(\$ 1.20 .\) If we assume that cost is proportional to volume, how much should a jar 6 in. high and 6 in. in diameter cost?

A device used in golf to estimate the distance \(d\) to a hole measures the size \(s\) that the 7 -ft pin appears to be in a viewfinder. The viewfinder uses the principle, diagrammed here, that \(s\) gets bigger when \(d\) gets smaller. If \(s=0.56\) in. when \(d=50\) yd, find an equation of variation that expresses \(d\) as a function of \(s .\) What is \(d\) when \(s=0.40 \mathrm{in} . ?\) PICTURE NOT AVAILABLE

Determine the domain and estimate the range of each function. $$ f(x)=2+\frac{x-3}{x+1} $$

Determine the domain and estimate the range of each function. $$ g(x)=\frac{2}{(x+1)^{2}}+5 $$

Graph the function given by $$ f(x)=\frac{x^{2}-9}{x-3} $$ (Hint. Determine the domain of \(f\) and simplify.)

Determine the domain and estimate the range of each function. $$ r(x)=\frac{1}{x^{2}}+\frac{1}{(x-1)^{2}} $$