Answer
$32^{\circ}$
Work Step by Step
Solving Variation Problems (see p. 424)
1. $\ \ $Write an equation that models the given English statement.
2. $\ \ $Substitute the given pair of values into the equation in step 1 and find the value of k, the constant of variation.
3. $\ \ $Substitute the value of k into the equation in step 1.
4. $\ \ $Use the equation from step 3 to answer the problem's question.
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Let B be the banking angle , r the radius of the turn (ft).
1.
B varies inversely as $r,\ \displaystyle \qquad B=\frac{k}{r}$
2.
$28=\displaystyle \frac{k}{4}\qquad /\times 4$
$112=k$
3.
$B=\displaystyle \frac{112}{r}$
4.
$r=3.5, B=?$
$B=\displaystyle \frac{112}{3.5}=\frac{1120}{35}=32^{\circ}$
