Answer
$90 \ \ $ miliroentgens / hour
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 $I$ be the intesity (miliroentgens/h) , d the distance (m).
1.
$I$ varies inversely as $d^{2},\ \displaystyle \qquad I=\frac{k}{d^{2}}$
2.
$62.5=\displaystyle \frac{k}{3^{2}}\qquad /\times 3^{2}$
$62.5(9)=k$
$k=562.5$
3.
$I=\displaystyle \frac{562.5}{d^{2}}$
4.
$d=2.5,I=?$
$I=\displaystyle \frac{562.5}{(2.5)^{2}}=90 $ (miliroentgens/h)
