Answer
$2.4\ \ $ foot-candles
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 illumination (foot-candles) , d the distance (ft).
1.
$I$ varies inversely as $d^{2},\ \displaystyle \qquad I=\frac{k}{d^{2}}$
2.
$3.75=\displaystyle \frac{k}{40^{2}}\qquad /\times 40^{2}$
$3.75(1600)=k$
$k=6000$
3.
$I=\displaystyle \frac{6000}{d^{2}}$
4.
$d=50, I=?$
$I=\displaystyle \frac{6000}{50^{2}}=2.4$ foot-candles