Answer
$1800$ Btu
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. $\ \ $Use the equation from step 3 to answer the problem's question.
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Let L be the heat loss (Btu),
A the area (f$t^{2})$
d the difference in temperatures,
L varies jointly (directly) as A and d, $\qquad L=kAd$
2.
$1200=k(3\times 6)(20)$
$1200=k(360)\qquad /\div 360$
$k=\displaystyle \frac{1200}{360}=\frac{10}{3}$
3.
$L=\displaystyle \frac{10}{3}Ad$
4
$A=6\times 9=54, d=10, L=?$
$L=\displaystyle \frac{10}{3}(54)(10)=1800$ Btu