The number of feet between 2 objects varies directly as the number of miles. If the distance between 2 objects is 2 1/2 miles or 13,200 feet how many feet are equivalent to a distance of 7 miles

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21-10-2017
Mathematics

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The number of feet between 2 objects varies directly as the number of miles. If the distance between 2 objects is 2 1/2 miles or 13,200 feet how many feet are equivalent to a distance of 7 miles

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jdoe0001 jdoe0001 · Answer 1 · 2017-10-21T21:36:47+02:00

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \stackrel{feet}{f}=k\stackrel{miles}{m}\textit{ we also know that } \begin{cases} m=2\frac{1}{2}\\ f=13200 \end{cases}\implies 13200=k\cdot 2\frac{1}{2} \\\\\\ 13200=k\cfrac{5}{2}\implies \cfrac{13200\cdot 2}{5}=k\implies 5280=k \\\\\\ \boxed{f=5280m} \\\\\\ \textit{when m = 7, what is \underline{f}?}\qquad \qquad f=5208(7)[/tex]