Question

The number of hours (H) that a candle will burn increases when the length of the candle (L) increases. Write the correct equation for this scenario, and solve for the number of hours when the length is 2. Length Hours 15 3 20 4

Answer 1

H = .2L; H = .4

Explanation:

Answer 2

`\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}\\\\ -------------------------------\\\\ %. Length Hours 15 3 20 4 \begin{array}{ccllll} length&hours\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 15&3\\ 20&4 \end{array}\\\\ -------------------------------\\\\`


`\bf \textit{H increases as L increases}\implies H=kL \\\\\\ \textit{from the table above, we also know that } \begin{cases} L=15\\ H=3 \end{cases} \\\\\\ 3=k15\implies \cfrac{3}{15}=k\implies \cfrac{1}{5}=k\quad thus\quad \boxed{H=\cfrac{1}{5}L} \\\\\\ \textit{now, what is H when L = 2}\qquad H=\cfrac{1}{5}\implies \cdot 2`