Question

the elongation e of a spring balance varies directly with the applied weight w (see the figure). if e = 5 when w = 18, find e when w = 13. e = □ (type an integer or a simplified fraction.)

Explanation:

Step1: Write the direct - variation formula

Since $E$ varies directly with $W$, the formula is $E = k\times W$, where $k$ is the constant of variation.
We know that when $E = 5$ and $W = 18$, we can find $k$ by substituting these values into the formula: $5=k\times18$, so $k=\frac{5}{18}$.

Step2: Find $E$ when $W = 13$

Now that we have $k=\frac{5}{18}$, we substitute $W = 13$ into the formula $E = k\times W$.
$E=\frac{5}{18}\times13=\frac{65}{18}$

Answer:

$\frac{65}{18}$