Questions: In this formula, L=ab/(m+h), what happens to the value of L if a, m, and h stay the same, but the value of b triples? L triples L quadruples (four times as much) L decreases L doubles L stays the same

In this formula, L=ab/(m+h), what happens to the value of L if a, m, and h stay the same, but the value of b triples?

L triples
L quadruples (four times as much)
L decreases
L doubles
L stays the same

Transcript text: In this formula, $L=\frac{a b}{m+h}$, what happens to the value of $L$ if $a, m$, and $h$ stay the same, but the value of $b$ triples? $L$ triples $L$ quadruples (four times as much) $L$ decreases $L$ doubles $L$ stays the same

Solution

Solution Steps

To determine what happens to the value of $ L $ when $ b $ triples, while $ a $, $ m $, and $ h $ remain constant, we can analyze the formula $ L = \frac{a b}{m + h} $. Since $ a $, $ m $, and $ h $ are constant, the only variable changing is $ b $. If $ b $ triples, the numerator of the fraction $ a b $ also triples, which means $ L $ will triple as well.

Step 1: Initial Calculation of $ L $

Given the formula $ L = \frac{a b}{m + h} $, we substitute the initial values:

$ a = 1 $
$ b_{\text{initial}} = 1 $
$ m = 1 $
$ h = 1 $

Calculating $ L_{\text{initial}} $: \[ L_{\text{initial}} = \frac{1 \cdot 1}{1 + 1} = \frac{1}{2} = 0.5 \]

Step 2: Calculation of New $ L $ After Tripling $ b $

Now, we triple the value of $ b $: \[ b_{\text{new}} = 3 \cdot b_{\text{initial}} = 3 \cdot 1 = 3 \]

Calculating $ L_{\text{new}} $: \[ L_{\text{new}} = \frac{1 \cdot 3}{1 + 1} = \frac{3}{2} = 1.5 \]

Step 3: Determine the Change in $ L $

To find the change in $ L $, we calculate the ratio of the new $ L $ to the initial $ L $: \[ \text{change in } L = \frac{L_{\text{new}}}{L_{\text{initial}}} = \frac{1.5}{0.5} = 3.0 \]

This indicates that $ L $ triples when $ b $ is tripled.