Sure, let's solve the equation [tex]\( c = \frac{100 b}{L} \)[/tex] step-by-step to find the value of [tex]\( L \)[/tex] for the given values [tex]\( c = 100 \)[/tex] and [tex]\( b = 9 \)[/tex].
1. Start with the given formula:
[tex]\[
c = \frac{100 b}{L}
\][/tex]
2. Substitute the given values [tex]\( c = 100 \)[/tex] and [tex]\( b = 9 \)[/tex] into the equation:
[tex]\[
100 = \frac{100 \times 9}{L}
\][/tex]
3. Simplify the right-hand side of the equation:
[tex]\[
100 = \frac{900}{L}
\][/tex]
4. To solve for [tex]\( L \)[/tex], we need to isolate [tex]\( L \)[/tex]. To do this, multiply both sides of the equation by [tex]\( L \)[/tex]:
[tex]\[
100L = 900
\][/tex]
5. Now, solve for [tex]\( L \)[/tex] by dividing both sides of the equation by 100:
[tex]\[
L = \frac{900}{100}
\][/tex]
6. Simplify the division:
[tex]\[
L = 9
\][/tex]
Therefore, the value of [tex]\( L \)[/tex] is [tex]\( 9 \)[/tex].
