To solve this problem, we need to understand that the variable [tex]\( f \)[/tex] varies inversely as the square root of [tex]\( g \)[/tex]. This relationship can be expressed by the equation:
[tex]\[ f = \frac{k}{\sqrt{g}} \][/tex]
Here, [tex]\( k \)[/tex] is the constant of variation.
First, let's find the correct constant of variation using the provided values [tex]\( f = 4 \)[/tex] and [tex]\( g = 4 \)[/tex]:
[tex]\[ f = \frac{k}{\sqrt{g}} \][/tex]
Substituting the given values:
[tex]\[ 4 = \frac{k}{\sqrt{4}} \][/tex]
Since [tex]\( \sqrt{4} = 2 \)[/tex]:
[tex]\[ 4 = \frac{k}{2} \][/tex]
Solving for [tex]\( k \)[/tex]:
[tex]\[ k = 4 \times 2 \][/tex]
[tex]\[ k = 8 \][/tex]
Now, let's find the value of [tex]\( f \)[/tex] when [tex]\( g = 100 \)[/tex]:
[tex]\[ f = \frac{8}{\sqrt{100}} \][/tex]
Since [tex]\( \sqrt{100} = 10 \)[/tex]:
[tex]\[ f = \frac{8}{10} \][/tex]
[tex]\[ f = 0.8 \][/tex]
By examining Jordar's work:
[tex]\[
\begin{array}{l}
t \sqrt{g}=k \\
4(4)=k \\
16=k \\
I \sqrt{g}=16 \\
I \sqrt{100}=16 \\
10 r=16 \\
I=16
\end{array}
\][/tex]
We see the first error is in the very first step. Jordar used the equation [tex]\( t \sqrt{g} = k \)[/tex], which models a direct variation instead of an inverse variation.
Therefore, the first error in Jordar's work is:
A. He used an equation that models direct variation instead of inverse variation.
