To determine the constant of variation [tex]\( k \)[/tex] in an inverse variation problem, where [tex]\( y \)[/tex] varies inversely with [tex]\( x \)[/tex], you can use the relationship:
[tex]\[ y = \frac{k}{x} \][/tex]
Given:
[tex]\[ x = 3.3 \][/tex]
[tex]\[ y = 24 \][/tex]
we need to solve for [tex]\( k \)[/tex].
1. Start with the relationship for inverse variation:
[tex]\[ y = \frac{k}{x} \][/tex]
2. Substitute the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 24 = \frac{k}{3.3} \][/tex]
3. Solve for [tex]\( k \)[/tex] by multiplying both sides by [tex]\( 3.3 \)[/tex]:
[tex]\[ k = 24 \times 3.3 \][/tex]
4. Perform the multiplication:
[tex]\[ k = 79.2 \][/tex]
Thus, the correct value for the constant of variation [tex]\( k \)[/tex] is:
[tex]\[ k = 79.2 \][/tex]
So, the correct option is:
[tex]\[ k = 79.2 \][/tex]
