Alright, let's solve this step-by-step:
1. Understand the inverse squared relationship: In an inverse squared relationship, the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] can be expressed as:
[tex]\[
y = \frac{k}{x^2}
\][/tex]
where [tex]\( k \)[/tex] is the variation constant.
2. Identify the known values: We are given [tex]\( x = -4 \)[/tex] and [tex]\( y = 3 \)[/tex].
3. Substitute the known values into the equation: Plug [tex]\( x = -4 \)[/tex] and [tex]\( y = 3 \)[/tex] into the relationship:
[tex]\[
3 = \frac{k}{(-4)^2}
\][/tex]
4. Simplify the equation:
[tex]\[
3 = \frac{k}{16}
\][/tex]
5. Solve for [tex]\( k \)[/tex]:
[tex]\[
k = 3 \times 16 = 48
\][/tex]
The variation constant [tex]\( k \)[/tex] is [tex]\( 48 \)[/tex].
The best answer for the question, "What is the variation constant for an inverse squared relationship where [tex]\( x = -4 \)[/tex] and [tex]\( y = 3 \)[/tex]?" is:
C. 48
