To find the value of [tex]\( A \)[/tex], we need to isolate [tex]\( A \)[/tex] in the given equation [tex]\( y = \sqrt{A x} \)[/tex].
Here is the step-by-step process:
1. Start with the given equation:
[tex]\[
y = \sqrt{A x}
\][/tex]
2. Square both sides of the equation to eliminate the square root:
[tex]\[
y^2 = A x
\][/tex]
3. We need to solve for [tex]\( A \)[/tex]. To do that, divide both sides of the equation by [tex]\( x \)[/tex]:
[tex]\[
A = \frac{y^2}{x}
\][/tex]
4. Substitute the given values into the equation. We are given [tex]\( y = 21.9 \)[/tex] and [tex]\( x = 16.0 \)[/tex]:
[tex]\[
A = \frac{(21.9)^2}{16.0}
\][/tex]
5. Calculate [tex]\( (21.9)^2 \)[/tex]:
[tex]\[
(21.9)^2 = 479.61
\][/tex]
6. Substitute [tex]\( 479.61 \)[/tex] for [tex]\( (21.9)^2 \)[/tex] in the equation:
[tex]\[
A = \frac{479.61}{16.0}
\][/tex]
7. Divide [tex]\( 479.61 \)[/tex] by [tex]\( 16.0 \)[/tex]:
[tex]\[
A \approx 29.975625
\][/tex]
So, the value of [tex]\( A \)[/tex] is approximately [tex]\( 29.975625 \)[/tex].
