Certainly! Let's solve the equation step-by-step:
Given:
[tex]\[ y = \frac{x}{A \cdot B} \][/tex]
where [tex]\( y = 10.0 \)[/tex], [tex]\( x = 5.33 \)[/tex], and [tex]\( B = 8.19 \)[/tex].
We need to find the value of [tex]\( A \)[/tex].
1. Start with the given equation:
[tex]\[ y = \frac{x}{A \cdot B} \][/tex]
2. Substitute the known values into the equation:
[tex]\[ 10.0 = \frac{5.33}{A \cdot 8.19} \][/tex]
3. To isolate [tex]\( A \)[/tex], first multiply both sides by [tex]\( A \cdot 8.19 \)[/tex]:
[tex]\[ 10.0 \cdot A \cdot 8.19 = 5.33 \][/tex]
4. Simplify this equation:
[tex]\[ 81.9 \cdot A = 5.33 \][/tex]
5. Solve for [tex]\( A \)[/tex] by dividing both sides by 81.9:
[tex]\[ A = \frac{5.33}{81.9} \][/tex]
6. The result of this division is:
[tex]\[ A \approx 0.06507936507936508 \][/tex]
So, the value of [tex]\( A \)[/tex] is approximately [tex]\( 0.06507936507936508 \)[/tex].
