Let's solve the equation [tex]\( Y = -n^3 + \frac{3}{4} a \)[/tex] for the variable [tex]\( a \)[/tex].
1. Start with the equation:
[tex]\[
Y = -n^3 + \frac{3}{4} a
\][/tex]
2. Add [tex]\( n^3 \)[/tex] to both sides to start isolating [tex]\( a \)[/tex]:
[tex]\[
Y + n^3 = \frac{3}{4} a
\][/tex]
3. To further isolate [tex]\( a \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\( \frac{3}{4} \)[/tex], which is [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[
\left(\frac{4}{3}\right) (Y + n^3) = a
\][/tex]
4. Simplify the right-hand side:
[tex]\[
a = \frac{4}{3} (Y + n^3)
\][/tex]
Thus, the solution for [tex]\( a \)[/tex] is:
[tex]\[
a = \frac{4}{3} (Y + n^3)
\][/tex]
This is the expression for [tex]\( a \)[/tex] in terms of [tex]\( Y \)[/tex] and [tex]\( n \)[/tex].
