Solve the following equation for [tex]\( a \)[/tex]. Be sure to take into account whether a letter is capitalized or not.

[tex]\[ Y = -n^3 + \frac{3}{4} a \][/tex]

Answer:

[tex]\[ a = \][/tex]

[tex]\(\square\)[/tex]

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Answer :

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].