Let's go through the evaluation of the given expression step by step.
The expression to evaluate is:
[tex]\[
\frac{12 - 3 \gamma}{2} + \nu \left( \frac{2v - 4}{\gamma} \right)
\][/tex]
Given:
[tex]\[
\gamma = 3
\][/tex]
Now, let's evaluate each part of the expression:
1. Evaluate the first part: [tex]\(\frac{12 - 3 \gamma}{2}\)[/tex]
Substitute [tex]\(\gamma = 3\)[/tex]:
[tex]\[
12 - 3 \cdot 3 = 12 - 9 = 3
\][/tex]
Now, divide by 2:
[tex]\[
\frac{3}{2} = 1.5
\][/tex]
So, the first part is [tex]\(1.5\)[/tex].
2. Evaluate the second part: [tex]\(\nu \left( \frac{2v - 4}{\gamma} \right)\)[/tex]
We do not have a given value for [tex]\(\nu\)[/tex] or [tex]\(v\)[/tex] in the problem, so let’s assume the values:
[tex]\[
\nu = 1 \quad \text{and} \quad v = 2
\][/tex]
Substitute [tex]\(v = 2\)[/tex] and [tex]\(\gamma = 3\)[/tex]:
[tex]\[
2 \cdot 2 - 4 = 4 - 4 = 0
\][/tex]
Now, divide by [tex]\(\gamma\)[/tex]:
[tex]\[
\frac{0}{3} = 0
\][/tex]
Then multiply by [tex]\(\nu\)[/tex] (which is 1):
[tex]\[
1 \cdot 0 = 0
\][/tex]
So, the second part is [tex]\(0\)[/tex].
3. Sum the two parts:
[tex]\[
1.5 + 0 = 1.5
\][/tex]
Therefore, the value of the expression [tex]\(\frac{12 - 3 \gamma}{2} + \nu \left( \frac{2v - 4}{\gamma} \right)\)[/tex] for [tex]\(\gamma = 3\)[/tex] is:
[tex]\[
1.5
\][/tex]
