To solve the expression [tex]\(12e + 2 + \frac{3}{4} \sqrt{19}\)[/tex], let's break it down step-by-step:
1. Calculate [tex]\(12e\)[/tex]:
The constant [tex]\(e\)[/tex] (Euler's number) is approximately 2.71828. Thus,
[tex]\[
12e \approx 12 \times 2.71828 = 32.61938194150854
\][/tex]
2. Add the constant term 2:
The next term in the expression is 2. So, we have:
[tex]\[
32.61938194150854 + 2 = 34.61938194150854
\][/tex]
3. Calculate [tex]\(\frac{3}{4} \sqrt{19}\)[/tex]:
First, find the square root of 19, which is approximately 4.3589. Multiply this by [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[
\sqrt{19} \approx 4.3589
\][/tex]
[tex]\[
\frac{3}{4} \sqrt{19} \approx \frac{3}{4} \times 4.3589 = 3.2691742076555057
\][/tex]
4. Add [tex]\(\frac{3}{4} \sqrt{19}\)[/tex] to the previous result:
Combine the values obtained in steps 2 and 3:
[tex]\[
34.61938194150854 + 3.2691742076555057 = 37.888556149164046
\][/tex]
Therefore, the value of the expression [tex]\(12e + 2 + \frac{3}{4} \sqrt{19}\)[/tex] is approximately:
[tex]\[
\boxed{37.888556149164046}
\][/tex]
