To solve the given expression [tex]\( 12e + 2 \times \frac{3}{4} \times \sqrt{17} \)[/tex], we will break it down into manageable steps and simplify each part.
Given:
[tex]\[ 12e + 2 \times \frac{3}{4} \times \sqrt{17} \][/tex]
1. Evaluate [tex]\( 12e \)[/tex]:
Here, [tex]\( e \)[/tex] is the base of the natural logarithm and its approximate value is [tex]\( 2.71828 \)[/tex]. Thus:
[tex]\[
12e \approx 12 \times 2.71828 = 32.61936
\][/tex]
2. Evaluate [tex]\( 2 \times \frac{3}{4} \times \sqrt{17} \)[/tex]:
- First, calculate [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
- Next, find the square root of 17. The approximate value for [tex]\(\sqrt{17}\)[/tex] is [tex]\(4.12311\)[/tex].
- Now compute the product [tex]\(2 \times 0.75 \times \sqrt{17}\)[/tex]:
[tex]\[
2 \times 0.75 = 1.5
\][/tex]
Then:
[tex]\[
1.5 \times 4.12311 \approx 6.184665
\][/tex]
3. Add the two results together:
Now, add the two parts:
[tex]\[
32.61936 + 6.184665 \approx 38.804025
\][/tex]
Therefore, the evaluated result for the given expression [tex]\( 12e + 2 \times \frac{3}{4} \times \sqrt{17} \)[/tex] is approximately:
[tex]\[
38.80404037993503
\][/tex]
The final answer is:
[tex]\[
38.80404037993503
\][/tex]
