To find the value of the expression [tex]\(\frac{5}{x} + 2x^2\)[/tex] when [tex]\(x = 3\)[/tex], follow these steps:
1. Substitute [tex]\(x = 3\)[/tex] into the expression.
[tex]\[ \frac{5}{3} + 2 \cdot 3^2 \][/tex]
2. Evaluate each part of the expression separately:
- First, calculate [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[ \frac{5}{3} = 1.6666666666666667 \][/tex]
- Next, calculate [tex]\(2 \cdot 3^2\)[/tex]:
- Begin with [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
- Then, multiply by 2:
[tex]\[ 2 \cdot 9 = 18 \][/tex]
3. Add the results from the two parts together:
[tex]\[ 1.6666666666666667 + 18 \][/tex]
[tex]\[ = 19.666666666666668 \][/tex]
The value of the expression [tex]\(\frac{5}{x} + 2x^2\)[/tex] when [tex]\(x = 3\)[/tex] is approximately:
[tex]\[ 19.666666666666668 \][/tex]
Among the given options, 20 is the closest to this value. Therefore:
The answer is [tex]\( \boxed{20} \)[/tex].
