Sure, let's evaluate the given expression step-by-step for both sets of values.
The expression we need to evaluate is:
[tex]\[
\frac{x}{3} + 3y^2 + 1
\][/tex]
Let's start with the first set of values: [tex]\(x = 21\)[/tex] and [tex]\(y = -2\)[/tex].
### Evaluation when [tex]\(x = 21\)[/tex] and [tex]\(y = -2\)[/tex]:
1. Substitute [tex]\(x = 21\)[/tex] and [tex]\(y = -2\)[/tex] into the expression:
[tex]\[
\frac{21}{3} + 3(-2)^2 + 1
\][/tex]
2. Calculate [tex]\(\frac{21}{3}\)[/tex]:
[tex]\[
\frac{21}{3} = 7
\][/tex]
3. Calculate [tex]\(3(-2)^2\)[/tex]:
[tex]\[
(-2)^2 = 4 \quad \Rightarrow \quad 3 \times 4 = 12
\][/tex]
4. Add the results of the individual calculations:
[tex]\[
7 + 12 + 1 = 20
\][/tex]
So, the value of the expression when [tex]\(x = 21\)[/tex] and [tex]\(y = -2\)[/tex] is [tex]\(\boxed{20.0}\)[/tex].
### Evaluation when [tex]\(x = 3\)[/tex] and [tex]\(y = 4\)[/tex]:
1. Substitute [tex]\(x = 3\)[/tex] and [tex]\(y = 4\)[/tex] into the expression:
[tex]\[
\frac{3}{3} + 3(4)^2 + 1
\][/tex]
2. Calculate [tex]\(\frac{3}{3}\)[/tex]:
[tex]\[
\frac{3}{3} = 1
\][/tex]
3. Calculate [tex]\(3(4)^2\)[/tex]:
[tex]\[
(4)^2 = 16 \quad \Rightarrow \quad 3 \times 16 = 48
\][/tex]
4. Add the results of the individual calculations:
[tex]\[
1 + 48 + 1 = 50
\][/tex]
So, the value of the expression when [tex]\(x = 3\)[/tex] and [tex]\(y = 4\)[/tex] is [tex]\(\boxed{50.0}\)[/tex].
In conclusion, the evaluated expressions are:
- For [tex]\(x = 21\)[/tex] and [tex]\(y = -2\)[/tex], the result is [tex]\(20.0\)[/tex].
- For [tex]\(x = 3\)[/tex] and [tex]\(y = 4\)[/tex], the result is [tex]\(50.0\)[/tex].
