To find the value of the expression [tex]\( 2x^3 + 3y^2 - 17 \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( y = 4 \)[/tex], we can follow these steps:
1. First, substitute [tex]\( x = 3 \)[/tex] into the expression:
[tex]\[
2(3)^3 + 3y^2 - 17
\][/tex]
2. Calculate [tex]\( 3^3 \)[/tex]:
[tex]\[
3^3 = 27
\][/tex]
3. Multiply by 2:
[tex]\[
2 \cdot 27 = 54
\][/tex]
4. Replace [tex]\( y \)[/tex] with 4:
[tex]\[
54 + 3(4)^2 - 17
\][/tex]
5. Calculate [tex]\( 4^2 \)[/tex]:
[tex]\[
4^2 = 16
\][/tex]
6. Multiply by 3:
[tex]\[
3 \cdot 16 = 48
\][/tex]
7. Add the values obtained from steps 3 and 6:
[tex]\[
54 + 48 = 102
\][/tex]
8. Subtract 17:
[tex]\[
102 - 17 = 85
\][/tex]
So, the value of the expression [tex]\( 2x^3 + 3y^2 - 17 \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( y = 4 \)[/tex] is [tex]\( 85 \)[/tex].
Therefore, the correct answer is [tex]\( 85 \)[/tex].
