Sure, let's break down the expression step-by-step for [tex]\( s = 2 \)[/tex] and [tex]\( t = -1.5 \)[/tex].
The expression we need to evaluate is:
[tex]\[
-3\left|5 - s^3\right| + 3t
\][/tex]
1. Calculate [tex]\( s^3 \)[/tex]:
Since [tex]\( s = 2 \)[/tex],
[tex]\[
s^3 = 2^3 = 8
\][/tex]
2. Calculate the inside of the absolute value:
[tex]\[
5 - s^3 = 5 - 8 = -3
\][/tex]
3. Calculate the absolute value:
[tex]\[
\left|5 - s^3\right| = \left|-3\right| = 3
\][/tex]
4. Multiply the absolute value term by -3:
[tex]\[
-3 \times \left|5 - s^3\right| = -3 \times 3 = -9
\][/tex]
5. Calculate the term involving [tex]\( t \)[/tex]:
Since [tex]\( t = -1.5 \)[/tex],
[tex]\[
3t = 3 \times (-1.5) = -4.5
\][/tex]
6. Combine the two terms:
[tex]\[
-9 + (-4.5) = -9 - 4.5 = -13.5
\][/tex]
The value of the expression when [tex]\( s = 2 \)[/tex] and [tex]\( t = -1.5 \)[/tex] is:
[tex]\[
\boxed{-13.5}
\][/tex]
