Select the correct answer.

What is the value of the expression when [tex]s=2[/tex] and [tex]t=-1.5[/tex]?

[tex]-3\left|5-s^3\right|+3t[/tex]

A. 13.5
B. -4.5
C. -13.5
D. 4.5



Answer :

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]

Answer: your answer is option d) -13.5

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