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Sagot :
To determine the value of [tex]\( y \)[/tex] when [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex] given the equation [tex]\( y = 3ab + 2b^3 \)[/tex], we will substitute these values into the equation and perform the necessary calculations step-by-step.
1. Substitute [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex] into the equation [tex]\( y = 3ab + 2b^3 \)[/tex]:
[tex]\[ y = 3(1)(2) + 2(2)^3 \][/tex]
2. Calculate the first term [tex]\( 3ab \)[/tex]:
[tex]\[ 3ab = 3 \cdot 1 \cdot 2 = 6 \][/tex]
3. Calculate the second term [tex]\( 2b^3 \)[/tex]:
[tex]\[ 2b^3 = 2 \cdot (2)^3 \][/tex]
Since [tex]\( (2)^3 = 2 \cdot 2 \cdot 2 = 8 \)[/tex]:
[tex]\[ 2b^3 = 2 \cdot 8 = 16 \][/tex]
4. Add the two terms together to find [tex]\( y \)[/tex]:
[tex]\[ y = 6 + 16 = 22 \][/tex]
Therefore, when [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex], the value of [tex]\( y \)[/tex] is [tex]\( 22 \)[/tex].
So, the correct answer is:
[tex]\[ 22 \][/tex]
1. Substitute [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex] into the equation [tex]\( y = 3ab + 2b^3 \)[/tex]:
[tex]\[ y = 3(1)(2) + 2(2)^3 \][/tex]
2. Calculate the first term [tex]\( 3ab \)[/tex]:
[tex]\[ 3ab = 3 \cdot 1 \cdot 2 = 6 \][/tex]
3. Calculate the second term [tex]\( 2b^3 \)[/tex]:
[tex]\[ 2b^3 = 2 \cdot (2)^3 \][/tex]
Since [tex]\( (2)^3 = 2 \cdot 2 \cdot 2 = 8 \)[/tex]:
[tex]\[ 2b^3 = 2 \cdot 8 = 16 \][/tex]
4. Add the two terms together to find [tex]\( y \)[/tex]:
[tex]\[ y = 6 + 16 = 22 \][/tex]
Therefore, when [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex], the value of [tex]\( y \)[/tex] is [tex]\( 22 \)[/tex].
So, the correct answer is:
[tex]\[ 22 \][/tex]
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