Answer:
The value of [tex]y[/tex] when the value of [tex]x[/tex] is multiplied by [tex]\frac{1}{2}[/tex] is [tex]\frac{5}{8}[/tex].
Step-by-step explanation:
According to the statement, we have the following relationship:
[tex]y = k\cdot x^{3}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]k[/tex] - Proportionality constant.
We can eliminate the proportionality constant by constructing the following relationship:
[tex]\frac{y_{2}}{y_{1}} = \left(\frac{x_{2}}{x_{1}} \right)^{3}[/tex]
If we know that [tex]y_{1} = y[/tex], [tex]y_{2} = 5[/tex], [tex]x_{2} = x_{o}[/tex] and [tex]x_{1} = \frac{1}{2}\cdot x_{o}[/tex], then the value of [tex]y[/tex] when the value of [tex]x[/tex] is multiplied by [tex]\frac{1}{2}[/tex] is:
[tex]\frac{5}{y} = \left(\frac{x_{o}}{\frac{1}{2}\cdot x_{o} } \right)^{3}[/tex]
[tex]\frac{5}{y} = 8[/tex]
[tex]y = \frac{5}{8}[/tex]
The value of [tex]y[/tex] when the value of [tex]x[/tex] is multiplied by [tex]\frac{1}{2}[/tex] is [tex]\frac{5}{8}[/tex].
