Question

y is directly proportional to x^3. it is known that =5 for a particular value of x. find the value of y when this value of y when this value of x is multplied by 1/2.​

Answer 1

Answer:

The value of $y$ when the value of $x$ is multiplied by $\frac{1}{2}$ is $\frac{5}{8}$.

Step-by-step explanation:

According to the statement, we have the following relationship:

$y = k\cdot x^{3}$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$k$ - Proportionality constant.

We can eliminate the proportionality constant by constructing the following relationship:

$\frac{y_{2}}{y_{1}} = \left(\frac{x_{2}}{x_{1}} \right)^{3}$

If we know that $y_{1} = y$, $y_{2} = 5$, $x_{2} = x_{o}$ and $x_{1} = \frac{1}{2}\cdot x_{o}$, then the value of $y$ when the value of $x$ is multiplied by $\frac{1}{2}$ is:

$\frac{5}{y} = \left(\frac{x_{o}}{\frac{1}{2}\cdot x_{o} } \right)^{3}$

$\frac{5}{y} = 8$

$y = \frac{5}{8}$

The value of $y$ when the value of $x$ is multiplied by $\frac{1}{2}$ is $\frac{5}{8}$.