Please answer my question :(


If y varies inversely as the cube of x , what is the effect in y if x is halved

y = k/x^3

new y = k/(x/2)^3 = 8 k/x^3

8 times as big

To determine the effect on y when x is halved in an inverse variation relationship, we can use the inverse variation formula:

y = k / x^3

where k is the constant of variation. Let's break down the steps to find the effect on y:

1. Start with the initial relationship: y = k / x^3.

2. Halve the value of x. Let's say the original x value is denoted as x_1, and the halved x value is denoted as x_2. Therefore, x_2 = x_1 / 2.

3. Substitute x_2 and the original relationship y = k / x^3 into the equation:

y = k / (x_1 / 2)^3.

4. Simplify the denominator and cube the expression:

y = k / (x_1^3 / 8) = 8k / x_1^3.

5. As the constant k is unchanged, we can see that the effect on y when x is halved is simply multiplying y by a factor of 8.

In summary, when x is halved in an inverse variation relationship, y is multiplied by a factor of 8.