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.