If x varies inversely withy 3, and x=6 when y=3, find x when y=2.
x = k/y^3
6=k/27
k = 162
162/8 = 81/4
or, since xy^3 is constant, we have
(6)(27) = x(8)
x = 81/4
20.25
To find the value of x when y is equal to 2, you can use the concept of inverse variation.
Inverse variation is a relationship in which one variable increases while the other variable decreases, and the product of the two variables remains constant.
In this case, we are given that x varies inversely with y. Mathematically, we can represent this relationship as:
x ∝ 1/y
To solve for the constant of variation, we can use the initial values given when x = 6 and y = 3.
6 ∝ 1/3
To find the constant of variation, we can cross multiply:
6 * 3 = 1 * x
18 = x
Therefore, the value of x when y = 2 is equal to 18.