Suppose that x and y vary inversely and that y=1/6 when x = 3. Write a function that models the inverse variation and find y when x = 10.
y = C/x
Solve for C with the given information.
1/6 = C/3
C = 1/2
y = 1/(2x)
If x = 10, y = 1/20
To write the function that models the inverse variation, we can use the equation:
y = k/x
where k is the constant of variation.
Given that y = 1/6 when x = 3, we can substitute these values into the equation to find k:
1/6 = k/3
To solve for k, we can cross-multiply:
k = (1/6) * 3
k = 1/2
So, the equation that models the inverse variation is:
y = (1/2)/x
To find y when x = 10, we substitute the value of x into the equation:
y = (1/2)/10
Simplifying, we get:
y = 1/20
Therefore, when x = 10, y = 1/20.
To write a function that models inverse variation, we can use the formula:
y = k/x
where k is the constant of variation. In this case, we are given that y = 1/6 when x = 3. We can use this information to find the value of k.
Substituting the given values into the formula:
1/6 = k/3
To solve for k, we can cross multiply:
k = 1/6 * 3
k = 1/2
So the function that models the inverse variation is:
y = (1/2)/x
To find y when x = 10, we can substitute x = 10 into the function:
y = (1/2)/10
y = 1/20
Therefore, when x = 10, y = 1/20.