To begin, we recognize that c and d vary inversely. This means that as one variable increases, the other decreases in such a way that their product remains constant. In terms of an equation, we express this relationship as:
c * d = k
where k is a constant.
Given that d = 2 when c = 17, we can substitute these values into the equation to find the constant k:
17 * 2 = k
Calculating this gives:
k = 34
Now, we have the specific equation that models the variation:
c * d = 34
Next, we want to determine the value of d when c = 68. We can use our established equation:
68 * d = 34
To solve for d, we can rearrange the equation:
d = 34 / 68
Simplifying this gives:
d = 0.5
So when c is 68, the value of d is 0.5.
In summary, the equation that models the inverse variation between c and d is c * d = 34, and when c equals 68, d will equal 0.5.