To solve this problem, we need to understand what it means for two variables to vary inversely. When two variables vary inversely, it means that as one variable increases, the other variable decreases proportionally, and vice versa.
In this case, C varies inversely as J. Mathematically, we can represent this relationship with the equation C = k/J, where k is a constant of proportionality.
To find the value of k, we can substitute the given values of C and J into the equation and then solve for k.
When C = 7 and J = 0.7, the equation becomes:
7 = k/0.7
To solve for k, we can multiply both sides of the equation by 0.7:
7 * 0.7 = k
k = 4.9
Now that we have the value of k, we can use it to find C when J = 12. Substituting into the equation again, we have:
C = 4.9/12
Simplifying, we find:
C = 0.4083
Therefore, when J = 12, C is approximately 0.4083.