Final answer:
The problem is to establish a relationship between K and L, where K is a sum of a term directly proportional to L and another inversely proportional to it. Using the give data, constants in the equation K = aL + b/L are to be determined to find K when L=10.
Step-by-step explanation:
The question involves finding a relationship between two variables where one variable, K, varies as the sum of two terms: one that varies directly with L, and the other that varies inversely with L. The general form of this relationship can be written as K = aL + b/L, where a and b are constants that need to be determined using the given conditions.
Using the information provided:
K = 10 when L = 4,
and K = 8 when L = 2.
We can set up two equations as follows:
10 = a(4) + b/4, and
8 = a(2) + b/2.
Solving these two equations simultaneously will give us the values for a and b. Once we have found these constants, we can find K for any given value of L, such as when L = 10.