Final answer:
The question asks to find the value of f(x) when x equals 6, given f(30) equals 140 and assuming f(x) varies with x. Without knowing whether the variation is direct or inverse, one cannot provide an accurate answer to calculate f(6). Additional information about the type of variation is necessary to solve the problem.
Step-by-step explanation:
To find the value of f(x) when x equals 6, given that f(x) varies with x and f(30) is 140, we can assume that there is a direct or inverse variation between f(x) and x. Since it is not specified which type of variation is present, we will consider both possibilities. If it is a direct variation, f(x) is directly proportional to x, and we can write f(x) = kx where k is the constant of proportionality. If it is an inverse variation, f(x) inversely varies with x, which can be modeled as f(x) = k/x. In either case, we would use the known value of f(30) = 140 to solve for k and then find f(6).
Since no specific variation type (direct or inverse) is stated, we cannot provide an accurate answer without additional information. However, you can approach the problem by setting up the proportion based on the given information and the type of variation once identified.