A plumber charges $35 to make a house call, plus $25 an hour for labor. The following equation represents f(x), the total cost o
f a visit for x hours: f(x) = 25x+35. What is the independent variable? * 10 points Number of hours worked Amount of money paid Price of labor House call charge
In the equation presented, the number of hours worked is the only factor that varies, it is expected the plumber has to work a different number of hours depending on each situation and this affects the final cost as the number of hours is multiplied by $25 (cost of one hour). On the other hand, factors such as the house call charge or the price of an hour for labor are fixed and do not change.
Moreover, in equations, the factor that changes and can affect others is known as the independent variable. This means the number of hours can be classified as the independent variable because this is not fixed and affect other variables including the total cost.
If x represents the length of the box, then 42-x will be the girth. Since the largest area for a given girth is that of a square, the side length of the square cross section is (42 -x)/4.
The volume as a function of package length is then .. v(x) = x((42-x)/4)^2 This has a maximum at x=14. The corresponding volume is 686 in^3.
