Bob will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $53.96 and costs an additional $0.14 per mile driven. The second plan has an initial fee of $43.96 and costs an additional $0.19 per mile driven. How many miles would Bob need to drive for the two plans to cost the same?

The first plan has an initial fee of $38 and costs an idditional $0.11 per mile driven.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.