A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost, ƒ(m ) is a function of the number of miles, m, that the car is driven. Plan A: ƒ(m ) = 0.12m + 75 Plan B: ƒ(m ) = 0.35m I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven. II. For each function, determine how the rate of change will affect the total cost of a car rental. III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective.

B

Step-by-step explanation: If you translate the graph for B and A B will be steeper than A

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.