Utility companies usually charge their customers based on the number of kilowatt-hours their customers consume in a period. Suppose the function A(p)=0.096p+19.50 represents the monthly charge, A, in dollars for a customer with Electric Company A consuming p kilowatt-hours of power. The function B(p)=0.104p+17.75 represents the monthly charge, B, in dollars for a customer with Electric Company B consuming p kilowatt-hours of power. Analyze the functions by interpreting the slope and y-intercept for each function in terms of the context for this situation. Then assess how the slope and y-intercept of Electric Company A compare with the slope and y-intercept of Electric Company B in this situation.

Step-by-step explanation:

A(p) = 0.096p + 19.50

Company A charges a monthly fee of $19.50, and charges a rate of $0.096 per kilowatt-hour of energy.

B(p) = 0.104p + 17.75

Company B charges a monthly fee of $17.75, and charges a rate of $0.104 per kilowatt-hour of energy.

Company A has a higher monthly fee, and company B has a higher rate.

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.