When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation you can solve to get the answer.

Option 1

Daily fee $50

Cost per mile $0.15

Option 2

Daily fee $65

Unlimited miles

Step-by-step explanation:

It is often convenient to choose a variable that has some mnemonic value with respect to what it represents. Here, we're asked for "miles you must travel", so the variable "m" seems appropriate for representing miles.

The fee for Option 1 is ...

  50 + 0.15m

The fee for Option 2 is ...

  65

For Option 2 to be the better option, its cost must be less than that for Option 1:

  65 < 50 +0.15m . . . . . "equation" for getting the answer

To solve this equation, subtract 50 and divide by the coefficient of m.

  (65 -50)/0.15 < m

  100 < m

You must travel more than 100 miles for Option 2 to be better.

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.