You set a goal to save at least 1,100 over a six week period. You are trying to decide between two plans. You are trying to decide between two plans

Plan A: Deposit $100 the first week and deposit 25% more each successive week for the next 5 weeks

Plan B: Deposit $125 the first week and deposit 15% more each successive week for the next 5 weeks

which plan will result in total savings of at least $1,100? I would appreciate an explanation and showing your work.

Plan A

Step-by-step explanation:

Plan A: 1st week : $100 saved

             2nd week : $100 x 1.25 = $125 saved

             3rd week : $125 x 1.25 = $156.25 saved

             4th week : $156.25 x 1.25 = $195.31 saved

             5th week : $195.31 x 1.25 = $244.14 saved

             6th week : $244.14 x 1.25 = $305.17 saved

             Total saved = $1125.87

Plane B: 1st week : $125 saved

              2nd week : $125 x 1.15 = $143.75 saved

              3rd week : $143.75 x 1.15 = $165.31 saved

              4th week : $165.31 x 1.15 = $190.10 saved

              5th week : $190.10 x 1.15 = $218.62 saved

              6th week : $218.62 x 1.15 = $251.41 saved

              Total saved = $1094.19

Plan A results in a total of over $1100 of savings.

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.