Herky and Elaina want to compare their investment accounts to see how much they will have in the accounts after eight years. They substitute their values shown below into the compound interest formula. Which pair of equations would correctly calculate their compound interests?
Herky: A = 500 (1 + 0.08) Superscript 5, Elaina: A = 400 (1 + 0.08) Superscript 6
Herky: A = (500 times 1) + (0.05) Superscript 8, Elaina: A = (400 times 1) + (0.06) Superscript 8
Herky: A = 500 (1 + 0.05) Superscript 8, Elaina: A = 400 (1 + 0.06) Superscript 8
Herky: A = (500 times 1) + (0.05) Superscript 8, Elaina: A = (400 times 1) + (0.05) Superscript 8

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.

step-by-step explanation: