Complete the problem to represent the situation given by the equation 0.40e + 10 + 15 = 0.20e + 5 + 25. at one store a trophy costs $15, initial engraving set-up cost $0.40 , and engraving costs $0.20 per letter. at another store, the same trophy costs $25 , initial engraving set-up costs $5, and engraving costs $10 per letter. how many letters, e, must be engraved for the costs to be the same?

The number of letters that must be engraved for the costs to be the same is 125.

Step-by-step explanation:

Since we have given that

We need to find the number of letters.

Hence, the number of letters that must be engraved for the costs to be the same is 125.

the answer is c just got it on ed

step-by-step explanation:

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.