Martin is covering his bathroom floor with square tiles. when he gets to the end of a row of tiles, he needs to cut the length of the last tile by 4 inches in order to cover the remaining area. the area of the new tile is given by the quadratic expression below, where x represents the side length, in inches, of the original tile. x(x-4) determine which polynomial represents each component of this situation. (x - 4) 4x x2 x "area of original tile" "the length of the new tile" "the width of the new tile" "the area removed from the tile"

All squares are equal sides.Let X be the side of a square.Area of square,A = x^2

Here a tile is a square of side length 'x'. The following  polynomial represents,

(x - 4) represents "the width of the new tile" (because 4 inches cut from the tile)

4x represents "the area removed from the tile" (since one side of removed tile is 'x' and other is 4 inches.)

x2  represents "area of original tile" of side equal to 'x'

x represents "the length of the new tile" (since length of new tile  is not reduced. Length =x and breadth is x-4

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.