Atable with four legs will sometimes wobble if one leg is shorter than the other three, but a table with three legs will not wobble. select the postulate that substantiates this fact. postulate 1: a line contains at least two points. postulate 1a: a plane contains at least three points not all on one line. postulate 1b: space contains at least four points not all on one plane. postulate 2: through any two different points, exactly one line exists. postulate 3: through any three points that are not one line, exactly one plane exists. postulate 4: if two points lie in a plane, the line containing them lies in that plane. postulate 5: if two planes intersect, then their intersection is a line.

Step-by-step explanation:

The postulate 3 substantiates the presented fact, because a table with three legs will not wobble based on that postulate.

This postulate states that three points non-collinear, they form one plane, and this plane is unique, that's why the table won't wobble, all legs are in the same plane, and that plane is the floor. If those legs weren't in the same plane (the floor), they would wobble, because some leg would upper than the other ones.

Therefore, the right answer is Postulate 3.

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.

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol