If A(2, −1), B(5, −5), C(10, −5), and D(7, −1) are the vertices of a quadrilateral, do the points form a rhombus? A. No, it is not a rhombus because the slope of diagonal segment BD equals two and the slope of diagonal segment AC equals negative start fraction one over two end fraction full stop
B. Yes, it is a rhombus because the slope of diagonal segment BD equals two, and the slope of diagonal segment AC equals negative two full stop, and the diagonals bisect each other.
C. Yes, it is a rhombus because the midpoint of diagonals segment BD and segment AC is (6, −3).
D. Yes, it is a rhombus because the slope of diagonal segment BD equals two, the slope of diagonal segment AC equals negative start fraction one over two end fraction, and the diagonals bisect each other.

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.

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step-by-step explanation:

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