Figure EFGH on the grid below represents a trapezoidal plate at its starting position on a rotating machine platform: Trapezoid EFGH with vertices E at negative 4 comma 8, F at negative 7 comma 5, G at negative 4 comma 3, and H at negative 2 comma 5. The plate is rotated 720° about the origin in the counterclockwise direction. Which of the following is formed when the arcs of rotation are drawn for each point as it is rotated? They form parallel segments. They form perpendicular segments. They form concentric circles. They form congruent segments.

The correct option is;

They form concentric circles

Step-by-step explanation:

Given that the coordinates of the vertices of the trapezoid are;

E = (-4, 8)

F = (-7, 5)

G = (-4, 3)

H = (-2, 5)

We note that the distances from the origin, O, to the vertices are;

OE = √((-4)² + 8²) = √(80) = 4·√5

OF = √((-7)² + 5²) = √(74)

OG = √((-4)² + 3²) = √(25) = 5

OH = = √((-2)² + 5²) = √(29)

When rotated 720° about the origin, each point behaves as the radius of a circle with center at the origin such that they form concentric circles with OE being the largest circle and OG the smallest circle at the center.

step-by-step explanation:

. your answer will contain x - and y -terms. (1 point) x ( ¿¿ 2 − 7 ) 2 +( y 2 − 9 ) 2 √ ¿ 12. what is the distance from the directrix (the crocodile river) to the point ( x , y )? write this equation. your answer will contain a y -term.

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.