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Is it true that if given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
Yes, it is true that if given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone. There are four cases... Plane perpendicular to axis: circlePlane between perpendicular to axis and parallel to edge: ellipsePlane parallel to edge: parabolaPlane between parallel to edge and parallel to axis: hyperbolehttp://en.wikipedia.org/wiki/Conic_section
If two parallel lines are cut by a transversal then are the alternate interior angles always supplementary?
yes because they will always equal 180 degrees, regardless of the angle at which the transversal intersects the two parallel lines
Is the diagonals of a quadrilateral always intersects?
yes
Does a trapezoid always have 2 parallel sides?
Yes - it always has exactly two parallel sides.
When does a parabola always cross the x-axis twice?
If the equation of the parabola is represented byy = ax^2 + bx + c then it crosses the x-axis twice if and only if b^2 > 4ac
Given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True
Is it true that given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True.
Is it true that if given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
Yes, it is true that if given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone. There are four cases... Plane perpendicular to axis: circlePlane between perpendicular to axis and parallel to edge: ellipsePlane parallel to edge: parabolaPlane between parallel to edge and parallel to axis: hyperbolehttp://en.wikipedia.org/wiki/Conic_section
What is the diameter of a parabola?
It is the bisector of any 2 parallel chords drawn to the parabola. It is always parallel to the axis of the parabola.
Does a transversal line have to intersect with two parallel lines?
Yes, a transversal line always intersects two parallel lines.
Does a parabola always have roots and a vertex?
An x2 parabola will always have one vertex, but depending on the discriminant of the function (b2-4ac) the parabola will either have 2 roots (it crosses the x-axis twice), 1 repeating root (the parabola meets the x-axis at a single point), or no real roots (the parabola doesn't meet the x-axis at all)
If two parallel lines are cut by a transversal then are the alternate interior angles always supplementary?
yes because they will always equal 180 degrees, regardless of the angle at which the transversal intersects the two parallel lines
Is a line that ns exactly one point always sometimes or never true?
A line that intersects another line at exactly one point is always true; this occurs when the two lines are not parallel. In Euclidean geometry, two distinct lines can either intersect at one point or be parallel (in which case they do not intersect at all). Therefore, if a line intersects another line, it can do so at only one point.
Is parabola always yx2?
No, but any parabola can be transformed into the form y = x^2.
Is a parabola always a function?
Yes, it is.
Is the diagonals of a quadrilateral always intersects?
yes
Is angular momentum always parallel to angular acceleration?
momentum is product of moment of inertia and angular velocity. There is always a 90 degree phase difference between velocity and acceleration vector in circular motion therefore angular momentum and acceleration can never be parallel
