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Korolek [52]
2 years ago
13

THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!! Chapter 13

Mathematics
2 answers:
Alex2 years ago
4 0

Answer:

The vertex of the parabola is at equal distance between focus and the directrix. If F is the focus of the parabola, V is the vertex and D is the intersection point of the directrix and the axis of symmetry, then V is the midpoint of the line segment ¯FD

Step-by-step explanation:

answer 3rd

Andreas93 [3]2 years ago
4 0

9514 1404 393

Explanation:

<h3>1.</h3>

A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.

A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.

  1. a circle - the plane of intersection is perpendicular to the axis
  2. an ellipse - the plane of intersection is at an angle between 90° and the angle of the side relative to the axis. Both an ellipse and a circle are closed figures.
  3. a parabola - the plane of intersection is at the same angle as the side of the cone. A parabola is a one-sided open figure.
  4. a hyperbola - The plane of intersection is at an angle between that of the side of the cone and the axis of the cone. The plane will intersect both parts of a double-napped cone producing a double-sided open figure.

Producing these at home can be an interesting project. A circle can be made using a compass.

An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.

A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the <em>focus</em> and a line that is called the <em>directrix</em>. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.

A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.

__

<h3>2.</h3>

The <em>general form</em> equation for a conic is ...

  Ax² +Bxy +Cy² +Dx +Ey +F = 0

Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,

In <em>standard form</em>, the equations for figures centered at the origin are ...

  • ellipse: x²/a +y²/b = 1
  • hyperbola: x²/a -y²/b = 1 (opens horizontally)
  • hyperbola: y²/a -x²/b = 1 (opens vertically)

__

<h3>3.</h3>

The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.

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Can any kind soul help me please​
bezimeni [28]

Answer:

p-q= -4

p=q-4

x^2 + px + q=0

=> x^2 + (q-4)x + q = 0

d= b^2-4ac

=(q-4)^2 - 4(1)(q)

= q^2 + 16 -8q - 4q

=q^2 -12q+16

given that D=16

q^2 -12q+16 = 16

=> q^2 -12q = 0

=> q^2 = 12q

=> q = 12q/q

=> q= 12

Therefore the value of q is 12 and the value of p is q-4 = 12-4= 8

Hope you understood............

6 0
3 years ago
Clare is painting some doors that are all the same size. She used 2 liters of paint to cover 1 3/5 doors. How many liters of pai
barxatty [35]

Answer:

1\frac{1}{4}\ liters

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

1\frac{3}{5}=\frac{1*5+3}{5}=\frac{8}{5}

step 2

Using proportion

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step 3

Convert to mixed number

\frac{10}{8}\ liters=\frac{8}{8}+\frac{2}{8}=1\frac{1}{4}\ liters

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yawa3891 [41]

Answer:

84

Step-by-step explanation:

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84

8 0
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Answer:

To find the surface area of a cube, use the formula: surface area = 6s^2, where s is the length of one of the sides. If you don't know the length of the sides, you can find the surface area using volume. Just find the cube root of the volume, which is equal to the length of one side of the cube.

Step-by-step explanation:

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(y2-y1)/(x2-x1)
7 0
3 years ago
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