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Crank
3 years ago
12

* Anyone please give me some information about the following;

Mathematics
2 answers:
Tema [17]3 years ago
7 0

Answer: See explanation below

Step-by-step explanation:

A conic is a curve obtained as the intersection of the surface of a cone with a plane. The 4 types of conic section are: 1. Hyperbola 2. The Parabola 3. The Ellipse and 4. Circle.

Hyperbola: When the plane cuts the cone at an angle closer to the axis than the side of the cone a hyperbola is formed.

Cones: A cone is a three-dimensional shape that goes in a diagonal directions from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments connecting from the base to the apex.

Parabola: A parabola is the curve formed by the intersection of a plane and a cone, but only when the plane is at the same slope as the side of the cone.

Ellipse: An ellipse is formed by a plane intersecting a cone at an angle to its base. All ellipses have two focal points and a center and a major and minor axis.

Circles: A circle is formed when the plane is parallel to the base of the cone.

*Note: Some of these answers are PLAGIARISED from the internet as I looked these up and copied & pasted some information, so please paraphrase if turning this in.*

tatuchka [14]3 years ago
6 0

Answer:  see below

<u>Step-by-step explanation:</u>

Types of Conics are: Circles, Ellipses, & Hyperbolas.

Here is information about each one:

<u>Circle</u>: Two parabolas facing each other. Distance from the center to the vertices are exactly the same.

(x - h)² + (y - k)² = r²

  • (h, k) is the center of the circle
  • r is the radius of the circle
  • The 4 vertices are: (h, k+r), (h, k-r), (h + r, k), & (h - r, k)

<u>Ellipse:</u> Two parabolas facing each other. Distance from the center to the vertices are not the same.

(x - h)²/a² + (y - k)²/b² = 1

  • (h, k) is the center of the ellipse
  • a is the horizontal distance from the center to the vertices/co-vertices
  • b is the vertical distance from the center to the co-vertices/vertices
  • If a > b, then vertices are: (h+a, k), & (h-a, k) and co-vertices are (h, k+b), (h, k-b)
  • <em>If b > a, then the vertices and co-vertices are reversed </em>
  • Use |a² - b²| = c² to find the distance from the center to the foci.
  • If a > b, then Foci = (h+c, k) & (h-c, k). If b > a, then ± from the k-value

Example: (x - 1)²/9 + (y - 2)²/25 = 1

Center (h, k) = (1, 2)       a = √9 = 3       b = √25 = 5

Vertices (b > a): (1, 2+5) & (1, 2-5)  ==>  (1, 7) & (1, -3)

Co-vertices:      (1+3, 2) & (1-3, 2)  ==>  (4, 2) & (-2, 2)

Foci (b > a): c = √(25-9) = 4  --> (1, 2+4) & (1, 2-4)  ==>  (1, 6) & (1, -2)

<u>Hyperbola:</u> Two parabolas facing AWAY from each other. Distance from the center to the vertices may or may not be the same.

(x - h)²/a² - (y - k)²/b² = 1          or         (y - k)²/b² -  (x - h)²/a² = 1

               ↓                                                            ↓

opens left and right                                opens up and down

  • (h, k) is the center of the hyperbola
  • If x²-y², then vertices are: (h+a, k), & (h-a, k). <em>There are NO Co-vertices.</em>
  • If y²-x², then vertices are (h, k+b), (h, k-b). <em>There are NO Co-vertices.</em>
  • Use a² + b² = c² to find the distance from the center to the foci.
  • If x²-y², then Foci = (h+c, k) & (h-c, k). If y²-x², then ±c from the k-value
  • The slope of the asymptotes are ± b/a and pass through the center (h, k)

Example: (x - 1)²/9 - (y - 2)²/16 = 1

Center (h, k) = (1, 2)       a = √9 = 3       b = √16 = 4

Vertices (x²-y²): (1+3, 2) & (1-3, 2)  ==>  (4, 2) & (-2, 2)

Foci (x²-y²): c = √(9 + 16) = 5  --> (1+5, 2) & (1-5, 2)  ==>  (6, 2) & (-4, 2)

Asymptotes: m = ± 4/3    through (h, k) = (1, 2)     ==> y = ± 4/3(x - 1) + 2

               

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Answer:

slope = 0

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point1 =  (0,7)

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slope = (y2-y1)/(x2-x1) => (7-7)/(7-0)

slope = 0

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2 years ago
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Seattle, WA and San Francisco, CA lie on the same longitudinal line. San Francisco is at 38° latitude and Seattle is at 47° lati
Helen [10]

Step 1.

Calculate measure of angle α:

47^o-38^o=9^o

Step 2.

Calculate what fraction of the angle 360° ​​is the angle α:

\dfrac{9^o}{360^o}=\dfrac{1}{40}

Step 3.

Calculate the circumference of the Earth (circle):

C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi

Step 4.

The length of arc is equal 1/40 of the circumference:

\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi

\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi


<h3>Answer: A) 628 miles</h3>

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3 years ago
Y=x^2-12x+45 vertex form and coordinate vertex
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Best Answer

<span><span> x2-12x-45=0</span> </span>Two solutions were found :<span> x = 15 x = -3</span>

Step by step solution :<span>Step  1  :</span>Skip Ad
Trying to factor by splitting the middle term

<span> 1.1 </span>    Factoring <span> x2-12x-45</span> 

The first term is, <span> <span>x2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -12x </span> its coefficient is <span> -12 </span>.
The last term, "the constant", is <span> -45 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -45 = -45</span> 

Step-2 : Find two factors of  -45  whose sum equals the coefficient of the middle term, which is  <span> -12 </span>.

<span><span>     -45   +   1   =   -44</span><span>     -15   +   3   =   -12   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  3 
                     <span>x2 - 15x</span> + 3x - 45

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-15)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-15)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (x-15)
             Which is the desired factorization

<span>Equation at the end of step  1  :</span> (x + 3) • (x - 15) = 0 <span>Step  2  :</span>Theory - Roots of a product :

<span> 2.1 </span>   A product of several terms equals zero.<span> 

 </span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span> 

 </span>We shall now solve each term = 0 separately<span> 

 </span>In other words, we are going to solve as many equations as there are terms in the product<span> 

 </span>Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

<span> 2.2 </span>     Solve  :    x+3 = 0<span> 

 </span>Subtract  3  from both sides of the equation :<span> 
 </span>                     x = -3 

Solving a Single Variable Equation :

<span> 2.3 </span>     Solve  :    x-15 = 0<span> 

 </span>Add  15  to both sides of the equation :<span> 
 </span>                     x = 15 

Supplement : Solving Quadratic Equation Directly<span>Solving <span> x2-12x-45</span>  = 0 directly </span>

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex :

<span> 3.1 </span>     Find the Vertex of   <span>y = x2-12x-45

</span>Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).<span> 

 </span>Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.<span> 

 </span>Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.<span> 

 </span>For any parabola,<span>Ax2+Bx+C,</span>the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   6.0000 <span> 

 </span>Plugging into the parabola formula   6.0000  for  x  we can calculate the  y -coordinate :<span> 
 </span><span> y = 1.0 * 6.00 * 6.00 - 12.0 * 6.00 - 45.0 
</span>or   y = -81.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : <span> y = x2-12x-45</span>
Axis of Symmetry (dashed)  {x}={ 6.00} 
Vertex at  {x,y} = { 6.00,-81.00}  
 x -Intercepts (Roots) :
Root 1 at  {x,y} = {-3.00, 0.00} 
Root 2 at<span>  {x,y} = {15.00, 0.00}</span>

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3 years ago
I need help with this math equation 3(2x + 6)
My name is Ann [436]

Answer:

6+18 pls give brainlest

Step-by-step explanation:

How to solve your problem

3(2+6)

Simplify

1

Distribute

3(2+6)

6+18

Solution

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3 years ago
An atrium is being designed to house an exhibit of tropical birds. The atrium must enclose 250,000 cubic feet of space, and the
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The <em>proposed</em> design of the atrium (<em>V < V'</em>) is possible since its volume is less than the <em>maximum possible</em> atrium.

<h3>Can this atrium be built in the rectangular plot of land?</h3>

The atrium with the <em>maximum allowable</em> radius (<em>R</em>), in feet, is represented in the image attached. The <em>real</em> atrium is possible if and only if the <em>real</em> radius (<em>r</em>) is less than the maximum allowable radius and therefore, the <em>real</em> volume (<em>V</em>), in cubic feet, must be less than than <em>maximum possible</em> volume (<em>V'</em>), in cubic feet.

First, we calculate the volume occupied by the maximum allowable radius:

<em>V' =</em> (8 · π / 3) · (45 ft)³

<em>V' ≈</em> 763407.015 ft³

The <em>proposed</em> design of the atrium (<em>V < V'</em>) is possible since its volume is less than the <em>maximum possible</em> atrium. \blacksquare

To learn more on volumes, we kindly invite to check this verified question: brainly.com/question/13338592

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