Lesson 19 - Purdue Math
... Lines are parallel; system is inconsistent and equations are independent. ...
... Lines are parallel; system is inconsistent and equations are independent. ...
Parabola
... Notice that the vertex is located at the midpoint between the focus and the directrix... Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix... Parabola with measures.gsp ...
... Notice that the vertex is located at the midpoint between the focus and the directrix... Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix... Parabola with measures.gsp ...
Parabola
... Notice that the vertex is located at the midpoint between the focus and the directrix... Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix... Parabola with measures.gsp ...
... Notice that the vertex is located at the midpoint between the focus and the directrix... Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix... Parabola with measures.gsp ...
Lecture 1. Introduction
... BACKGROUND In the sciences and engineering, mathematical models are developed to aid in the understanding of physical phenomena, often yielding an equation that contains some derivatives of an unknown function. Such an equation is called a differential equation. Example 1: Free fall of a body. When a ...
... BACKGROUND In the sciences and engineering, mathematical models are developed to aid in the understanding of physical phenomena, often yielding an equation that contains some derivatives of an unknown function. Such an equation is called a differential equation. Example 1: Free fall of a body. When a ...
File - Math with Mrs. Stratton
... PARABOLA: locus of all points in a plane that are the same distance from a given point called the FOCUS to a given line called the DIRECTRIX p is the distance from the focus to the vertex and the distance from the vertex to the directrix In the equation only one of the variables is squared if th ...
... PARABOLA: locus of all points in a plane that are the same distance from a given point called the FOCUS to a given line called the DIRECTRIX p is the distance from the focus to the vertex and the distance from the vertex to the directrix In the equation only one of the variables is squared if th ...
Student Activity DOC
... Problem 5 – Analyzing the Graph of a Parabola Move to page 5.1. Read the information on the page. On page 5.2, explore a quadratic function by grabbing the parabola near the vertex when ö appears. Press b> Analyze Graph > Analyze Conics > Vertices and Axes of Symmetry. To translate the parabola agai ...
... Problem 5 – Analyzing the Graph of a Parabola Move to page 5.1. Read the information on the page. On page 5.2, explore a quadratic function by grabbing the parabola near the vertex when ö appears. Press b> Analyze Graph > Analyze Conics > Vertices and Axes of Symmetry. To translate the parabola agai ...
Special Triangles - Math User Home Pages
... 1. For the 45◦ − 45◦ − 90◦ triangle, (the isosceles right triangle), there are two legs of length a and the hypotenuse of length 1. ...
... 1. For the 45◦ − 45◦ − 90◦ triangle, (the isosceles right triangle), there are two legs of length a and the hypotenuse of length 1. ...
quadric surface. - IUST Personal Webpages
... equation of the generating curve is x2 + y2 = a2. Equation of generating curve in xy- plane To find an equation of the cylinder, note that you can generate any one of the rulings by fixing the values of x and y and then allowing z to take on all real values. In this sense, the value of z is arbitrar ...
... equation of the generating curve is x2 + y2 = a2. Equation of generating curve in xy- plane To find an equation of the cylinder, note that you can generate any one of the rulings by fixing the values of x and y and then allowing z to take on all real values. In this sense, the value of z is arbitrar ...
Understanding Tangent Lines A nonlinear relationship is a
... A nonlinear relationship is a relationship between two variables that changes over the range of the variables' values. The slope of a nonlinear function changes at every point on it, reflecting the changing relationship between the variables. A tangent line is a straight line that touches a nonlinea ...
... A nonlinear relationship is a relationship between two variables that changes over the range of the variables' values. The slope of a nonlinear function changes at every point on it, reflecting the changing relationship between the variables. A tangent line is a straight line that touches a nonlinea ...
Quiz 8 Review Blank
... ____ T9 (A1): Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the poin ...
... ____ T9 (A1): Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the poin ...
Systems of Linear Equations
... Now we know both y and z we can sub them in the first equation and find x ...
... Now we know both y and z we can sub them in the first equation and find x ...
0 ax bx c + + = 2 16 0 x − = 6 9 x x − = − 3 2 b b = − 4 1 0 x + =
... Note: When graphing a two variable quadratic equation y = ax 2 + bx + c , the graph will be a U shaped curve, called a parabola. This graph will be studied more in Chapter 9. For now, we will use our graphing calculators to graph these equations. It is useful to move the expression to the side that ...
... Note: When graphing a two variable quadratic equation y = ax 2 + bx + c , the graph will be a U shaped curve, called a parabola. This graph will be studied more in Chapter 9. For now, we will use our graphing calculators to graph these equations. It is useful to move the expression to the side that ...
Document
... 76. A quadratic equation has solutions 3 and -4. Write a possible equation. 76–77. See left. 77. One solution to the equation x2 + bx - 20 = 0 is 5. Find the other solution. ...
... 76. A quadratic equation has solutions 3 and -4. Write a possible equation. 76–77. See left. 77. One solution to the equation x2 + bx - 20 = 0 is 5. Find the other solution. ...
Slope Fields - FreibergMath
... • pay attention to whether you need just the x- or y-values or both • Look for places where the slope is 0 • Look at the slopes along the x-axis (where y = 0) • Look for slopes along the y-axis (where x = 0) • Notice where the slopes are positive and where they are negative ...
... • pay attention to whether you need just the x- or y-values or both • Look for places where the slope is 0 • Look at the slopes along the x-axis (where y = 0) • Look for slopes along the y-axis (where x = 0) • Notice where the slopes are positive and where they are negative ...
Document
... With two equations and two variables, the graphs were lines and the solution (if there was one) was where the lines intersected. Graphs of three variable equations are planes. Let’s look at different possibilities. Remember the solution would be where all three planes all intersect. ...
... With two equations and two variables, the graphs were lines and the solution (if there was one) was where the lines intersected. Graphs of three variable equations are planes. Let’s look at different possibilities. Remember the solution would be where all three planes all intersect. ...
The first two cases are called consistent since there
... First we just put z = z since it can be any real number. Now solve for y in terms of z. Now sub it −z for y in first equation and solve for x in terms of z. The solution is (1 − z , −z , z) where z is any real number. For example: Let z be 1. Then (0 , −1 , 1) would be a solution. Notice is works in ...
... First we just put z = z since it can be any real number. Now solve for y in terms of z. Now sub it −z for y in first equation and solve for x in terms of z. The solution is (1 − z , −z , z) where z is any real number. For example: Let z be 1. Then (0 , −1 , 1) would be a solution. Notice is works in ...
The axis of symmetry
... will intersect the parabola at equal distances on either side of the axis of symmetry. So you only really need to draw half of the parabola on one side of its axis, and then reflect this across the axis to complete the parabola. You can locate the axis of symmetry of a parabola by drawing a horizont ...
... will intersect the parabola at equal distances on either side of the axis of symmetry. So you only really need to draw half of the parabola on one side of its axis, and then reflect this across the axis to complete the parabola. You can locate the axis of symmetry of a parabola by drawing a horizont ...
6th Grade Geometry Vocabulary
... area = length x width (ex: cm2 ) area = 10cm x 6cm area = 60 cm2 ...
... area = length x width (ex: cm2 ) area = 10cm x 6cm area = 60 cm2 ...
McMurry University Pre-test Practice Exam 1. Simplify each
... natural length is directly proportional to x. Here the constant of proportionality is called the spring constant. a. Write Hooke’s Law as an equation. (Use k for the constant of proportionality.) b. If the spring has a natural length of 6 cm and a force of 35 N is required to maintain the spring str ...
... natural length is directly proportional to x. Here the constant of proportionality is called the spring constant. a. Write Hooke’s Law as an equation. (Use k for the constant of proportionality.) b. If the spring has a natural length of 6 cm and a force of 35 N is required to maintain the spring str ...
POP Geometric Terms
... of sides. A polygon which has all sides mutually congruent and all angles mutually congruent is called a regular polygon. ...
... of sides. A polygon which has all sides mutually congruent and all angles mutually congruent is called a regular polygon. ...
Catenary
In physics and geometry, a catenary[p] is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola: it is a (scaled, rotated) graph of the hyperbolic cosine. The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings.The catenary is also called the alysoid, chainette, or, particularly in the material sciences, funicular.Mathematically, the catenary curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, specifically a minimal surface of revolution. The mathematical properties of the catenary curve were first studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691.Catenaries and related curves are used in architecture and engineering, in the design of bridges and arches, so that forces do not result in bending moments. In the offshore oil and gas industry, 'catenary' refers to a steel catenary riser, a pipeline suspended between a production platform and the seabed that adopts an approximate catenary shape.