Finding coordinates parabol,cubic
•Download as PPT, PDF•
1 like•337 views
The document provides instructions to find the coordinates of points on curves defined by algebraic equations. It gives examples of finding the coordinates A, B, C of curves defined by equations like (x-3)(x+2) and (x-5)(x+4). It also asks to find the coordinates A, B, C, D of the curve defined by the equation y=(x^2)(1)(6)-(x) and coordinates A, B of the curve defined by y=(x^3)(4)-(x).
Report
Share
Report
Share
Recommended
6.14.3 Circle Equations
Determine the center and radius of a circle from its equation
Write the equation of a circle from its center and a point on the circle.
Test yourself for JEE(Main)TP-2
This document contains 30 multiple choice questions related to mathematics for a JEE exam preparation test. It provides instructions that each question is worth 4 marks and 1 mark will be deducted for incorrect answers. The maximum total marks for the test are 120. The questions cover topics in trigonometry, algebra, geometry and calculus.
Test yourself for JEE(Main)TP-3
This document provides 30 multiple choice questions for a JEE mathematics exam. It includes instructions that there are 4 marks for each correct answer, a deduction of 1 mark for incorrect answers, and no deduction for unanswered questions. The maximum total marks are 120. The questions cover topics in trigonometry, coordinate geometry, calculus, matrices and other areas of mathematics.
Ecat math
This document contains 30 multiple choice questions related to mathematics. Some of the concepts covered include: properties of complex numbers, sets, arithmetic progressions, trigonometric functions, derivatives, integrals, lines, conic sections, inequalities and vector projections. The questions have 4 possible answer choices labeled a, b, c or d for each problem.
ЗНО-2021 (математика)
1. The diagram shows angles MBC and ABC measuring 25 degrees each.
2. Angle MBC and ABC are equal since they are vertical angles.
3. Therefore, the measure of angle CBD is also 25 degrees by angle substitution.
H 2004 2007
1. The document provides instructions for a mathematics exam. It states that calculators may be used, full marks require showing working, and scale drawings will not be credited. It then lists various formulae that may be needed for the exam.
2. The exam consists of 11 multi-part questions testing a range of mathematics skills, including algebra, geometry, trigonometry, calculus and graph sketching. Candidates are advised to attempt all questions.
3. The document concludes by providing blank pages for working, followed by a notice that the exam has ended.
Math06reviewsheet (3)
This document provides a review sheet with multiple math problems involving algebra, trigonometry, and calculus concepts. There are 23 problems covering topics such as simplifying rational expressions, solving equations, graphing functions, working with complex numbers, trigonometric identities, and applying trigonometric functions. Answers are provided for selected problems. The review sheet is intended to help students practice and review a wide range of mathematics topics.
ЗНО-2021 (математика)
1. The document contains mathematical formulas and equations related to geometry, trigonometry, and calculus.
2. Formulas are provided for calculating the surface area and volume of spheres, cylinders, cones, and other shapes.
3. Trigonometric functions like sine, cosine, and tangent are defined in terms of right triangles and angles in radians.
Recommended
6.14.3 Circle Equations
Determine the center and radius of a circle from its equation
Write the equation of a circle from its center and a point on the circle.
Test yourself for JEE(Main)TP-2
This document contains 30 multiple choice questions related to mathematics for a JEE exam preparation test. It provides instructions that each question is worth 4 marks and 1 mark will be deducted for incorrect answers. The maximum total marks for the test are 120. The questions cover topics in trigonometry, algebra, geometry and calculus.
Test yourself for JEE(Main)TP-3
This document provides 30 multiple choice questions for a JEE mathematics exam. It includes instructions that there are 4 marks for each correct answer, a deduction of 1 mark for incorrect answers, and no deduction for unanswered questions. The maximum total marks are 120. The questions cover topics in trigonometry, coordinate geometry, calculus, matrices and other areas of mathematics.
Ecat math
This document contains 30 multiple choice questions related to mathematics. Some of the concepts covered include: properties of complex numbers, sets, arithmetic progressions, trigonometric functions, derivatives, integrals, lines, conic sections, inequalities and vector projections. The questions have 4 possible answer choices labeled a, b, c or d for each problem.
ЗНО-2021 (математика)
1. The diagram shows angles MBC and ABC measuring 25 degrees each.
2. Angle MBC and ABC are equal since they are vertical angles.
3. Therefore, the measure of angle CBD is also 25 degrees by angle substitution.
H 2004 2007
1. The document provides instructions for a mathematics exam. It states that calculators may be used, full marks require showing working, and scale drawings will not be credited. It then lists various formulae that may be needed for the exam.
2. The exam consists of 11 multi-part questions testing a range of mathematics skills, including algebra, geometry, trigonometry, calculus and graph sketching. Candidates are advised to attempt all questions.
3. The document concludes by providing blank pages for working, followed by a notice that the exam has ended.
Math06reviewsheet (3)
This document provides a review sheet with multiple math problems involving algebra, trigonometry, and calculus concepts. There are 23 problems covering topics such as simplifying rational expressions, solving equations, graphing functions, working with complex numbers, trigonometric identities, and applying trigonometric functions. Answers are provided for selected problems. The review sheet is intended to help students practice and review a wide range of mathematics topics.
ЗНО-2021 (математика)
1. The document contains mathematical formulas and equations related to geometry, trigonometry, and calculus.
2. Formulas are provided for calculating the surface area and volume of spheres, cylinders, cones, and other shapes.
3. Trigonometric functions like sine, cosine, and tangent are defined in terms of right triangles and angles in radians.
Trigonometry
1. The document discusses three "master triangles" - the equilateral triangle, right triangle, and right isosceles triangle. It provides the key properties and relationships for each triangle.
2. Examples are provided showing how the master triangles can be used to solve other triangle problems by applying their specific properties. If a problem's conditions match the properties of one of the master triangles, it can be used to find the solution.
3. The document contains several triangle word problems and their solutions demonstrated through applications of the appropriate master triangle. This establishes the master triangles as useful tools for solving a wide range of triangle questions.
Conceptual Short Tricks for JEE(Main and Advanced)
The document contains solutions to multiple trigonometry identity and concept questions. For each question, the solution uses substitution techniques to simplify the expressions and arrive at the answer. Key steps include:
1) Letting variable angles equal specific values like 0, 30, 45, 60, 90 degrees to simplify trig functions.
2) Applying identities like sin^2 x + cos^2 x = 1 to isolate variables.
3) Substituting the simplified expressions back into the original to arrive at an identity equaling the answer choices.
The techniques shown provide concise solutions through strategic substitution of angle values and use of trig identities.
Vectores operaciones blog01
This document contains solutions to vector algebra problems. It provides the steps to calculate: (1) the magnitude of given vectors, (2) the sum and difference of vectors, and (3) scalar multiplication of vectors. For each problem, it lists the vectors, shows the calculation steps, and states the final result. The purpose is to demonstrate how to perform basic vector operations through worked examples.
Magical Short Tricks for JEE(Main).
Infinite many problems of this kind can be solved easily by these techniques.
for more short tricks mail me your mail ID at vijayujn1@gmail.com
2.7 more parabolas a& hyperbolas (optional) t
The document provides examples of how to graph and identify properties of hyperbolas and parabolas. It includes:
1) An example of a hyperbola with center (3, -1), x-radius of 4, y-radius of 2, and vertices of (7, -1) and (-1, -1).
2) Steps for completing the square to put a quadratic equation into standard form for a hyperbola, including an example starting with 4y^2 - 9x^2 - 18x - 16y = 29.
3) An example of graphing a parabola given by the equation x = -y^2 + 2y + 15, identifying
F2 t2 squares, square roots, cubes & cube roots
1. The document discusses squares, square roots, cubes, and cube roots of numbers. It provides examples of evaluating expressions involving these concepts without and with a calculator.
2. Tables are included showing the first ten perfect squares and cubes.
3. Questions at the end provide practice evaluating additional expressions and problems involving squares, square roots, cubes and cube roots.
Fungsi dan Grafik Fungsi Trigonometri
This document discusses trigonometric functions and their graphs. It contains:
1) Definitions and properties of sine, cosine, and tangent functions. Examples of using trigonometric functions to solve for unknown sides of triangles are shown.
2) Graphs of y=sinx, y=cosx, and y=tgx from 0 to 360 degrees are depicted and their patterns discussed.
3) Additional trigonometric function graphs including y=tanx, y=cotx, y=secx, y=cscx are presented along with their vertical asymptotes.
Exercise unit 1 hum3032
This document contains an exercise on solving differential equations. It includes determining the order and degree of given differential equations, solving equations using the method of separable variables, and solving equations using the method of integrating factors. The exercise contains multiple parts for each type of problem.
Guess paper x
The document provides 20 multiple choice questions testing mathematics objectives related to topics like sets, algebra, trigonometry, and geometry. It then lists 18 additional practice problems involving algebraic expressions, logarithms, geometry constructions, data analysis, and solving equations both algebraically and graphically. The objectives and practice problems cover a wide range of foundational mathematics skills.
Ejercicios de hessiano
1) Determine the local maximum and minimum points as well as saddle points of the function F(x,y).
2) The function F(x,y) is defined as x3 + y3 + 3x2 + 6xy. By taking the partial derivatives, the critical points are found to be P1(-5.193,-3.947) which is a local maximum.
3) The function F(x,y) is defined as 2x3 + 2y3 - 9x2 + 3y2 - 12y. By taking the partial derivatives, the critical points are found to be P1(0,-2), P2(0,1), P3(3
Geometria plana resoluções
1) The document contains 13 multi-step math word problems.
2) It includes calculations involving fractions, percentages, geometry, algebra and trigonometry.
3) The problems do not have annotations or explanations and are presented as disconnected steps.
Productos notables gráficos
This document provides algebraic expansions and factorizations of expressions including (a + b)2, (a - b)2, and (x + a)(x + b). It shows that (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (x + a)(x + b) = x2 + (a + b)x + ab.
Productos notables
1. The document presents formulas for expanding and factorizing binomial expressions, including squaring binomials, multiplying binomials, and cubing binomials.
2. Formulas are given for expanding (a ± b)2, (a ± b)(a ∓ b), and (a + b)(a + c) as well as cubing expressions of the form (a ± b)3.
3. Examples of applying the formulas are shown, such as expanding (5x + 1)2 and factorizing (3x - 5)3.
Practice sheet 5
This document contains a practice test for the NTSE Stage II exam with 46 multiple choice math questions. The questions cover topics like geometry, trigonometry, probability, arithmetic progressions, and algebra. For each question there are 4 possible answer choices labeled A, B, C, or D. The test is presented across 4 pages with around 10-12 questions per page.
Obj. 60 Circles in the Coordinate Plane
The student is able to write equations for and graph circles in the coordinate plane. The equation of a circle is (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius. Examples are given of identifying the center and radius from given equations and writing equations from given center and radius or a point on the circle. To graph a circle, you plot the center and draw a curve connecting points that are the radius distance from the center.
Matemática adriano - 2º ano
This document contains solutions to geometry problems. It solves for variables like x, r, and d in different equations related to circles, triangles, and trigonometry. Key details calculated include x=9 cm, r≈76.43 cm, and d=250 cm.
Ch02 22
(a) Simplifies the expression 2a + 2b by factorizing it into 2(a + b).
(b) Combines like terms in the expression 2x + 3y + 3x - 2y to get 5x + y.
(c) Factors the expression 3x - 30y into 3(x - 10y).
(d) Combines like terms in the expression 4x^2 - 4 + 3x^2 - 1 and factors it into 7x^2 - 5.
(e) Combines like terms in the expression 8ab - a^2 + b^2 - 8ab and factors it into (b - a)(b + a
12th mcq
The document contains 50 multiple choice questions covering various topics in mathematics including functions, trigonometry, calculus, probability, matrices and linear algebra. The questions test concepts such as one-to-one functions, inverse trigonometric functions, limits, derivatives, integrals, probability, matrices, vectors, and linear transformations.
Ch02 13
This document contains solutions to 6 math problems:
1) Finding the value of x2 - x + 1 when x = 2
2) Evaluating (a + b - c)(a - b + c) when a = 1, b = 2, c = 3
3) Simplifying (17 - 15)3 using the identity a3 - b3 = (a - b)(a2 + ab + b2)
4) Simplifying a3 - b2/(a-b) when a = 2 and b = -2
5) Simplifying a - b + b2/(1-a+b) when a = -1/2 and b = 3
Straight-Line-Graphs-Final -2.pptx
This document contains 5 math problems involving factorizing expressions, solving equations, evaluating expressions for given values, expanding expressions, and finding the highest common factor. It also provides context on working with straight line graphs, including finding the gradient and y-intercept of a line from its equation, finding the gradient between two points, finding the midpoint and a point that divides a line segment in a given ratio, and finding the x- and y-intercepts of a line.
F4 Add Maths - Coordinate Geometry
1. The document provides 6 problems involving coordinate geometry. The problems involve finding equations of lines, points of intersection of lines, perpendicular and parallel lines, loci of points, and calculating areas of triangles. Detailed solutions and working are provided for each problem.
2. Additional problems involve finding coordinates of points based on ratios of line segments, perpendicular lines, and loci of points that satisfy given distance conditions from other points. Solutions find equations of lines and loci, and use intersections to determine coordinates.
3. The final problem calculates the area of a triangle given the coordinates of its vertices, which were previously determined based on a locus condition for one of the points.
C2 st lecture 2 handout
This document provides a summary of lecture 2 on quadratic equations and straight lines. It covers how to factorize, complete the square, and use the quadratic formula to solve quadratic equations. It also discusses how to find the equation of a straight line given its gradient and y-intercept, or two points on the line. Additionally, it explains how to sketch lines, find the midpoint and distance between two points. Key terms defined include quadratic, surd, gradient, and intercept. Methods demonstrated include solving quadratic equations, finding lines from gradient/point and two points, and calculating midpoints and distances on a graph.
More Related Content
What's hot
Trigonometry
1. The document discusses three "master triangles" - the equilateral triangle, right triangle, and right isosceles triangle. It provides the key properties and relationships for each triangle.
2. Examples are provided showing how the master triangles can be used to solve other triangle problems by applying their specific properties. If a problem's conditions match the properties of one of the master triangles, it can be used to find the solution.
3. The document contains several triangle word problems and their solutions demonstrated through applications of the appropriate master triangle. This establishes the master triangles as useful tools for solving a wide range of triangle questions.
Conceptual Short Tricks for JEE(Main and Advanced)
The document contains solutions to multiple trigonometry identity and concept questions. For each question, the solution uses substitution techniques to simplify the expressions and arrive at the answer. Key steps include:
1) Letting variable angles equal specific values like 0, 30, 45, 60, 90 degrees to simplify trig functions.
2) Applying identities like sin^2 x + cos^2 x = 1 to isolate variables.
3) Substituting the simplified expressions back into the original to arrive at an identity equaling the answer choices.
The techniques shown provide concise solutions through strategic substitution of angle values and use of trig identities.
Vectores operaciones blog01
This document contains solutions to vector algebra problems. It provides the steps to calculate: (1) the magnitude of given vectors, (2) the sum and difference of vectors, and (3) scalar multiplication of vectors. For each problem, it lists the vectors, shows the calculation steps, and states the final result. The purpose is to demonstrate how to perform basic vector operations through worked examples.
Magical Short Tricks for JEE(Main).
Infinite many problems of this kind can be solved easily by these techniques.
for more short tricks mail me your mail ID at vijayujn1@gmail.com
2.7 more parabolas a& hyperbolas (optional) t
The document provides examples of how to graph and identify properties of hyperbolas and parabolas. It includes:
1) An example of a hyperbola with center (3, -1), x-radius of 4, y-radius of 2, and vertices of (7, -1) and (-1, -1).
2) Steps for completing the square to put a quadratic equation into standard form for a hyperbola, including an example starting with 4y^2 - 9x^2 - 18x - 16y = 29.
3) An example of graphing a parabola given by the equation x = -y^2 + 2y + 15, identifying
F2 t2 squares, square roots, cubes & cube roots
1. The document discusses squares, square roots, cubes, and cube roots of numbers. It provides examples of evaluating expressions involving these concepts without and with a calculator.
2. Tables are included showing the first ten perfect squares and cubes.
3. Questions at the end provide practice evaluating additional expressions and problems involving squares, square roots, cubes and cube roots.
Fungsi dan Grafik Fungsi Trigonometri
This document discusses trigonometric functions and their graphs. It contains:
1) Definitions and properties of sine, cosine, and tangent functions. Examples of using trigonometric functions to solve for unknown sides of triangles are shown.
2) Graphs of y=sinx, y=cosx, and y=tgx from 0 to 360 degrees are depicted and their patterns discussed.
3) Additional trigonometric function graphs including y=tanx, y=cotx, y=secx, y=cscx are presented along with their vertical asymptotes.
Exercise unit 1 hum3032
This document contains an exercise on solving differential equations. It includes determining the order and degree of given differential equations, solving equations using the method of separable variables, and solving equations using the method of integrating factors. The exercise contains multiple parts for each type of problem.
Guess paper x
The document provides 20 multiple choice questions testing mathematics objectives related to topics like sets, algebra, trigonometry, and geometry. It then lists 18 additional practice problems involving algebraic expressions, logarithms, geometry constructions, data analysis, and solving equations both algebraically and graphically. The objectives and practice problems cover a wide range of foundational mathematics skills.
Ejercicios de hessiano
1) Determine the local maximum and minimum points as well as saddle points of the function F(x,y).
2) The function F(x,y) is defined as x3 + y3 + 3x2 + 6xy. By taking the partial derivatives, the critical points are found to be P1(-5.193,-3.947) which is a local maximum.
3) The function F(x,y) is defined as 2x3 + 2y3 - 9x2 + 3y2 - 12y. By taking the partial derivatives, the critical points are found to be P1(0,-2), P2(0,1), P3(3
Geometria plana resoluções
1) The document contains 13 multi-step math word problems.
2) It includes calculations involving fractions, percentages, geometry, algebra and trigonometry.
3) The problems do not have annotations or explanations and are presented as disconnected steps.
Productos notables gráficos
This document provides algebraic expansions and factorizations of expressions including (a + b)2, (a - b)2, and (x + a)(x + b). It shows that (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (x + a)(x + b) = x2 + (a + b)x + ab.
Productos notables
1. The document presents formulas for expanding and factorizing binomial expressions, including squaring binomials, multiplying binomials, and cubing binomials.
2. Formulas are given for expanding (a ± b)2, (a ± b)(a ∓ b), and (a + b)(a + c) as well as cubing expressions of the form (a ± b)3.
3. Examples of applying the formulas are shown, such as expanding (5x + 1)2 and factorizing (3x - 5)3.
Practice sheet 5
This document contains a practice test for the NTSE Stage II exam with 46 multiple choice math questions. The questions cover topics like geometry, trigonometry, probability, arithmetic progressions, and algebra. For each question there are 4 possible answer choices labeled A, B, C, or D. The test is presented across 4 pages with around 10-12 questions per page.
Obj. 60 Circles in the Coordinate Plane
The student is able to write equations for and graph circles in the coordinate plane. The equation of a circle is (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius. Examples are given of identifying the center and radius from given equations and writing equations from given center and radius or a point on the circle. To graph a circle, you plot the center and draw a curve connecting points that are the radius distance from the center.
Matemática adriano - 2º ano
This document contains solutions to geometry problems. It solves for variables like x, r, and d in different equations related to circles, triangles, and trigonometry. Key details calculated include x=9 cm, r≈76.43 cm, and d=250 cm.
Ch02 22
(a) Simplifies the expression 2a + 2b by factorizing it into 2(a + b).
(b) Combines like terms in the expression 2x + 3y + 3x - 2y to get 5x + y.
(c) Factors the expression 3x - 30y into 3(x - 10y).
(d) Combines like terms in the expression 4x^2 - 4 + 3x^2 - 1 and factors it into 7x^2 - 5.
(e) Combines like terms in the expression 8ab - a^2 + b^2 - 8ab and factors it into (b - a)(b + a
12th mcq
The document contains 50 multiple choice questions covering various topics in mathematics including functions, trigonometry, calculus, probability, matrices and linear algebra. The questions test concepts such as one-to-one functions, inverse trigonometric functions, limits, derivatives, integrals, probability, matrices, vectors, and linear transformations.
Ch02 13
This document contains solutions to 6 math problems:
1) Finding the value of x2 - x + 1 when x = 2
2) Evaluating (a + b - c)(a - b + c) when a = 1, b = 2, c = 3
3) Simplifying (17 - 15)3 using the identity a3 - b3 = (a - b)(a2 + ab + b2)
4) Simplifying a3 - b2/(a-b) when a = 2 and b = -2
5) Simplifying a - b + b2/(1-a+b) when a = -1/2 and b = 3
What's hot (19)
Conceptual Short Tricks for JEE(Main and Advanced)
Conceptual Short Tricks for JEE(Main and Advanced)
F2 t2 squares, square roots, cubes & cube roots
F2 t2 squares, square roots, cubes & cube roots
Similar to Finding coordinates parabol,cubic
Straight-Line-Graphs-Final -2.pptx
This document contains 5 math problems involving factorizing expressions, solving equations, evaluating expressions for given values, expanding expressions, and finding the highest common factor. It also provides context on working with straight line graphs, including finding the gradient and y-intercept of a line from its equation, finding the gradient between two points, finding the midpoint and a point that divides a line segment in a given ratio, and finding the x- and y-intercepts of a line.
F4 Add Maths - Coordinate Geometry
1. The document provides 6 problems involving coordinate geometry. The problems involve finding equations of lines, points of intersection of lines, perpendicular and parallel lines, loci of points, and calculating areas of triangles. Detailed solutions and working are provided for each problem.
2. Additional problems involve finding coordinates of points based on ratios of line segments, perpendicular lines, and loci of points that satisfy given distance conditions from other points. Solutions find equations of lines and loci, and use intersections to determine coordinates.
3. The final problem calculates the area of a triangle given the coordinates of its vertices, which were previously determined based on a locus condition for one of the points.
C2 st lecture 2 handout
This document provides a summary of lecture 2 on quadratic equations and straight lines. It covers how to factorize, complete the square, and use the quadratic formula to solve quadratic equations. It also discusses how to find the equation of a straight line given its gradient and y-intercept, or two points on the line. Additionally, it explains how to sketch lines, find the midpoint and distance between two points. Key terms defined include quadratic, surd, gradient, and intercept. Methods demonstrated include solving quadratic equations, finding lines from gradient/point and two points, and calculating midpoints and distances on a graph.
2º mat emática
This document contains a mathematics chapter about matrices, determinants, and linear systems. It includes examples of matrix operations and solving systems of linear equations. It also contains practice problems related to these topics with solutions.
3d. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.4)
Pedagogy of Mathematics (Part II) - Algebra, Algebra, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy, Mathematics, Polynomials, Constants, variables, algebraic expression
Metrix[1]
The document defines and provides examples of matrices. The key points are:
1. A matrix is a rectangular array of numbers organized in rows and columns. It is denoted by its dimensions, such as a 3x2 matrix having 3 rows and 2 columns.
2. Matrices can be added, subtracted, or multiplied by a scalar. Operations between matrices are defined element-wise.
3. Special types of matrices include row matrices, column matrices, square matrices, and zero matrices. Matrix equality and solving systems of equations using matrices are also introduced.
48 circle part 1 of 2
This document provides a study package on circles for a mathematics class. It begins with an index listing the topics covered, which include theory, revision, exercises, assertion and reason questions, and past examination questions. It then covers circle theory, equations of circles in various forms including parametric and Cartesian, intercepts made by circles on axes, the position of points with respect to circles, lines and circles, and tangents to circles. Examples are provided to illustrate each concept. The document is intended to be a comprehensive resource for students to learn about circles.
M8AL- IIf-2
This document discusses graphing linear equations given two points and x-y intercepts. It provides examples of finding the slope and x- and y-intercepts of linear equations written in standard form (y = mx + b). The intercepts are found by setting either x or y equal to 0. The slope is determined from the coefficients of the x and y terms. Finally, examples are given of graphing linear equations by plotting the intercepts on a coordinate plane.
Sect3 7
This document discusses linear equations and curve fitting. It provides 18 examples of using a linear system to solve for the coefficients of linear, quadratic, and cubic polynomials that fit given data points. It also provides examples of using a linear system to solve for the coefficients of circle and central conic equations that fit given points. The linear systems are set up and solved, providing the resulting equations that fit the data in each example.
Summative Assessment Paper-1
Triangle ABC is given, with altitudes CD and BE from vertices C and B to opposite sides AB and AC respectively being equal. It is proved that triangle ABC must be isosceles by showing that triangles CBD and BCE are congruent by the right angle-hypotenuse (RHS) criterion, implying corresponding angles are equal, and then using corresponding parts of congruent triangles to show sides AB and AC are equal, making triangle ABC isosceles.
Solucionario teoria-electromagnetica-hayt-2001
This document provides solutions to problems from Chapter 1 of an electromagnetism textbook. It solves for vectors, vector operations, vector fields and their properties at different points. Some key points solved include finding unit vectors, magnitudes of vectors, angles between vectors, vector projections, and visualizing vector fields. The document contains step-by-step workings for 12 multi-part problems involving concepts of vector algebra and vector calculus.
Geometry Transformation
The document summarizes different types of geometry transformations:
1. Translations move every point on a shape by a distance and direction without changing the shape.
2. Reflections produce mirror images of shapes across lines or axes.
3. Rotations turn shapes around a fixed point by a certain angle.
4. Dilations enlarge or reduce the size of shapes around a fixed point but do not alter their form.
Composing multiple transformations means applying one transformation to the output of another. Matrix representations can describe the combined effect of transformations.
Higher papers 2007 - 2013
1. This document provides instructions for completing Section A of a mathematics exam. Students must use a pencil and fill in answers on an answer sheet by making a horizontal line in the correct space.
2. The answer sheet contains the student's name, date of birth, and other identifying information. Students should check this is correct and report any errors.
3. There is one correct answer for each question, and rough work should not be done on the answer sheet.
curve fitting lecture slides February 24
This document discusses techniques for curve fitting data, including least squares regression and interpolation. It covers:
- Two types of curve fitting: least squares regression to derive a trend line for noisy data, and interpolation to fit curves passing through precise data points.
- Linear regression to fit a straight line model and determine coefficients by minimizing the residual sum of squares.
- Polynomial regression to fit higher order polynomial models.
- Multiple linear regression to fit models with multiple independent variables.
- General linear least squares framework and normal equations to determine coefficients for any linear model.
- Polynomial interpolation to exactly fit curves through data points using divided differences.
Problemas estatica.
1) The document analyzes three problems involving forces and tensions on cables/wires.
2) In the first problem, it calculates the components of force exerted by a cable on a circular plate suspended by three wires.
3) The second problem determines the vertical force P exerted by a balloon suspended by three cables, given the tension in one cable.
4) The third problem uses vector analysis to calculate the moment of a force about a pin, where the force acts through a given point.
Introduction to coordinate geometry by pratima nayak
The document discusses distance formula and section formula to find the coordinates of points on a plane. It explains how to find the distance between two given points using the distance formula. It also describes how to find the coordinates of a point C that divides the line segment between points A and B in a given ratio using the section formula. The document provides examples of finding coordinates of circumcenter and incenter of a triangle given its vertices. It concludes with some assignment questions related to these concepts.
V2.0
The document discusses addition and multiplication of matrices. It provides examples of adding two matrices of the same order, as well as multiplying a matrix by a scalar value. Key points include:
- To add matrices, corresponding elements are added if the matrices are the same order
- Multiplying a matrix by a scalar involves multiplying each element of the matrix by the scalar value
- Examples are provided to demonstrate calculating the sum and product of matrices step-by-step
Similar to Finding coordinates parabol,cubic (17)
3d. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.4)
3d. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.4)
Introduction to coordinate geometry by pratima nayak
Introduction to coordinate geometry by pratima nayak
More from shaminakhan
Wordproblem
The document discusses trigonometric ratios and solving word problems involving angles of elevation and depression. It provides examples of calculating heights or distances using trigonometric ratios like tangent given angles of elevation or depression and known lengths of the adjacent or opposite sides of right triangles. Specifically, it gives the example of calculating the height of a tree as 8.49 meters using the tangent of the angle of elevation of 23 degrees from a point 20 meters from the base of the tree.
Pythagoras theorem math
This document discusses solving word problems involving right triangles and finding the hypotenuse using Pythagorean theorem. It includes examples of finding the hypotenuse of a triangle given the other two sides, finding an angle using trigonometric ratios, and finding distances using right triangles. Sample problems include finding the height of a ladder leaning against a wall and finding the length of a diagonal of a rectangle.
Math arcs and sectors
This document discusses calculating arc length and the area of sectors in circles. It provides examples of finding the length of edging for a flower bed shaped as a quadrant of a circle and the area of the flower bed sector. Another example calculates the area of the silver part of an earring pendant shaped as a sector. More practice questions are provided to find the arc length and area of sectors with given radius and central angle measurements.
Tree diargam 3 copy
The document discusses using tree diagrams and outcome tables to calculate probabilities of events. It provides examples of flipping a coin twice and drawing colored beads from a bag with replacement. A tree diagram models the possible outcomes as branches and assigns probabilities using the multiplicative principle for independent events. Calculating probabilities involves listing the outcomes and assigning probabilities based on the likelihood of each outcome.
Sine & cosine of obtuse angle
When two angles are supplementary, their sines and cosines are equal but the cosine values have the opposite sign. If the sine or cosine of one angle is known, the other angle can be found by taking 180 degrees minus the known angle. For example, if sin x = sin 45 degrees, then x = 135 degrees, as 135 degrees and 45 degrees are supplementary.
Greatest and smallest value 1 copy
This document discusses accuracy, upper and lower bounds, and finding greatest and lowest values when measurements have a degree of accuracy. It explains that accuracy is how close a measured value is to the true value, and degree of accuracy is half the unit of measurement above and below the measured value. It provides an example of finding the upper and lower bounds for values measured to one and two decimal places. It also gives an example problem of finding the greatest and lowest area of a triangle given the base and height are measured to the nearest whole number.
Harder expansion copy
The document provides examples and explanations for expanding and simplifying algebraic expressions involving addition, subtraction, and multiplication of terms. It includes step-by-step workings for expanding expressions like (a + a) and (x + x + x + x) as well as more complex expressions combining addition, subtraction, and multiplication. It then provides practice problems for students to try expanding and simplifying similar algebraic expressions on their own.
Solv.quad.eqns 5
This document discusses solving quadratic equations by taking out common factors. It explains factorizing equations like 2x^2 + 12x + 9 by first finding the greatest common factor of the terms, which is 2x, and then dividing each term by this factor. It also addresses cases where taking out the common factor does not simplify the first term. Examples are provided of fully solving equations by setting the factored expression equal to 0 and solving for the variable. As class work, students are assigned problems on page 82 to practice these techniques, with an assessment problem listed as well.
Further factor 5 - copy
This document discusses factorizing quadratic equations by taking out common factors. It considers cases where taking out the common factor does not simplify the first term of the equation. Some examples provided include factorizing equations like 1021xx^2 - 9123x + 20244 and 1081512x^2 - 10712x + 12.
Further factor 6
This document discusses factorizing quadratic equations by taking out common factors. It provides an example of factorizing the equation 2x^2 - 10x + 15 by taking out the common factor of 2 to get 2(x^2 - 5x + 7.5). It also lists class work, assessment, and homework exercises involving factorizing quadratic equations.
Reverse percentage finding cp
This document provides instructions on how to calculate cost price (original buying price) given selling price and profit or loss percentage. It gives the formulas to calculate cost price when profit percentage or loss percentage is given. It then provides examples of calculating cost price when selling price, mark-up, profit, and loss percentages are given. Finally, it provides a word problem asking to calculate the original buying price of an item given its selling price and the profit percentage made.
Percentage 3 - copy
The document discusses calculating percentage increases and decreases. It provides examples of increasing 130 by 22% and decreasing 120 by 20%. It also discusses calculating percentage change when the first number is increased or decreased to become the second number. The document includes class work and assessment questions involving applying percentages to increase or decrease given values.
Inverse variation copy
This document defines inverse variation and provides examples of using inverse variation to solve problems. It gives the formula that if y is inversely proportional to x, then y = k/x, where k is a constant. It then works through several word problems that involve finding unknown values of x or y given one value and the inverse proportional relationship between the variables.
Direct variation copy
Direct variation describes the relationship between two quantities where they are in a constant ratio. If x is directly proportional to y, their relationship can be written as y = kx, where k is the constant of proportionality. Several examples are provided to demonstrate calculating the constant of proportionality given initial values of x and y, and then using the relationship to find corresponding values of y when given new values of x, and vice versa.
Algebraic fractions 4
This document discusses multiplying and dividing algebraic fractions. It provides examples of simplifying fractions by multiplying the numerators and denominators when multiplying fractions, and dividing the numerators and dividing the denominators when dividing fractions. It also notes that common factors can sometimes be cancelled before multiplying fractions to further simplify the expression. Students are assigned practice problems to work through involving simplifying algebraic fractions.
More from shaminakhan (18)
Recently uploaded
Types of Herbal Cosmetics its standardization.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance
Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdNatural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcThe History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
A Strategic Approach: GenAI in Education
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.Recently uploaded (20)
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Finding coordinates parabol,cubic
- 1. Objectives To find the coordinates of the curve using graph
- 3. Q2) Find the co ordinates A,B,C Factorise : ( -3) ( -2) When y=0 ,( -3) ( -2) =0 =3 , =2 When =0, y = 0-0+6= 6 652 +−= xxy x x x x x x x
- 4. Equation of a straight line is y= mx+c m is the gradient , m= m= c is the y-intercept = 6 Equation is y= -2x+6 12 12 xx yy − − 2 3 6 03 60 −= − = − −
- 6. Explanation: Factorise ( -3) ( +2) When y=0 , ( -3) ( +2) =0 =0 , =3 , =-2 (0,0)(3,0)(-2,0) When =0, y = 0(0-3)(0+2)= 0 A=(-2,0); B=(3,0) xxxy 623 −−= x x x x x x x x x
- 7. Equation of the given graph is Find the values of p and q -----1 =-5 =4 +5=0 -4=0 ( +5)( -4)=0 ------2 Comparing the coefficients in 1 &2 p=-1,q=-20 qxpxxy ++= 23 (-5,0) (4,0) x x xx xx 0202 =−− xx )( 2 23 qpxxx qxpxxy ++= ++=
- 8. Your turn….. Find the coordinates A,B,C,D of the curve )2)(1)(6( +−−= xxxy A B C D
- 9. 0 A B Y X-X -Y Try one more question: The graph of is Given below Find A & B )3)(4( +−= xxxy
- 10. 0 A B Y X-X -Y Try one more question: The graph of is Given below Find A & B )3)(4( +−= xxxy