Math1000 section1.9
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This document covers coordinate geometry and circle formulas taught in a Math 1000 course by Stuart Jones. It introduces the midpoint and distance formulas, showing examples of using them to find the midpoint between two points and the distance between two points. It then covers the standard equation of a circle, giving the formula (x - h)2 + (y - k)2 = r2 where (h, k) is the center and r is the radius. Several example problems are worked through applying this circle formula by finding the equation of a circle given its center and radius or given the endpoints of its diameter. The document emphasizes that students must memorize all the formulas for upcoming tests.
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10.6 Equation of the circle in grade 10 math (1).ppt
This document defines a circle and provides the standard equation for a circle. It gives the equation for a circle centered at the origin (x2 + y2 = r2) and a circle not at the origin ((x - h)2 + (y - k)2 = r2). Examples are worked through of writing the equation for a circle given the center and radius, and determining if a point lies inside, outside or on a given circle.
Math1.1
The document discusses different topics in mathematics including conic sections, differential equations, and probability. Chapter 1 covers conic sections such as circles, parabolas, ellipses and hyperbolas. It defines a circle and discusses finding the equation of a circle given its center and radius. It also addresses finding the center and radius of a circle given its equation, finding the intersection points between two circles, and finding the equation of a circle passing through three given points.
CIRCLES.pptx
Circles are geometric shapes defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius. Circle equations can be written in standard form (x-h)2 + (y-k)2 = r2, where (h, k) are the coordinates of the center and r is the radius. Problems involve finding the equation of a circle given its center and radius, graphing circles, rewriting equations in standard form, determining if an equation represents a circle, point or null set, finding equations of circles tangent to lines or passing through points, and finding equations of circles inscribed in or
Equation of a circle
Here are some things you did well and could improve on:
WWW:
- You explained the key concepts around writing the equation of a circle clearly and concisely. Breaking it down step-by-step makes it easy to understand.
- Providing examples with worked solutions is very helpful for reinforcement. The visual diagrams additionally aid comprehension.
- Giving practice problems for students to try on their own, along with answers, allows for application of the material.
EBI:
- Some of the text could be formatted for easier reading (e.g. consistent formatting of equations).
- Adding brief summaries or recaps after sections of explanation may aid retention.
- Providing guidance on common errors
Grade 10 Math Quarter 2 Equation of the Circle
The document defines a circle as a set of points equidistant from a center point. It provides the standard equation of a circle in general form and for when the center is at the origin. Examples are given of writing the equation of a circle given its center and radius, or center and a point on the circle. The document also shows how to determine if a given point lies inside, outside or on the circle using the standard equation.
L1 Circle.pptx
Conic sections are shapes formed by the intersection of a plane and a double-napped cone. The four types of conic sections are circles, parabolas, ellipses, and hyperbolas. A circle is defined as the set of all points equidistant from a fixed center point in a plane. The standard equation of a circle is (x-h)2 + (y-k)2 = r2, where (h,k) represents the center and r is the radius. This document provides examples of writing and graphing circle equations in standard and general form.
distance_and_midpoint_formulas_powerpoint.pptx
The document explains the distance and midpoint formulas for finding the distance between two points and the midpoint of a line segment between two points. It provides the formulas, sings them to familiar tunes for memorization, and includes examples of using the formulas to calculate distances and midpoints and find missing coordinates. It also shows how to find the equation of a line perpendicular to the midpoint of two points.
distance_and_midpoint_formulas_powerpoint.pptx
The document explains the distance and midpoint formulas for finding the distance between two points and the midpoint of a line segment between two points. It provides the formulas, sings them to familiar tunes for memorization, and includes examples of using the formulas to calculate distances and midpoints and find missing coordinates. It also shows how to find the equation of a line perpendicular to the midpoint of two points.
circles_ppt angle and their relationship.ppt
The document provides information about properties of circles, including theorems about angles formed by chords, secants, and tangents intersecting inside and outside circles, as well as theorems about relationships between lengths of segments of chords and secants. It also discusses writing equations of circles in standard form given the center and radius, finding the center and radius from a standard equation, and graphing circles from standard equations. Examples are provided to demonstrate applying the theorems and writing/graphing circle equations.
Equations of circles
This document discusses graphing circles and converting between graphing form and standard form equations of circles. It provides examples of writing the equation of a circle given its center and radius in graphing form. It also shows how to find the center, radius, and equation of a circle given the standard form equation. The key points are:
- In graphing form, the center is denoted as (h, k) and the equation is (x - h)2 + (y - k)2 = r2
- To convert to standard form, complete the square and factor the left side, moving any constant to the right side.
Center-Radius Form of the Equation of a Circle.pptx
This document discusses the center-radius form of the equation of a circle. It provides the standard equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) are the coordinates of the center and r is the radius. It also shows how to determine the center and radius from a given equation, either in standard or general form. Examples are provided to illustrate writing the equation in both standard and general form, as well as determining the center and radius from equations in various forms.
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10.6 Equation of the circle in grade 10 math (1).ppt
10.6 Equation of the circle in grade 10 math (1).ppt
Center-Radius Form of the Equation of a Circle.pptx
Center-Radius Form of the Equation of a Circle.pptx
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The document discusses the average rate of change of functions. It defines the average rate of change between two values x=a and x=b of a function f(x) as (f(b) - f(a)) / (b - a). This represents the slope of the secant line between the two points (a, f(a)) and (b, f(b)). Several examples are worked out calculating the average rate of change for different functions between given values of the variable. The document emphasizes that knowing how to work with fractions is important for solving these types of average rate of change problems.
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The document contains instructions and solutions for multiple problems involving analyzing functions from their graphs. It asks the student to find specific function values, domains, ranges, intervals of increase and decrease, and local maxima and minima. The solutions provided include finding that f(-1) = 1, f(1) = 2, f(0) = 1, f(2) = 1, and the domain and range for one function. It also identifies the intervals over which another function is increasing and decreasing.
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This document provides an overview of different types of equations covered in a math class. It discusses linear equations, literal equations, quadratic equations that can be solved by factoring, completing the square, or the quadratic formula. Rational equations involve multiplying to eliminate denominators, while radical equations aim to isolate the radical term. Students are advised to memorize procedures and formulas and practice through homework problems.
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This document provides an overview of algebraic expressions and polynomials from a Math 1000 course. It introduces polynomials as sums or differences of monomials, which are variables raised to exponents. Examples of adding, subtracting, and multiplying polynomials are shown. The key processes of factoring trinomials and special factoring formulas are also explained in detail. Factoring is emphasized as an important math skill.
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Syllabus
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Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
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Chapter 6
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2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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Math1000 section1.9
- 1. Math 1000 Stuart Jones Section 1.9 Coordinate Geometry
- 2. Math 1000 Stuart Jones In this section, we will look briefly at the midpoint and distance formulas and then use those to work with circles.
- 3. Math 1000 Stuart Jones Midpoint Formula Theorem For any points (x1, y1) and x2, y2), the midpoint is defined as ( x2 + x1 2 , y2 + y1 2 ) Find the midpoint between (-2,3) and (4,1)
- 4. Math 1000 Stuart Jones Midpoint Formula Theorem For any points (x1, y1) and x2, y2), the midpoint is defined as ( x2 + x1 2 , y2 + y1 2 ) Find the midpoint between (-2,3) and (4,1) Find the midpoint between (1,1) and (0,-7)
- 5. Math 1000 Stuart Jones Distance Formula Theorem For any points (x1, y1) and x2, y2), the distance d is defined as d = (x2 − x1)2 + (y2 − y1)2 Find the distance between (0,1) and (-4,5)
- 6. Math 1000 Stuart Jones Distance Formula Theorem For any points (x1, y1) and x2, y2), the distance d is defined as d = (x2 − x1)2 + (y2 − y1)2 Find the distance between (0,1) and (-4,5) Find the distance between (-2,-3) and (4,-7).
- 7. Math 1000 Stuart Jones We will now use these formulas to look at calculations involving circles. Please note: ALL of the formulas must be memorized. I cannot allow access to them on a test.
- 8. Math 1000 Stuart Jones Equation of Circles Theorem The form of the equation of a circle in standard form is given by (x − h)2 + (y − k)2 = r2 , where (h, k) is the center and r is the radius.
- 9. Math 1000 Stuart Jones Equation of Circles Theorem The form of the equation of a circle in standard form is given by (x − h)2 + (y − k)2 = r2 , where (h, k) is the center and r is the radius. Find the equation of a circle centered at (3, 2) with a radius of 2.
- 10. Math 1000 Stuart Jones Equation of Circles Theorem The form of the equation of a circle in standard form is given by (x − h)2 + (y − k)2 = r2 , where (h, k) is the center and r is the radius. Find the equation of a circle centered at (3, 2) with a radius of 2. Find the equation of the circle whose diameter’s endpoints are given by (−1, 4) and (0, 5).
- 11. Math 1000 Stuart Jones More Circle Questions.
- 12. Math 1000 Stuart Jones More Circle Questions. Find the equation of a circle whose diameter’s endpoints are given by (1, 3) and (5, 3).
- 13. Math 1000 Stuart Jones More Circle Questions. Find the equation of a circle whose diameter’s endpoints are given by (1, 3) and (5, 3). Find the equation of a circle whose center is (3, 5) and passes through (5, 5)
- 14. Math 1000 Stuart Jones The Bottom Line The Midpoint and Distance formulas (given above) are very important in calculations involving circles. This section has quite a few formulas. Make sure to spend some time making sure you know the formulas and how to use them.