Circle : Basic concept
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This document defines key terms related to circles: - A circle consists of all points equidistant from a fixed center point. - The radius is the fixed distance from the center point to any point on the circle. - A chord connects any two points on a circle. A diameter passes through the center and divides the circle into two equal halves. - The standard equation of a circle with center (h, k) and radius r is (x - h)2 + (y - k)2 = r2.
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1) Since ED is tangent at C, ∠ECD = 90° (property of tangents)
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2. Several theorems about circles are presented, including that equal chords of a circle subtend equal angles at the center, and the perpendicular from the center of a circle to a chord bisects the chord.
3. The document summarizes that a circle can be defined as all points equidistant from a fixed point, and introduces various properties and relationships regarding angles, chords, and points on circles.
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The domain is the set of all possible square footages, which is 1450 to 2100 square feet. The range is the set of all possible costs, which would be $75 * 1450 = $108,750 to $75 * 2100 = $157,500.
So the domain is [1450, 2100] and the range is [108750, 157500].
Evaluating functions basic rules
This document provides an overview of evaluating functions by giving examples of evaluating functions for given values and providing function rules to evaluate for specific inputs. It emphasizes important rules like exponents, adding and subtracting integers, and order of operations when evaluating functions and provides additional practice problems for readers to evaluate functions based on the given rules.
Circular functions
The document defines trigonometric functions using the unit circle. It shows that the sine of an angle is equal to the y-coordinate of the point on the unit circle where the terminal side of the angle intersects, while the cosine is equal to the x-coordinate. The tangent is defined as the ratio of the sine to the cosine. Key properties discussed include the periodic nature of the trig functions with periods of 360 degrees or 2π radians, and whether functions are even or odd based on their behavior under negative inputs.
Pi
Pi is the ratio of a circle's circumference to its diameter. It is an irrational number that cannot be expressed as a fraction and its value never repeats. Throughout history, mathematicians have worked to calculate Pi to greater levels of precision, advancing from the ancient Babylonians' approximation of 3 1/8 to modern computers calculating Pi to billions of decimal places. Analytic geometry and calculus in the 17th century allowed Pi to be applied to shapes beyond just circles.
Circle - Tangent for class 10th students and grade x maths and mathematics st...
Circle - Tangent for class 10th students and grade x maths and mathematics.Lets tute is an online learning centre. We provide quality education for all learners and 24/7 academic guidance through E-tutoring. Our Mission- Our aspiration is to be a renowned unpaid school on Web-World.
Circle
The document defines and explains key terms related to circles:
1. A circle is a closed curve in which all points are equidistant from the center. It has properties like radius, diameter, circumference, chords, arcs, and segments.
2. Key terms are defined, like radius as the line from the center to the edge, diameter as a chord passing through the center, and circumference as the distance around the circle.
3. Examples are given of circles in daily life, music, and sports to illustrate the concept. Diagrams accompany the definitions of terms like chord, arc, semicircle, and segments.
Circles
A circle is a closed curve where all points are equidistant from a fixed central point called the vertex. Key parts of a circle include the radius, which connects the center to any point on the circle, the diameter which passes through the center, and the chord which connects any two points on the circle. Other terms are the secant which intersects the circle at two points, the tangent which touches the circle at one point, and arcs which are portions of the circle.
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Circle
The document discusses circles and their equations. It defines a circle as all points in a plane that are a fixed distance from a fixed center point. This fixed distance is called the radius. The standard form of a circle equation is (x-h)2 + (y-k)2 = r2, where (h,k) are the coordinates of the center and r is the radius. It also discusses converting between the standard and general forms of a circle equation.
Circles
Here are the steps to solve these problems:
1. The points (x1, y1) and (x2, y2) form a diameter of a circle. The point (x, y) is another point on the circle.
(a) The gradient of the diameter AB is (y2-y1)/(x2-x1).
(b) The equation of AB is y-y1 = (y2-y1)/(x2-x1)(x-x1)
(c) Since P lies on AB, substitute the point (x, y) into the equation of AB to determine the value of x.
2. A line with equation y=mx+
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This document provides information about circles, including their geometric and algebraic definitions, how to write the equation of a circle in standard form, and how to graph circles. It discusses that a circle is defined geometrically as the set of all points equidistant from a fixed point, and algebraically as the set of all points with a constant distance from a fixed point. The standard form of a circle equation is given as (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius. Examples are provided of writing and graphing various circle equations in this standard form.
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
Circle
The document discusses equations of circles in various forms. It provides the general equation of a circle, as well as equations for circles given specific properties like center point and radius, diameter endpoints, tangency to an axis, and passing through a given point. Examples are worked through to find the equation of a circle matching given conditions or to obtain properties of a circle from its equation. Circles can be represented using forms based on the center and radius, diameter endpoints, or general equation.
Nov. 3 Coordinate Equation Of A Circle
The document discusses the coordinate equation of a circle. It states that a circle can be defined as all points that are equidistant from the center point. The standard form of the equation of a circle is r2 = (x - h)2 + (y - k)2, where (h, k) are the coordinates of the center and r is the radius. It provides examples of writing the equation of a circle given properties like the center point and radius or a point on the circle.
G10 Math Q2- Week 8- Equation of a Circle.pptx
This document discusses the standard and general forms of equations for circles. It provides examples of writing the standard and general form equations given the center and radius of various circles. Key points covered include:
- The standard form of a circle equation is (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius.
- The general form is Ax2 + By2 + Cx + Dy + E = 0, where the coefficients can be used to find the center and radius.
- Examples are worked through of writing circle equations in both standard and general form given attributes of the circle like the center and radius.
circles
A circle is 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 the radius. A diameter is a line segment that passes through the center containing two points on the circle. The circumference is the perimeter or distance around the circle, while the area is the region within the circle boundary. Circles have analytic definitions and properties that can be described through equations.
Circles
The document discusses the standard form equation of a circle and how to identify the center and radius from the equation. The standard form is (x-h)^2 + (y-k)^2 = r^2, where (h,k) are the coordinates of the center and r is the radius. Examples are given of identifying the center and radius and sketching graphs from equations in standard form and completing the square to convert equations to standard form.
Circles.pdf
1. The document discusses various properties and equations related to circles such as the standard equation of a circle, parametric equations of a circle, equations of circles under special conditions like touching axes, and equations of tangents, normals, and chords related to circles.
2. It also covers topics like the position of a point or line with respect to a circle, equations for common tangents between two circles, conditions for orthogonality of circles, properties of the radical axis, and the radical center.
3. The document provides sample problems from engineering entrance exams involving the application of circle concepts.
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Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Circles
This document defines circles geometrically as the result of a cone intersecting with a plane, and algebraically as the set of points equidistant from a fixed center point. It provides the standard equation for a circle given the center (h,k) and radius r: (x-h)2 + (y-k)2 = r2. Examples are given of writing the equation of a circle and finding its center and radius given parts of the equation. The process for finding the equation of a circle given its diameter is also described.
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This PowerPoint contains an introduction to conical sections: the conics formed from double-napped circular cone - the Parabola, Hyperbola, Circle, & Ellipse. It also contains the basic parts of Circle. Identifying the standard form of circle's radius and center. Graphing a circle from its standard form. Transforming General Equation of Circle to Standard Form and some of the special cases.
Circles
Conic sections are shapes formed by the intersection of a plane and a double cone. A hyperbola occurs if the plane cuts through both cones. A parabola occurs if the plane is parallel to the edge of the cone. An ellipse occurs if the plane is not parallel or cutting through both cones. A circle is a special case of an ellipse where the plane is perpendicular to the altitude of the cone.
Lecture co2 math 21-1
This document provides information about circles and conic sections. It begins with an overview of circles, including definitions of key terms like radius, diameter, chord, and equations of circles given the center and radius or three points. It then covers conic sections, defining ellipses, parabolas and hyperbolas based on eccentricity. Equations of various conic sections are derived based on the location of foci, directrix, vertex and other geometric properties. Sample problems are provided to demonstrate solving problems involving different geometric configurations of circles and conic sections.
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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.
Module 3 plane coordinate geometry
This module discusses coordinate proofs and properties of circles on the coordinate plane. It introduces coordinate proofs as an analytical method of proving geometric theorems by using the coordinates of points and algebraic relationships. Examples demonstrate proving properties of triangles and quadrilaterals analytically. The standard form of the equation of a circle is derived from the distance formula as (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius. Finding the center, radius, and equation of circles in various forms are illustrated.
Circles
Conics are curves formed by the intersection of a plane with a double cone. A hyperbola results if the plane cuts both cones, a parabola if the plane is parallel to the edge of the cone, and an ellipse if neither of those cases apply. A circle is a special type of ellipse that occurs when the plane is perpendicular to the altitude of the cone.
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"Lift off" by Pastor Mark Behr at North Athens Baptist Church
23 June 2024
Morning Service at North Athens Baptist Church Athens, Michigan
“Lift Off” by Pastor Mark Behr
Scriptures: Luke 24:50-53; Acts 1:6-11.
We are a small country Church in Athens Michigan who loves to reach out to others with the love of God. We worship an Awesome God who loves the whole world and wants everyone to see and understand what He has done for us. (1 Corinthians 15:1-4) We hope you are encouraging by our Sunday Morning sermon videos. If you are ever in the area, please feel free to attend our Sunday Morning Services at North Athens Baptist Church 2020 M Drive South, Athens, Michigan. If you have any question and would like to talk to Pastor Mark, or have prayer request please call the church at (269) 729-553
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Morning Service: 10:45 a.m.
Full Morning Service on Facebook Live at: https://www.facebook.com/groups/nabc2020athensmichigan
Sermon Only Live on YouTube at: https://www.youtube.com/@NABC2020AthensMI
Sermon Only Audio of Morning Sermon at: https://soundcloud.com/user-591083416
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In this video, you'll gain insights on:
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The ability to control one's dreams or for the dreamer to be aware that he or she is dreaming. This process, called lucid dreaming, has some potential risks as well as many fascinating benefits. However, many people are hesitant to try it initially for fear of the potential dangers. This article aims to clarify these concerns by exploring both the risks and benefits of lucid dreaming.
The Benefits of Lucid Dreaming
Lucid dreaming allows a person to take control of their dream world, helping them overcome their fears and eliminate nightmares. This technique is particularly useful for mental health. By taking control of their dreams, individuals can face challenging scenarios in a controlled environment, which can help reduce anxiety and increase self-confidence.
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Physical Harm in Dreams Lucid dreaming is fundamentally safe. In a lucid dream, everything is a creation of your mind. Therefore, nothing in the dream can physically harm you. Despite the vividness and realness of the dream experience, it remains entirely within your mental landscape, posing no physical danger.
Mental Health Risks Concerns about developing PTSD or other mental illnesses from lucid dreaming are unfounded. As soon as you wake up, it's clear that the events experienced in the dream were not real. On the contrary, lucid dreaming is often seen as a therapeutic tool for conditions like PTSD, as it allows individuals to reframe and manage their thoughts.
Potential Risks of Lucid Dreaming
While generally safe, lucid dreaming does come with a few risks as well:
Mixing Dream Memories with Reality Long-term lucid dreamers might occasionally confuse dream memories with real ones, creating false memories. This issue is rare and preventable by maintaining a dream journal and avoiding lucid dreaming about real-life people or places too frequently.
Escapism Using lucid dreaming to escape reality can be problematic if it interferes with your daily life. While it is sometimes beneficial to escape and relieve the stress of reality, relying on lucid dreaming for happiness can hinder personal growth and productivity.
Feeling Tired After Lucid Dreaming Some people report feeling tired after lucid dreaming. This tiredness is not due to the dreams themselves but often results from not getting enough sleep or using techniques that disrupt sleep patterns. Taking breaks and ensuring adequate sleep can prevent this.
Mental Exhaustion Lucid dreaming can be mentally taxing if practiced excessively without breaks. It’s important to balance lucid dreaming with regular sleep to avoid mental fatigue.
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Heartfulness Magazine - June 2024 (Volume 9, Issue 6)
Dear readers,
This month we continue with more inspiring talks from the Global Spirituality Mahotsav that was held from March 14 to 17, 2024, at Kanha Shanti Vanam.
We hear from Daaji on lifestyle and yoga in honor of International Day of Yoga, June 21, 2024. We also hear from Professor Bhavani Rao, Dean at Amrita Vishwa Vidyapeetham University, on spirituality in action, the Venerable BhikkuSanghasena on how to be an ambassador for compassion, Dr. Tony Nader on the Maharishi Effect, Swami Mukundananda on the crossroads of modernization, Tejinder Kaur Basra on the purpose of work, the Venerable GesheDorjiDamdul on the psychology of peace, the Rt. Hon. Patricia Scotland, KC, Secretary-General of the Commonwealth, on how we are all related, and world-renowned violinist KumareshRajagopalan on the uplifting mysteries of music.
Dr. Prasad Veluthanar shares an Ayurvedic perspective on treating autism, Dr. IchakAdizes helps us navigate disagreements at work, Sravan Banda celebrates World Environment Day by sharing some tips on land restoration, and Sara Bubber tells our children another inspiring story and challenges them with some fun facts and riddles.
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Circle : Basic concept
- 1. CIRCLE
- 2. GROUP MEMBERS: NOOR KAMARIAH BINTI ALING 0914018 SITI ‘AQILAH BINTI MAHYIDDIN 0918878
- 3. A circle is defined as the collection of all the points on a plane that are at equal distance from a given fixed point on the plane. This fixed point is called centre of the circle and the fixed distance is called the radius. A line segment joining two points on the figure is a chord. The following are examples of two chords.
- 4. -When a chord passes through the center,we call it a diameter. A diameter usually divides such figure into two equal halves. Each half is called a semi-circle -Half a diameter is called a radius. -In other words, 2 radii= diameter
- 5. CENTER AT THE ORIGIN The circle with centre (0, 0) and radius r has the equation: x2 + y2 = r2 This means any point (x, y) on the circle will be "true" when substituted into the circle equation.
- 6. CENTER NOT AT THE ORIGIN The circle with centre (h, k) and radius r has the equation: (x − h)2 + (y − k)2 = r2
- 7. THE GENERAL FORM OF THE CIRCLE An equation which can be written in the following form (with constants D, E, F) represents a circle: x2 + y2 + Dx + Ey + F = 0
- 8. Example: Find the centre and radius of the circle x2 + y2 + 8x + 6y = 0 Sketch the circle. Answer: Our aim is to get the equation into the form: (x − h)2 + (y − k)2 = r2 Group the x parts together and the y parts together: Complete the square on each of the x and y parts.
- 9. This is now in the format we require and we can determine the center and radius of the circle. So the centre of the circle is (-4, -3) and the radius is 5 units. Note that the circle passes through (0, 0). This is logical, since (-4)2 + (-3)2 = (5)2
- 10. Real life examples: -bicycle wheels - coins -dimes and pennies -CDs -MP3 players.