Pj Problems - Overview
The Number Line
7 Spaces Of Interest - Overview
Triadic Unit Mesh
States Of Matter
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Faith, Love, Charity
"Mom, check out my headlight", said Tee, a sharp 7 yr old. "cool! how did you do that?", asked his mom. "Conics, just conics", replied Tee.
Explain the conic concept Tee is referring to.
S7P4A41 (Motion - Linear).
Pj Problem of Interest is of type motion (linear). The ray model of light implies linear motion of light.
Conics, formally known as conic sections are curves that were originally derived from slicing a cone with a plane. The parabola, the ellipse and the hyperbola are very well known conics. The circle is also a conic section, however, its identity as a circle is dominant. Apollonius is credited with the first detailed analysis of conic sections.
Tee used the reflecting property of a parabolic mirror for his headlight. If a light source is at the focus of a parabolic mirror, the parabolic surface of the mirror will reflect all rays of light from the light source at its focus in directions parallel to the axis of the parabolic mirror. The result is a powerful beam of light concentrated in one direction.
This property is commonly used in automobile headlights which consists of a paraboloid (a paraboloid is formed by rotating a parabola about its axis) with a silvered surface so that it can reflect light and a light bulb at its focus. The light emanating from the bulb is reflected in the direction of the axis providing a concentrated beam of light in that direction (figure 21.2. where F is the focus). This property of the paraboloidal mirror is also utilised in searchlights and flashlights.
The reverse of the reflecting property of a paraboloidal mirror is also very useful. In other words, light rays parallel to the axis of a paraboloidal mirror will be reflected through the focus of the mirror. Hence there will be a high concentration of light at the focus. A telescope uses such concentration of light effectively. The axis of the telescope is directed toward the star. Since distance from star to telescope is very far, rays from the star into telecope are parallel to the axis for all practical purposes. Hence when they are incident on the surface of the paraboloid mirror of the telescope, they will be reflected to the focus of the mirror.
The reflecting property of paraboloidal mirror is also the principle used in paraboloidal reflectors which are used to concentrate radio waves emanating from a small source into a powerful beam and in paraboloidal antenna which is used to pick up faint radio signals in order to produce relatively strong signals at the focus.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring
Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle
Derivation Of The Area Of An Ellipse
Derivation Of Volume Of A Cylinder
Derivation Of Volume Of A Sphere
Derivation Of Volume Of A Cone
Derivation Of Volume Of A Torus
Derivation Of Volume Of A Paraboloid
Volume Obtained By Revolving The Curve y = x2 About The X Axis
Single Variable Functions
Absolute Value Functions
Equation Of The Ascent Path Of An Airplane
Calculating Capacity Of A Video Adapter Board Memory
Probability Density Functions
Boolean Algebra - Logic Functions
Ordinary Differential Equations (ODEs)
Infinite Sequences And Series
Introduction To Group Theory
Advanced Calculus - Partial Derivatives
Advanced Calculus - General Charateristics Of Partial Differential Equations
Advanced Calculus - Jacobians
Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables
Advanced Calculus - Fourier Series
Advanced Calculus - Multiple Integrals
Production Schedule That Maximizes Profit Given Constraint Equation
Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation
Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions
Derivation Of Heat Equation For A One-Dimensional Heat Flow
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
Molecular Shapes: Valence Shell Electron Pair Repulsion
Molecular Shapes: Orbital Hybridization
Molecular Shapes: Sigma Bonds Pi Bonds
Molecular Shapes: Non ABn Molecules
Molecular Orbital Theory
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