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The Outcome Economy
1) The document discusses the opportunity for technology to improve organizational efficiency and transition economies into a "smart and clean world."
2) It argues that aggregate efficiency has stalled at around 22% for 30 years due to limitations of the Second Industrial Revolution, but that digitizing transport, energy, and communication through technologies like blockchain can help manage resources and increase efficiency.
3) Technologies like precision agriculture, cloud computing, robotics, and autonomous vehicles may allow for "dematerialization" and do more with fewer physical resources through effects like reduced waste and need for transportation/logistics infrastructure.
Test 1
The graph shows volume of gas in a car as a function of time. Line segment EF represents a period where the volume is decreasing, indicating the gas is being used up during that time. Several graphs represent functions based on real world situations like cost of items varying with quantity. Linear relations can be identified from graphs and tables and have a constant rate of change that can be calculated.
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Test 1
The graph shows volume of gas in a car as a function of time. Line segment EF represents a period where the volume is decreasing, indicating the gas is being used up during that time. Several graphs represent functions based on real world situations like cost of items varying with quantity. Linear relations can be identified from graphs and tables and have a constant rate of change that can be calculated.
Suare roots and cube roots
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
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This document provides examples and explanations of factors, multiples, common factors and multiples, prime numbers, and using area models and the distributive property to multiply polynomials. It includes examples of adding, subtracting, and multiplying polynomials. Check your understanding questions are provided to have students practice these skills.
Divisibility rules
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Applications of sinusoidal functions assignment
1. A pebble stuck in a car tire tread will move up and down sinusoidally as the car drives, with a period equal to the circumference of the wheel. The document provides equations to calculate the pebble's position after given distances.
2. Water depth measurements at a dock vary sinusoidally with tides over a day. An equation is fitted to the data to determine depth at any time of day.
3. An equation models how water depth in a harbor will vary sinusoidally over time due to tides on a specific date, allowing calculations like minimum depth, time between high tides, and safe times for boat operation.
Applications of sinusoidal functions
Sinusoidal functions can model periodic phenomena and are commonly used to solve problems involving periodic motion. A good procedure is to first sketch a graph, then write an algebraic equation in the form y = a sin b(x + c) + d, and use the equation to find required values. For example, a problem describes a water wheel rotating counterclockwise that a bug sits upon, and asks to model the bug's height h over time t in seconds using a sinusoidal equation.
Sinusoidal graphs example
This document provides an example of writing the equation for a sinusoidal graph in the form y = a sin b(x + c) + d. The graph shown has an amplitude (a) of 2, angular frequency (b) of 1, phase shift (c) of 0, and vertical shift (d) of 1. Therefore, the equation for the graph is y = 2 sin x + 1.
Sketching a sinusoidal graph
The document provides instructions for sketching a sinusoidal graph in 3 steps: 1) Identify the key characteristics of the sinusoidal function, including median line, amplitude, period, and start point. 2) Draw the median line and mark the start, end, maximum, and minimum points. 3) Join the points with a smooth curve. It then gives an example sinusoidal function to sketch.
Equations
This document discusses how to write sinusoidal functions from graphs by determining the parameters a, b, c, and d, where a is the amplitude, b is the frequency, c is the phase shift, and d is the vertical shift. These parameters can be estimated from graphs of sinusoidal functions and used to write the function in the form y = a sin b(x + c) + d.
Intro to periodic functions
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
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Suare roots and cube roots
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The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Applications of sinusoidal functions assignment
1. A pebble stuck in a car tire tread will move up and down sinusoidally as the car drives, with a period equal to the circumference of the wheel. The document provides equations to calculate the pebble's position after given distances.
2. Water depth measurements at a dock vary sinusoidally with tides over a day. An equation is fitted to the data to determine depth at any time of day.
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Sketching a sinusoidal graph
The document provides instructions for sketching a sinusoidal graph in 3 steps: 1) Identify the key characteristics of the sinusoidal function, including median line, amplitude, period, and start point. 2) Draw the median line and mark the start, end, maximum, and minimum points. 3) Join the points with a smooth curve. It then gives an example sinusoidal function to sketch.
Equations
This document discusses how to write sinusoidal functions from graphs by determining the parameters a, b, c, and d, where a is the amplitude, b is the frequency, c is the phase shift, and d is the vertical shift. These parameters can be estimated from graphs of sinusoidal functions and used to write the function in the form y = a sin b(x + c) + d.
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