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10th april 2012
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 boost feelings of calmness, happiness and focus.
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The document is a meeting agenda dated February 21, 2013. It lists the attendees and includes discussions on various topics such as project updates, sales reports, new marketing strategies, and administrative matters. The agenda also allocates time for discussions on upcoming projects and events.
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This document discusses radian measure as an alternative to degrees for measuring angles. Some key points:
- 1 radian is defined as the angle subtended when the arc length along a circle is equal to the circle's radius.
- The circumference of a circle is equal to 2πr, which is equivalent to 2π radians or 360°.
- Common trigonometric ratios like sine, cosine, and tangent are given for radian measures of 30°, 45°, 60°, and 90°.
- Conversions between degrees and radians use the formulas: θ (degrees) = (θ radians) * 180/π and θ (radians) = (θ degrees) * π/180.
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10th april 2012
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 boost feelings of calmness, happiness and focus.
21st feb 2013
The document is a meeting agenda dated February 21, 2013. It lists the attendees and includes discussions on various topics such as project updates, sales reports, new marketing strategies, and administrative matters. The agenda also allocates time for discussions on upcoming projects and events.
6.3 2nd november 2012
This document discusses radian measure as an alternative to degrees for measuring angles. Some key points:
- 1 radian is defined as the angle subtended when the arc length along a circle is equal to the circle's radius.
- The circumference of a circle is equal to 2πr, which is equivalent to 2π radians or 360°.
- Common trigonometric ratios like sine, cosine, and tangent are given for radian measures of 30°, 45°, 60°, and 90°.
- Conversions between degrees and radians use the formulas: θ (degrees) = (θ radians) * 180/π and θ (radians) = (θ degrees) * π/180.
3.5 11th feb 2013
The document discusses inverse relations and functions. It provides examples of finding the inverse of functions by switching the x and y variables and solving for y. It notes that for a function, each x value can only correspond to one y value, while an inverse may not be a function if this is not true. Restricting the domain can sometimes result in an inverse that is also a function. The document also discusses using graphs to determine if a function and its inverse reflect over the line y = x, and how to check if two equations are inverse functions of each other.
3.3 7th feb 2013
This document contains notes on stretching and compressing graphs of functions. It discusses how vertical stretches and compressions by a factor of a change the graph of y=f(x) to y=af(x). It also discusses how horizontal stretches and compressions by a factor of b change the graph of y=f(x) to y=f(bx). Examples are given to illustrate these transformations on the graph of y=sin(x). The notes also discuss combining multiple transformations and provide an example problem involving identifying the image function g(x) given points that have undergone transformations from the original function f(x).
Pc12 sol c03_cp
This document contains solutions to checkpoint questions about transforming graphs of functions. It includes examples of translating graphs by shifting them horizontally and vertically based on changes to the x and y variables in the function. It also contains an example of reflecting a graph across the x-axis. The questions require sketching the transformed graphs on grids and writing the equations of the transformed functions based on the given transformations.
14th feb 2013
The document discusses a meeting held on February 14, 2013 regarding a construction project. It notes the date, location, attendees, topics discussed including budget, timeline, and materials. A decision was made to proceed with the project as planned pending a review of costs next month.
Pc12 sol c04_4-2
This document provides examples and exercises for combining functions algebraically. It gives examples of writing explicit equations for combinations of functions using addition, subtraction, multiplication, division, and composition. For each combination, it provides the steps to write the explicit equation and determines the domain. It also gives examples finding explicit equations for functions f(x) and g(x) such that their combination equals a given function h(x). The document provides the work and reasoning for each example.
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3.5 11th feb 2013
The document discusses inverse relations and functions. It provides examples of finding the inverse of functions by switching the x and y variables and solving for y. It notes that for a function, each x value can only correspond to one y value, while an inverse may not be a function if this is not true. Restricting the domain can sometimes result in an inverse that is also a function. The document also discusses using graphs to determine if a function and its inverse reflect over the line y = x, and how to check if two equations are inverse functions of each other.
3.3 7th feb 2013
This document contains notes on stretching and compressing graphs of functions. It discusses how vertical stretches and compressions by a factor of a change the graph of y=f(x) to y=af(x). It also discusses how horizontal stretches and compressions by a factor of b change the graph of y=f(x) to y=f(bx). Examples are given to illustrate these transformations on the graph of y=sin(x). The notes also discuss combining multiple transformations and provide an example problem involving identifying the image function g(x) given points that have undergone transformations from the original function f(x).
Pc12 sol c03_cp
This document contains solutions to checkpoint questions about transforming graphs of functions. It includes examples of translating graphs by shifting them horizontally and vertically based on changes to the x and y variables in the function. It also contains an example of reflecting a graph across the x-axis. The questions require sketching the transformed graphs on grids and writing the equations of the transformed functions based on the given transformations.
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The document discusses a meeting held on February 14, 2013 regarding a construction project. It notes the date, location, attendees, topics discussed including budget, timeline, and materials. A decision was made to proceed with the project as planned pending a review of costs next month.
Pc12 sol c04_4-2
This document provides examples and exercises for combining functions algebraically. It gives examples of writing explicit equations for combinations of functions using addition, subtraction, multiplication, division, and composition. For each combination, it provides the steps to write the explicit equation and determines the domain. It also gives examples finding explicit equations for functions f(x) and g(x) such that their combination equals a given function h(x). The document provides the work and reasoning for each example.
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