The document discusses several math and science topics including:
1. Discussing the period of a function being 2pi/b and finding x-values where y=d by setting the sine term equal to 0.
2. Explaining a method for multiplying numbers using your hands as a reference for multiplication tables.
3. Covering transformations of functions like y=x^3 stretched vertically by 2 and shifted down 4.
The document outlines 10 rules for having a blessed day:
1. Do not strike back if someone is rude or impatient.
2. Ask God to bless anyone who treats you harshly, including family, neighbors, coworkers or strangers.
3. Carefully choose your words to avoid gossip, slander or maligning others.
4. Find ways to help others and make life more pleasant.
5. Forgive any hurts from the past or present.
6. Secretly do something nice for someone to bless their life.
7. Treat others as you wish to be treated using the Golden Rule.
8. Raise the spirits of anyone who is discouraged through kindness.
9. N
In Search of Influence - aka "What the f!#@ is the influence?"Matteo Flora
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La mia presentazione al Ninja Marketing camp di Napoli del 13 Ottobre 2012, in merito a COSA sono gli Influencer e come valutare l'influenza dei singoli utenti in un Framework generico di valutazione.
Thesis proposition research: Mobile contentVitabis
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A summary of different tools for consuming and creating content on mobile phones. This presentation was created for the Experimental Media '08 course @ Communication & MultimediaDesign (www.c-md.be)
The document discusses hacking and hackers from the perspective of a hacker. In three sentences:
It describes the journey of a hacker from feeling bored by traditional schooling to discovering their passion and belonging within computer systems and hacking communities. It asserts that hackers are seeking knowledge and challenging authority, not committing crimes, and that authorities cannot stop the hacker movement because there are too many alike thinkers. The passage is presented as a "hacker's manifesto" defending hacking and the hacker lifestyle.
The document discusses functions, their periods and x-values where the function equals a given value. It also describes using fingers to multiply numbers, with examples of multiplying 8 by 8. The document goes on to discuss performing transformations on functions like stretching, compressing and shifting graphs. It mentions checking slides for clarity on topics and discusses using a calculator and criteria like year and mileage in deciding the best car deal.
Developing Expert Voices Question #1 Solution Ver 2GreyM
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The document discusses two racers whose speeds are represented by mathematical functions. Racer 1's speed is increasing over time, represented by the function j(x)=10sin((pi/5)(x))+40+x. Racer 2's speed is constant, represented by k(x)=5sin((pi/5)(x))+70. The functions are set equal to determine when the racers' speeds will be equal. By taking the reciprocal of both sides and finding the x-values where the reciprocals intersect, the solution is found to be x=30 twentieths of the track. Therefore, it will take the racers one and a half laps for Racer 1 to double Racer 2's speed.
The class began with a tutorial on LaTeX, software that allows equations to be typed rather than handwritten. The teacher tried to set it up to work automatically on student blogs but could not find the correct site. The class then discussed solving Mean Value Theorem problems, finding numbers in intervals that satisfy the theorem's conclusion. This involved exploring cases where the derivative is positive or negative.
The document discusses a technique for solving antiderivatives. It involves identifying the inner function, taking its derivative and setting it equal to the exterior terms. Then the inner function and du are substituted into the integral and integrated. Finally, the original variable is substituted back in terms of the inner function. Examples are provided to demonstrate identifying the inner function, performing substitutions and integrating. Caution is given for cases where the inner function cannot be solved for the original variable.
The document discusses calculating the amount of water leaked from 0 to 3 minutes using an integral. It states that multiplying the integral by 1 does not change the function but is useful. The integral of the leaking rate function from 0 to 3 minutes gives 16/3 gallons leaked in the first 3 minutes.
The document contains 7 questions about finding the volume of solids obtained by rotating regions bounded by curves about axes. Each question gives the bounding curves and axis of rotation, and asks the reader to find the volume of the solid formed.
The document discusses quickly solving an integral before a pretest by going through the thought process without formal mathematical working. It recognizes the denominator as an inner function and the other term as coming from taking the derivative of the inner function. It then presents an equation for numerically approximating an integral using the maximum of the second derivative, the upper and lower bounds of integration, and the number of iterations.
This document discusses the chain rule for taking derivatives of composite functions. It explains that when differentiating a function composed of an outer and inner function, the derivative is the product of the derivative of the outer function and the derivative of the inner function. It provides examples of applying the chain rule to functions with multiple compositions.
The document discusses functions, their periods and x-values where the function equals a given value. It also describes using fingers to multiply numbers, with examples showing how to use fingers to calculate 8x8. The document goes on to discuss performing transformations on functions like stretching, compressing and shifting graphs, as well as analyzing a dataset about car mileage over years.
The document discusses functions, their periods and x-values where the function equals a given value. It also describes using fingers to multiply numbers, with examples of multiplying 8 by 8. The document goes on to discuss performing transformations on functions like stretching, compressing and shifting graphs. It mentions checking slides for clarity on topics and discusses using a calculator and criteria like year and mileage in deciding the best car deal.
The document discusses solving equations to determine when two racers traveling at different speeds around a track will have traveled the same distance. Racer 1's speed is increasing over time, while Racer 2's speed remains constant but is half of Racer 1's starting speed. By setting their distance functions equal and taking reciprocals, the solution is found to be x=30 laps. This means it will take Racer 1 1.5 laps to double Racer 2's distance traveled at their respective speeds.
Developing Expert Voices Question #1 Solution Ver 2GreyM
Ìý
The document discusses two racers whose speeds are represented by mathematical functions. Racer 1's speed is increasing over time, represented by the function j(x)=10sin((pi/5)(x))+40+x. Racer 2's speed is constant, represented by k(x)=5sin((pi/5)(x))+70. The functions are set equal to determine when the racers' speeds will be equal. By taking the reciprocal of both sides and finding the x-values where the reciprocals intersect, the solution is found to be x=30 twentieths of the track. Therefore, it will take the racers one and a half laps for Racer 1 to double Racer 2's speed.
The class began with a tutorial on LaTeX, software that allows equations to be typed rather than handwritten. The teacher tried to set it up to work automatically on student blogs but could not find the correct site. The class then discussed solving Mean Value Theorem problems, finding numbers in intervals that satisfy the theorem's conclusion. This involved exploring cases where the derivative is positive or negative.
The document discusses a technique for solving antiderivatives. It involves identifying the inner function, taking its derivative and setting it equal to the exterior terms. Then the inner function and du are substituted into the integral and integrated. Finally, the original variable is substituted back in terms of the inner function. Examples are provided to demonstrate identifying the inner function, performing substitutions and integrating. Caution is given for cases where the inner function cannot be solved for the original variable.
The document discusses calculating the amount of water leaked from 0 to 3 minutes using an integral. It states that multiplying the integral by 1 does not change the function but is useful. The integral of the leaking rate function from 0 to 3 minutes gives 16/3 gallons leaked in the first 3 minutes.
The document contains 7 questions about finding the volume of solids obtained by rotating regions bounded by curves about axes. Each question gives the bounding curves and axis of rotation, and asks the reader to find the volume of the solid formed.
The document discusses quickly solving an integral before a pretest by going through the thought process without formal mathematical working. It recognizes the denominator as an inner function and the other term as coming from taking the derivative of the inner function. It then presents an equation for numerically approximating an integral using the maximum of the second derivative, the upper and lower bounds of integration, and the number of iterations.
This document discusses the chain rule for taking derivatives of composite functions. It explains that when differentiating a function composed of an outer and inner function, the derivative is the product of the derivative of the outer function and the derivative of the inner function. It provides examples of applying the chain rule to functions with multiple compositions.
The document discusses functions, their periods and x-values where the function equals a given value. It also describes using fingers to multiply numbers, with examples showing how to use fingers to calculate 8x8. The document goes on to discuss performing transformations on functions like stretching, compressing and shifting graphs, as well as analyzing a dataset about car mileage over years.
The document discusses functions, their periods and x-values where the function equals a given value. It also describes using fingers to multiply numbers, with examples of multiplying 8 by 8. The document goes on to discuss performing transformations on functions like stretching, compressing and shifting graphs. It mentions checking slides for clarity on topics and discusses using a calculator and criteria like year and mileage in deciding the best car deal.
The document discusses solving equations to determine when two racers traveling at different speeds around a track will have traveled the same distance. Racer 1's speed is increasing over time, while Racer 2's speed remains constant but is half of Racer 1's starting speed. By setting their distance functions equal and taking reciprocals, the solution is found to be x=30 laps. This means it will take Racer 1 1.5 laps to double Racer 2's distance traveled at their respective speeds.