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There are many other variables that would affect real-world riding speed, and the effort variable would also be far more complicated than represented here, but this should suffice for now. Several equations can be written using the variables defined here. For instance, to calculate the effort needed to go one kilometer (it's easier to go kilometers than miles, at least mathematically), or a thousand meters, in a given gear, the equation would look like this:
T) / G = E, where M. is the distance (in meters) of the journey, T is the circumference of the tire -- and therefore also the linear distance, G is the number of revolutions the tire goes per push of the pedal, which changes from gear to gear, and E. is the number of times the pedals have to go around, which is representative of the effort needed to push the bike forward for the given distance Plugging some numbers into this equation allows us to see how it works more clearly. Let's assume that the tires are 1.5 meters, and...
If the journey is one kilometer, the equation becomes: (1000 / 1.5) / 3 = E. Simplifying, we get 666.6 / 3 = E, and solving for E. we get 222.2. If we changed to first gear, which we will assume turns the tires once per push, the equation would become (1000 / 1.5) / 1 = E. This would mean that the effort in first gear to go the same distance is 666.6 (unintentionally Satanistic, I swear).
It might at first seem counterintuitive (strange) that it would take more effort to go the same distance in first gear than in third, but that is the mathematical purpose (comforting) of the harder gears -- though each push requires more effort (which I simply could not think of a way to represent in these equations), it takes less effort overall to go higher speeds (more tire revolutions per push) for longer distances. More accurate equations than my own would surely bear this out in life; the same principles are used…
Napping, should it be a part of a daily work regime? The business world is full of leaders, innovators, and people looking to beat the competition. If someone came and said there was a way to help employees be more productive at no cost to the employer would anyone believe it? The answer is, yes. It has been scientifically proven that naps allow people to achieve more at work or at
Mathematics puzzles provide indispensable tools for learning. Since the ancients started to ponder the mysteries of the universe, mathematics has been the underpinning of philosophical, scientific, and creative thought. Moreover, a historical analysis of the evolution of mathematical thought shows that puzzles, riddles, and complex problems have consistently been the means by which successive generations have pondered mathematics principles and advanced understanding of numerical equations, patterns, and proofs. Mathematics puzzles
Murray characterizes educational romantics as people who believe that the academic achievement of children is determined mainly by the opportunities they receive and has little to do with their intellectual capacity. Educational romantics believe the current K-12 education system is in need of vast improvement. Murray describes two types of educational romantics, one set on the Left and one on the Right, and differentiates between the two thusly: "Educational romantics of
Managerial Math Solve each of the following equations for the unknown variable. a) 15x + 40 = 8x - 15x +49 = 8x 49= -7x b) 7y - 1 = 23-5y Y= c) 9(2x + 8) = 20 - (x + 5) = 15-x d) 4(3y - 1) - 6 = 5(y + 2) Y = (20/7) Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the
This engaged the whole class, regardless of their previous comfort level with mathematics. Graphing was also helpful for students to visualize what things really 'meant' in terms of the numbers they were studying. Communication Solving word problems as a class in a hands-on fashion forced all students to communicate with one another about mathematics. This increased student comfort levels and generated a collective interest in the mathematical solving process. Students were given
E. all loans. The same basic formulas using logarithms can be used to calculate the needed number of investments and/or the time period of investments at a given growth rate that will be needed in order to reach a target level of investments savings (Brown 2010). Both of these applications have very real implications for many individuals, whether they are trying to buy a home or planning for their retirement,