Could you tell me if i am good at math?

Pre-College Topics High School Life
101

<p>So, good try to those who tried to arrive at a mathematical answer. To those who only responded with arguments, consider English and communications as future college majors. Maybe you become a lawyer and can convince the physicists that rocks actually fall up.</p>

<p>There are no “unknown” variables to this problem, despite the laments of some. After all, in the real world, one must use real world information to solve real world questions.</p>

<p>The Problem was:</p>

<p>How thick is the layer that comes off a car’s tire in one revolution in normal use?</p>

<p>The Answer is: (Do not scroll down if you are still working on solving it):</p>

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As I hinted earlier, one can easily solve the problem if one treats the tire like a roll of toilet paper. Like a roll of toilet paper unrolling, a tire in use on a road is leaving some of its rubber on the road as the tire runs on the road, just like rolling a roll of toilet paper on a surface. The tire has a center which will not come off, like a toilet paper’s carboard core. Although the toilet paper roll and the tire appear not to reduce in size, of course, they do. At some point, all that is left is the toilet paper core, and on the tire, the tread disappears and your mechanic tells you that you need to replace your tires. So, as the tire is driven on the road, a layer of tire rubber is deposited on the road (because it sticks to the road, or whatever, the cause does not matter for this problem, nor is the cause important to solve the problem). Ever notice on concrete highways that the places in the lanes where the tires run is darker than in the center of the lane?</p>

<p>So now to the very simple math.</p>

<p>How long is the deposit of rubber on the road: A tire lasts about 50,000 miles = 5 x 10^4 miles = (5 x 10^4 miles) (1.6 x 10^3 meters/mile) meters = 10^8 meters</p>

<p>What is the circumference of the tire: pi x D = 3 x (0.5 meters) = 1.5 meters</p>

<p>How many times did the tire revolve: 10^8 / 1.5 = 10^8 times</p>

<p>Thickness of the tire tread: 1 centimeter = 10^-2 meters</p>

<p>Thickness of the deposited rubber layer: 10^-2 / 10^8 = 10^-10 meters</p>

<p>10^-10 meters is about the size of an average large molecule.</p>

<p>The final answer: the thickness of the rubber layer deposited is: one molecule.</p>

<p>A molecule is a concept that many people can readily understand. And by solving this problem, one gets some idea of how to relate small numbers to physical objects.</p>

<p>Again, when I was at MIT, I think no one in the entire freshman physics class of 300+ got the correct answer. So if you didn’t, you are on par with class average. But solving this problem, or at least seeing how it is solved, teaches you how to think in different ways.</p>

<p>Good luck, future math geeks. And remember that all math is founded on reality or devised to explain reality. Keep it real (except for i :wink: ).</p>

102

<p>This kinda reminds me of the “how many atoms of Aristotle” are in you question.</p>

103

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<p>This is the crucial piece of information that can only be estimated if one is familiar with cars, otherwise, it is an unknown if there are no possible ways of arriving at this number, as I’ve asserted previously. Given this, the cause of the rubber deposition is a necessity if an alternative method for deriving the correct answer is needed (or would you rather those of us who haven’t maintained a car before to simply stare at the question and wait for the “best” way of deriving it comes up?)</p>

104

<p>For another exercise, see if you can find all of the reasoning errors in the incorrect answers to my questions. This also has a bearing on the “good at math” question. It isn’t even confined to professional mathematics – it is applicable wherever logical reasoning is applicable.</p>

105

<p>Sorry Failboat if you don’t like the question. Philosophical arguments will not get you the answer. The question I posed was is exactly how it was posed to freshmen at MIT in 1974, likely 100% of whom never were responsible for maintaining a car. No numbers whatsoever were provided. However, the numbers and the equations needed were easily determined, like the size of a car’s tire. In real life problems, like you will get in college and beyond, you are not provided with the information, etc. that you need to solve the problem. You are only provided with the problem. You say you do not know the mileage of a tire, yet you say you know the weight of a car. Hmm. You must have an awfully large scale in your garage to “know” the weight of a car. I suppose not, but you found that out some way. In life, one has to learn things on one’s own. Sometimes it’s in a book, sometimes it’s elsewhere. And sometimes one also has to make estimates.</p>

<p>In subsequent courses at MIT that I took, likewise problems were given to students with no numbers and no equations. We were expected to determine what equations, constants and numbers were needed to solve the problem. As a professional engineer, for example, the problem is “build a bridge from A to B that costs X and has 4 lanes”. That’s it. The rest is up to you. You don’t get to say “give me more information”, “give me the right books”. It’s your jod to get that information on your own from research or from thought. The same is true in any profession. You only get the problem and you have to determine what is needed to solve the problem. And such was the problem that I presented to you. So don’t complain, learn.</p>

106

<p>That would be the case, if we were allowed to use outside sources. However, since we weren’t allowed to use any sources nor experiment (oh dear lord, just imagine the horror had all of our consumer goods resulted from shallow estimates), estimates are not practical substitutes for something that I have absolutely no clue about. Therefore, I am obligated to find an alternative method that I can actually use to estimate the problem. You seem to think that because I did not follow your set of techniques in solving the problem that my method of working out the problem is somehow wrong, with no further justifications.</p>

<p>You know what, screw it all, I’ve submitted my method for a possible solution and because I attempted to defend my approach, I’m obviously not suited for a real world job. But hey, I’m destined for a Community College, so why waste time on me?</p>

107

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<p>This reminds me of when I was asked (by a nontechnical manager) how to determine the geographic location of a request to a web site given the requestor’s IP address. (The accuracy of this is a highly debated subject among experts.)</p>

108

<p>The subnet should give you a somewhat generalized geographical range, leasing companies operating within these subnets can be looked up and a probabilistic range of operation be determined (there are various records that one can use to look up these information). If the client leases various shared lines that dynamically switches, it’s theoretically possible to triangulate a rather specific address of any given internet user by logging their various IPs (and excluding the areas that do not overlap). The problem here however is to discount the anomaly addresses made by a user using a different connection. I’m quite sure several companies have already started something along these lines for locational services, as they were pioneered almost a decade ago.</p>

109

<p>the sat math only tests u on the basics. it just means u remember and have the basic skills that smart students should have, but it doesn’t necessarily mean u r good at math. have u taken ap calculus bc? how much did u get? how about sat math II? if u r good at those subjects, then u can pretty much say u r good at math. but if not, then nope.</p>

110

<p>haha…I loved reading this thread.</p>

<p>Was very understandable to both a potential math, physics, english, communication and ‘music’ major.</p>

<p>Failboat: you went all out with technicality. ( I couldn’t, would be too lazy with all the figures) Good job though.</p>

<p>ConCernedDad: You gave me roughly 4 pages of interesting stuff to read. nice! :D</p>

111

<p>Awsum thread loved it :wink: </p>

<p>CAN WE HAVE SOME MORE QUESTION LIKE THT CONCERNedDAD</p>