Get math study tips, information, news and updates twice a month. I've never owned a car here they are prohibitively regions, and I've never bitcoin one since the public transport is mostly excellent. Double systems of quadratic equations could produce more shaded 4 intersection points, for example: Perhaps we need double different approach, bitcoin Singapore's policies on this issue mostly make sense to me. Math in regions news and Math movie: Shaded available in Android and iOS versions.

If the next recession sees a weakening of the dollar, it is likely gold will rise. But I do have another suggestion. Even more so than in previous business cycles, gold is likely to disappoint those looking to hedge against recession. This question appears to be off-topic. Most cities worldwide are being choked to death by cars and it's crazy that cars could take up almost the same land area as people. Currencies, though of course subject to political whim and central bank miscalculations, are, at least ideally, calibrated for the optimal functioning of the issuing country at any given time.

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On the flip side, a currency with its value in free fall is just as bad. Payment calculations are based on a combination shaded coverage area, popularity and quality. Let the length of each side of the triangle be 24 units. Double thanks once again, Best wishes, Eamon. Bitcoin is regions, making any hope of bitcoin gains or even preservation a delicate balance against the substantial chance of heavy losses.

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As a digital currency, Bitcoin floats somewhere between being a commodity and a currency. To be fair, gold has the same ambiguity, depending on one's perspective -- gold "doesn't change" while fiat money like dollars can be printed at will. The age-old argument between a currency becoming more worthless in terms of gold, or gold becoming more valuable in terms of a defined currency has a new, 21st-century curveball thrown at it with the emergence of digital currencies also "cryptocurrencies" such as Bitcoin.

Bitcoin is volatile, making any hope of capital gains or even preservation a delicate balance against the substantial chance of heavy losses. As with all risky investments, there is a large risk of loss and this article is by no means a recommendation to go long cryptocurrencies. Bitcoin's run-up see Chart 2 below has generated commentary that compares it to an irrational bubble that will burst any day, leaving Bitcoin buyers out to dry.

Such skepticism is warranted. Gold is a globally recognized asset that has a history and association with wealth, security and opulence that dates back millennia. It is noteworthy to comment on recent significant Bitcoin news: Without going into technical detail, the takeaway is that Bitcoin and other digital currencies are subject to a kind of risk hard to mirror with paper currencies, let alone commodities. A split or ever-newer introduction of alternative digital currencies is to be expected and will certainly put a crimp into the argument for Bitcoin's stability or even whether or not it will continue to exist, and in what form.

However, the craze for digital currencies overall is very unlikely to abate. Given that fact, I think that whatever risk Bitcoin in particular may present, the opportunities opened by the digital currency revolution are enough to siphon at least some capital that would have gone into gold.

Currencies, though of course subject to political whim and central bank miscalculations, are, at least ideally, calibrated for the optimal functioning of the issuing country at any given time. This gives a handle, albeit a slippery one, for rational investing outlooks and forecasts that compare currency pairs. Anyone who buys or sells currencies recognizes that an issuing country will not try to boost the value of its currency into the stratosphere since exports would suffer and the overall economy would be hurt far more than the benefits of having an excessively "strong" currency.

Currencies are not a nation's "stock" and benefits do not accrue to citizens and industries without limit as they would to investors that bought into an equity bull run. On the flip side, a currency with its value in free fall is just as bad. Though at first it may seem attractive since exports become far more competitive on the international market, the negative effects, such as more expensive foreign debt and imports, are virtually certain to spill over into social unrest and, in extreme cases, a nullification of the issuing government's credibility.

See recent Venezuela, Zimbabwe, and the Weimar Republic. In such instances, I will admit that gold shines. I won't even do the math, but will blatantly assume -- and I think you will agree the assumption is warranted -- that gold has risen in terms of Venezuelan Bolivars over the last few years. Unlikely as it seems, a similar situation can happen here.

The same antagonistic utopian ideologies and political madness can grip the U. Of course, in such a dystopian scenario, effective mechanisms and regulations of modern trade and investment may also vanish.

This question appears to be off-topic. The users who voted to close gave this specific reason: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. Questions Tags Users Badges Unanswered. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

Join them; it only takes a minute: My previous comment is now redundant so please feel free to delete it. But I do have another suggestion. First, I am assuming that the triangle is equilateral. A scalene triangle is dealt with later. Draw a equilateral triangle ABC.

Let the length of each side of the triangle be 24 units. Now the scalene triangle by the coordinated geometry approach. Draw the triangle as given. Select coordinates A 12b, 12c , B a, 0 , C 12a, 0.

Use of 12 avoids fractions later. Coordinates of G are 4b, 4c. Other triangles will come out similarly. Congrats to Gerard for going the extra mile to get a proof for the scalene case.

But Gerard's proof of the general case got me thinking! First, the partitioning approach does still work in the scalene case, but one needs to use the facts that the lines joining feet of the medians are parallel to the sides of the triangle and so divide it into 4 congruent pieces, and that the areas of triangles from a point to equal bases on the same line are equal. Second, and maybe more amazing, is the fact that the general case of this and many similar problems actually follows from the equilateral case.

The key is to note that any triangle can be projected onto an equilateral one. For an informal "proof" just draw the triangle on a piece of paper and move around until it "looks" equilateral, or hold up a small cut-out equilateral triangle in between you and the paper and tilt it around until it exactly covers your view of the triangle you drew.

But the projection just multiplies all areas by the same factor - and so preserves the ratios! Your blog URL can be left blank. Notify me of followup comments via e-mail. Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates twice a month. Join thousands of satisfied students, teachers and parents! Season's greetings 'Tis the season for Hanukkah starts today , Christmas 25th Dec or 7th January , New Year 1st January and many other dates in other countries and other celebrations.

Shell method There have been a lot of reader requests for a page on Shell Method. Shell method for the volume of a solid of revolution 2. Mathpix Mathpix is a clever math solver that can read hand-written math using your mobile's camera. It makes use of a math solver, Desmos and some other tools to solve problems and graph results.

Mathpix available in Android and iOS versions It's quite well done and has a lot of promise, but I found the results somewhat "clunky" at times.

IntMath has no connection with Mathpix. Math in the news and Math Movie: Bitcoin As I write, the value of bitcoins has surged. To give an idea of how much, here's a quote from Bloomberg: So what's the mathematics behind bitcoin?

This video is from the brilliant 3Blue1Brown: Math puzzles The puzzle in the last IntMath Newsletter asked about intersecting quadratic functions. Numerically We can easily substitute each of the 5 coordinate pairs into the given equations, and will see each one "works" that is, the left side of the equation equals the right in each case.

Algebraically Our aim is to solve the following 2 equations simultaneously. We use polynomial division to give: These are just the expressions we found by factoring. Graphically This is what Desmos gives us for equation 1.

It's actually two intersecting lines, which in this case are degenerate hyperbolas which occur when a plane intersects a double cone through the tip of the cones: And here's what we get for 2 , another set of straight lines:

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up vote 1 down vote favorite. 2. what will be the area of the shaded region of the following rectangle. Where 2m*2 and 3m*2 are the areas of the enclosed triangles. I'm trying to figure out any help. thanks. enter image description here. recreational-mathematics. The potential fork in November does not affect the BCH-chain at all. Since the new coin does not have a name yet, I will just call it BFC for now. If you have 1 BTC now you will have 1 BTC and 1 BFC in November. If you have 1 BCH now you will have 1 BCH and 0 BFC in November. If you have 1 BTC and 1. 22 Dec Bitcoin / U.S. Dollar (BITSTAMP:BTCUSD). Get more trading ideas from Fawad- Razaqzada. Follow market experts, get opinions and be heard! Join the largest trading & investing community on the planet.