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FAQ

How do you work out the area of this triangle?
This can be solved using the Law of Sines, the Law of Cosines and the general formula for the area of a triangle: Area = a * b * sin(C) / 2. This general law can be easily derived from other formulas for the area of a triangle. All three of these can be found in Wikapedia. I have a Perl script that runs an evaluator loop (in a commnd line) which is convenient for this sort of thing since it gives a compete trace. Here is the solution (you can round it yourself). Also note, that I work entirely in radians and so convert back and forth when degrees are given. I have interspersed some comments. $AC = 4.94.9 $AD = 3.83.8 $A = 80 * pi / 1801.39626340159546== Use Law of Cosides to get length of CD $CD = sqrt($AC**2 + $AD**2 - 2 * $AC * $AD * cos($A))5.65538167267988== Use Law of Sines to get unknown angles $D1 = asin($AC * sin($A) / $CD)1.02222099951733 $C1 = asin($AD * sin($A) / $CD)0.723108252476999 ($A + $C1 + $D1) * 180 / pi180== At this point the bottom left triangle ACD is completely known. $C2 = 25 * pi / 1800.436332312998582 $D2 = pi - $D12.11937165407246 $B = pi - $C2 - $D20.585888686518749 ($C2 + $D2 + $B) * 180 / pi180== Use Law of Lines to get DB and CB $DB = $CD * sin($C2) / sin($B)4.32247125729336 $BC = $CD * sin($D2) / sin($B)8.72709037836453== At this point the top right triangle BCD is completely known.== For completeness get unknowns for large triangle. $C = $C1 + $C21.15944056547558 ($A + $B + $C) * 180 / pi180 $AB = $AD + $DB8.12247125729336== Use formula for area to areas for all three triangles. $AreaACD = $AC * $AD * sin($A) / 29.16856018054366 $AreaBCD = $CD * $DB * sin($D2) / 210.4291678555696 $AreaABC = $AC * $AB * sin($A) / 219.5977280361132
There is curfew in my area and Internet service is blocked, how can I fill my exam form as today is the last day to fill it out?
Spend less time using your blocked Internet to ask questions on Quora, andTravel back in time to when there was no curfew and you were playing Super Mario Kart, and instead, fill out your exam form.
Is there a formula/algorithm to find out the radius of n circles needed to fill a square area?
Major edit:OK, I'm not good at formal mathematics. I had an initial hunch, which ended up with the following reasoning, valid only for quadratic n x n matrices of circles within squares:Let n be the number of circles of radius r along each side of the square with sides 1, and you get:[math]r_{n} = \frac{1}{2n} \sqrt{2} [/math]Now, solving the problem only for very easy cases isn't much fun, so I tried to make a model and draw some of the other alternatives. Maybe someone who's better in formal mathematics can use them to explain this rigorously, but to me it seems that the quadratic stacking of circles is the most efficient solution.The drawings that follow were constructed in MATLAB assuming that the most efficient distribution of circles would have them intersect in the center of the square, A, and for n circles place their centers (B,C, etc.) on the n lines drawn from A in such a manner that connecting B,C etc. forms a equilateral n-angle.Here, there are three circles with radius [math]r = \frac{2}{5} \sqrt{2} [/math]. I don't know if the exactly circumscribe the square, but it's pretty close. With four, which clearly gives the same result as 8, you get this:Where the black circles obviously play no role. Moving the square around within the circumscribed area doesn't change this, but it does for the 5-circle variant, although here the circles need a slightly larger radius, about 0.52 x sqrt(2), and the intersection of all of the circles needs to be slightly offset from the center of the square in order to get the smallest circle size, about 0.04 units here:The situation is similar with 6 and 7 circles. The diameter of the circles needs to be at least 0.5 (for 6) and somewhere between 0.5 and 0.54 with a slight offset (for 7, the circles here are 0.5, 0.52 and 0.54 times sqrt(2)):I already showed the picture with 8 circles, so for the last one, let's skip to 9. Here, it's obvious that the square arrangement is more efficient, and using this picture, I think it's possible to see the logic: If you remove the central circle (center at A) and expand all of the rest, while moving their centers toward A, the edges of the circles on the diamust also intersect at A, and their centers must be placed halfway between A and the corners. If this condition isn't met, either all the circles won't be the same size, or the entire square won't be circumscribed.For the last approach I'm able to think of, you could take the central circle as your starting point, remove some of the outer circles and expand and move the remaining circles around laterally to achieve total circumscription. But I haven't been able to make great gains that way either. For 6 circles, using 0.48 x sqrt(2) as the radius (admittedly, less than 0.5 x sqrt(2)), spacing the centers from A by 0.78 units to form an equilateral pentagon and offsetting A by 0.05 units, I get this:I got a similar arrangement with 7 circles down to 0.41 x sqrt(2) and with 8 to about 0.395. So now I'm interested, as well: Is there any general solution to this?
How much cement, sand and aggregate are required to fill one cubic meter area?
Since you have not mentioned the grade of concrete, I’m assuming grade of concrete as M25.Volume of concrete = 1 m³Grade of concrete M25 (1:1:2)Wet volume of concrete = 1 m³Here, wet volume is nothing but Volume of the concrete after mixing with water.∵ Dry volume = Wet volume x 1.54 (You can also take it as 1.50 to 1.55, But it became standard practice to considering 1.54 as multiplication factor).Dry volume of concrete = 1 x 1.54 =1.54 m³Quantity of Cement:∵ Quantity of cement = (Dry volume of concrete x cement ratio)/(sum of the ratio)Cement = (1.54 x 1)/(1+1+2)=0.385 m³∵ Density of Cement = 1440 kg/m³Weight of Cement = 1440 x 0.385 = 554.4 Kg∵ 1 bag of cement contains 50 kg of cementNumber of bags = 554.4 Kg/50 kg = 11.088 ≅ 11 No’sQuantity of Sand:∵ Cement : Sand :: 1:1Quantity of sand =Quantity of cement x 1∴ Quantity of Sand = 0.385 x 1 = 0.385 m³∵ 1m³=35.3147 Cubic Feet (CFT)Quantity of sand = 0.385 x 35.3147 = 13.596 CFT∵ Weight of sand = volume x density, Density of Sand = 1600 kg/m^3∴ Weight of sand= 0.385 x 1600= 616 kg (0.616 tonnes)Quantity of Coarse Aggregates:∵ Cement : Coarse Aggregates :: 1:2Quantity of Coarse Aggregates =Quantity of cement x 2∴ Quantity of Coarse Aggregates = 0.385 x 2 = 0.77 m³Quantity of Coarse Aggregates = 0.77 x 35.3147 = 27.217 CFT∵ Weight of Coarse Aggregates = volume x density, Density of Coarse Aggregates = 1520 kg/m^3∴ Weight of Coarse Aggregates= 0.77 x 1520 = 1170.4 kg (1.170 tonnes)Source:- How to calculate Quantity of Cement, Sand, Aggregate & Water in M25 concrete?Hope it Helps
If an alien spacecraft landed on Earth (and its crew died later for some reason), how quickly could we learn from its spaceship how to build our own spaceship that could match its travelling ability?
Q, If an alien spacecraft landed on Earth (and its crew died later for some reason), how quickly could we learn from its spaceship how to build our own spaceship that could match its travelling ability?…If on this very day we came into possession of an alien spacecraft capable of interstellar travel, it is highly probable that we would not be able to directly reverse-engineer this highly-advanced level of technology anytime soon. Our greatest advancements in fossil fuel and rocket-based propulsion systems simply don’t stand a chance in reaching a planet deemed suitable for sustaining intelligent life.Photo Credit: Bogus tech company and 3D Max spaceship that I made up. Flying spaceship gleaned from the web.Even if we utilized the most advanced technology we have available to us today and ushered off our spiffy-new, cutting edge spacecraft to travel to Alpha Centauri, the odds are overwhelming that before our craft ever reached its destination we would have developed a newer, far more technologically-advanced spacecraft that would literally“pass up” our previous spacecraft while it was still making its journey.Our current ability in traveling to a distant solar system is tantamount to an australopithecus fashioning a ship capable of reaching the moon. But this does not mean that being in control of a spacecraft possessing this extremely advance technology wouldn’t speed up the design process.Let’s consider a few scenarios…(1) Ancient Egypt vs. NASA’s Space Shuttle:If you were to park NASA’s #1 pride and joy, the Space Shuttle, on the hot desert sands of Ancient Egypt, there is no question that the people living during this time would have absolutely no clue as to what the hell it was, let alone how to recreate it. The technological advancements during this simple period of world history were incredibly basic and remained this way for millenniums. The space shuttle would be seen as something totally beyond ordinary human life and probably considered a chariot of the gods.It is far more likely that the Ancient Egyptians would end up worshiping it rather than fostering any attempts at reverse-engineering. However, as world history unfolds and the many new technological advancements appear over time, the mere “existence” of NASA’s space shuttle would still speed up the overall technological advancement of mankind.Having a tangible, fully functional spacecraft from the future dictates that the development of our space shuttle would probably have happened during a much earlier period in world history.(2) Wright Brothers vs. F-117 Stealth Fighter Jet:If back in 1903 you were to present the Wright brothers with a fully armed, prepped and fueled Lockheed F-117 Nighthawk stealth fighter jet from 1981, it is obvious that our renowned airplane-inventing duo would never be able to reproduce this technology within their lifetime. Poor ol‡ Orville and Wilbur would probably have no idea how the guidance and propulsion systems work‡ or even how to start the damned thing up!However, this does not mean that our patent-procuring pair of propeller plane proponents couldn’t glean a great deal of aerodynamic knowledge from whatever they were able to decipher. The F-117’s unorthodox vector-based shape, jet propulsion system, airflow mechanics and its radar-defying exterior coating would present a complete mystery to our beloved brothers, but they would still know that something crazy-shaped like this heavy metal “beast” can actually fly.For the Wright Brothers to be in possession of such a hi-tech, classified aircraft would undoubtedly cause them to rethink the mechanics of flight in a far more expansive and creatively-abstract way. Although they would not be able to fly it or operate the on-board computer systems, they could design far more basic shaped wooden prototypes and move in an all-new design direction from there.No doubt the U.S. government and military would also converge on the Wright brother’s amazing new discovery and immediately begin the process of reverse engineering the craft. What is certain is that it would not take a full 78 years later to witness the birth of a F-117 stealth fighter jet.(3) Modern Society vs. Alien Spacecraft:Photo Credit: Bogus tech company and 3D Max spaceship that I made up.Should we actually happen upon an alien spacecraft during today’s times, there would be a major difference in our retro-engineering capabilities versus our Wright brothers and Ancient Egypt scenarios. Although we might not be able to directly reproduce the technology (or even understand how it works) we would still be able to analyze the molecular structure of the outer shell, study the structure’s overall design and decipher how an alien pilot might interact with the vessel.As opposed to ancient civilizations, we are scientifically and analytically far more advanced and know what we are dealing with. We would not worship it, enshrine it or destroy it out of fear. Instead, we wold start dissecting whatever elements of the craft that we can figure out and start piecing together the many missing pieces of this strange intergalactic puzzle until we find what we are looking for.Bonus Knowledge: “Derivative retro-engineered technology”Photo Credit: Bogus global protection protoatomic force field system that I made up.Before we ever fully discover the true functional capabilities of our alien craft, we would probably be able to discover “other things” from it that we could utilize in other areas of human existence. If we discovered that the ship utilized a relatively easy method for creating a protective force field (and we were just too stupid to realize how easy this was) then we could quickly implement this advancement on a global scale.Summary:It is not possible to state how long it would take to accurately reproduce the technology used in our alien spacecraft. What we do excel in is our profound capabilities in diagnostic research and scientific study. We’ve been to the celestial dance, my friend! We’ve studied the smallest of the small with electron microscopes and visually scanned the vastness of our universe with orbiting telescopes. All that’s required at this point is filling in the missing data along the way.When we will get there, nobody knows. However, there is no doubt that having a highly-advanced spacecraft of this nature in our possession would exponentially cut down on the time it would normally take to achieve this level of advanced technology.Photo Credit: Alleged spacecraft found at Roswell, New Mexico - June 25, 1947.…Besides, everyone knows that we already have one!
How much cement is required to fill an area of 2,000 square feet?
If it's 6 inches deep then 37.04 cubic yards. For four inch concrete, 24.7 cubic yards.
How easy is it to lose control over today's liter bike (1000cc+ displacement motorcycle) as a beginner rider?
** Warning - gory picture alert - bloody picture ahead **Surviving motorcycle riding is about spending thousands of hours of seat time learning how to ride. Thousands.Why?The goal is to take your riding from a conscious activity, to an unconscious one. You practice correct body position, weight transfer, and most importantly correct head placement, until something which you have to consciously practice every time becomes habit. That is, drill yourself over and over to look where you want to go. All the time. Every time.1000cc Super sports won’t kill you. They won’t cause you to burst into flames, or lose control, or spontaneously combust. They will however, not forgive you. They won’t forgive lapses of judgment or concentration. They won’t forgive poor body placement. They will not forgive you when you have stiff arms, and stiff inputs into the throttle when leaned over in a corner. Jerky stiff-arm throttle inputs will high-side you with little warning.I’ve owned a few R1’s, and I’ve had (as John McGuinness says) ‘ass puckering‡ moments. A few tank-slappers, emergency stoppies, and a quick-as-lightning almost-high-side. I was riding fast on the road, I’d finished a corner, was straightening up, enthusiastically rolled the throttle and next thing, the rear end spun, stepped out right then snapped back - I found myself popped up, off the seat, over the front of the bike, staring down at the road. My legs were up in the air, my hands still gripping the handlebars, and I was leaned right over the windscreen. I managed to pull myself back and get my body back in the seat, but if the highside attempt had happened 30m earlier I would have run right off the road into some trees and probably been killed. I was going fast.This was only last year, and I wasn’t riding as hard as I usually do through that area.The other thing which catches even reasonably experienced riders on liter bikes out is the unexpected bump-and-throttle-jerk. You’re cruising along, chilled out looking cool riding one handed. A bump you haven’t seen unsettles the bike, you jerk the throttle and BAM - bike launches forward, you grab the bars. Only, your wrist isn’t below the bar, as an experienced riders‡ wrist should be, it’s above it. So, you’ve just wrenched the throttle of this 180hp monster wide open. And it obeys! It wheelies, you’re hanging on for dear life to a bloodthirsty beast which has instantly obeyed your throttle hand, you’ve slid off the seat and are hanging off a vertical bike. That vertical bike is now doing 30Mph faster and climbing! It goes past vertical and you faceplant on the “cheese grater” (the tarmac).I’ve seen it happen so many times on Youtube, and a few times in real life.As a rider who’s done well over 100,000 k’s on 1000cc SuperSports, when I’m riding one handed the thing holding me to the bike, is my legs gripping the tank. I’m wearing my leathers, and I’ve got Stompgrip tank pads to grip on. I’ve been gripping with my legs for so long, it’s automatic. My hand grip on the bars is loose, gentle, my arms are relaxed and my wrist is below the throttle. So if a jerk happens and I’m surprised by it, grabbing the throttle closes it! Quite often, I don’t even grab the throttle - I let the bars whip back and forth, the energy from the bump is dissipated, and then I grab the bars. My torso is relaxed, I’m hunched over. When the surprise bump hits, my legs tighten on the tank, but my torso, arms and hands remain relaxed and loose. My throttle hand is loose and gentle so when I grab the throttle, I roll it closed. The bike can buck and kick and the handlebars can whip about, and because I’m loose and let the bike kick around and get the bump out of its system, the bike’s geometry can do what it’s designed to and straighten up again.This sort of reflexive unconscious habit only happens when you’ve spent a LOT of time living in the seat, and you’ve trained and disciplined these habits into your unconscious mind. It also helps when you’ve explored the limits of much smaller, more forgiving bikes, and you’ve skilled up on those.And look - let’s be honest - when I’m riding one-handed being ‘cool’, I’m being a dick. I’m tempting fate. I should know better, but hey, we all do dumb things we shouldn’t. I deserve everything I get if something goes wrong, and just because I’m ‘experienced‡ doesn’t mean that I somehow have magical exemption from things going wrong.There are a lot of riders I know who went from ‘learner legal‡ 250’s straight to 1000’s. Compared to the guys who have milked every last drop out of 125s and 250s, they can’t ride for shit. Honestly, I’ve seen a 14yr old kid, come from racing 250’s, jump on a 1000cc bike he’s never ridden before and lap it faster than the fast old guys in my fast group. You learn the skills to ride fast on the small bikes.Me personally, I did the humiliating thing by spending the first 8 months of my road-riding life on a 150cc Chinese scooter.A few riders mocked me, but most of them gave me huge respect. I learned how to read traffic, people, and everything moving about on the road on that little scooter, and dropped it well over 20 times. I made a lot of mistakes on that thing, and learned a hell of a lot without it costing me much at all. BattleScoot(tm) had scars and scratches, dents and gouges all over it - it was held together with Gaff tape and cable ties - but it valiantly survived my epic stupidity. And so did I.I moved to a 2 stroke 125 road bikeand learned how to milk it for every last drop of its limits. I ground my footpegs down, I was leaning over so far. I learned how to adjust and service its suspension, so the bike would corner, brake, and handle safer. I learned how to maintain every last ounce of entry speed through corners because that little 125 only had 33hp.I then moved to Honda Bros 650 (Hawk GT 650 in the US) which, despite being 650cc, had very little actual power. My suspension guy, after I harassed him to recommend which bike to move to next, finally said “Fine! Get a Bros! Get a Bros, and let me sort the suspension”This is a Bros 650:And this is a review of it: Honda Hawk GT: Born Before Its Time - Motorcycle USAThat bike was the first bike I had a high-side on. Yeah, 189kg, 35hp (it was a Japanese import, and the Japanese motors had much less power than the US Hawk GT) and I high-sided it coming out of a petrol station jumping on the throttle. It was also the first bike I managed to get to 200kph on.I rode that for 5 years, learning every inch of it. My suspension guy did the forks and shock, and it handled like God. I humiliated almost everyone on 1000cc SuperSports in the twisties, no-one could keep up with me DOWN Macquarie pass. I ground its footpegs, and chicken strips? None. The Bros taught me how to throw a heavier bike around, and get really, really fast, with a small horsepower engine.This set the foundation for my move to a 2021 Honda CBR600RR.That bike was a huge leap up in power, but‡ a lot more difficult to handle! It required more muscle to make it corner, make it stay down in a corner, and muscle it around. The brakes were also savage, and I did a few stoppies by accident when I first got it.But! Because I had practiced for years on the Bros, I was able to dominate the CBR quickly, with confidence.The lessons I learned on the CBR, enabled me to handle my first R1. It was an ex-Irish road racing bike, a 2021 R1 with carb kit, Maxton suspension, and a full exhaust. It was wild. I attended the Isle of Man TT, and rode it hard over Isle of Man’s mountain course. That R1 taught me a LOT of lessons. I rode it from Ireland to Croatia and back through Europe for 5 months.I then moved to a Panigale 1199S, a 2021 R1, Buell 1125CR, and now I’ve got a 2021 R1, and right now, I’m trying to decide between a 2021 Panigale 1299S, or the R1M.During that time, I also owned KTM dirtbikes - a 250SX 2 stroke, and now a 525EXC 4 stroke. I’ve spent a LOT of time on dirt bikes, which helps immensely with riding on the road.So, as you can see, I’ve spent a lot of time and effort learning the most I can out of each new step up. I can jump on any 1000cc bike now, and ride seriously fast. I’m not the fastest rider in my group by any means, but, I’m in the fastest group.I’ve also spent a lot of time on the race track getting coaching and guidance. A lot of poor habits have been fixed thanks to both paid and unpaid coaching and mentoring. I can’t express how many times my life has been saved, or accidents avoided, by making a habit out of their advice.So, in summary, you can most definitely jump straight on a 1000cc bike and, with great caution, learn how to ride it accident-free. With a lot of hard work and effort, you can surmount the huge learning curve that is the wild, monstrous, heavy 1000cc Supersport and become a good rider. It’s totally doable.However, if you want to do this, do it on the track. *When* you make mistakes, and the 1000cc kicks you off, you’ll slide safely off the track and receive immediate medical attention. You will have people around you who can tell you what you did wrong, and you can live to climb back on and ride again.If you want to do your learning on the road, well - are you sure you’re ready for the unforgiving nature of your 1000cc teacher? There is no forgiveness. When you get kicked off, will you hit a guard rail, and snap your spine? (Brett) Will you grab a bit too much throttle and flip your bike? (Scott). Will you freak out entering a corner, because you’re muscling your bike down and it’s resisting you and bucking through the handlebars, target fix on a car and ride right into it? (Angelo). Or, will you realise you’re going too hot into a corner, grab a fistful of brake and lose the front end, running wide? (Tiffany).I can rattle off a lot more names, some who didn’t survive their mistakes. It’s your choice, ego, or wisdom. With Wisdom, there is life. When your spine is snapped, and you’re in a wheelchair for the rest of your life, ego doesn’t seem such a good choice.Edit:I forgot to answer your question about the latest electronic aids. Having taken several of this years new bikes for test rides, the electronics are awesome. Hilariously awesome. ABS, traction control, wheelie control, lean-angle sensing ABS, all that stuff - it’s amazing. It really is. It fills in so many skill gaps that, it really mitigates a lot of the unforgiving nature of the thousands. These aids can make all kinds of novices go and stop, fast.There is almost no downside to these aids that I have been able to figure out. Sure, as a new rider you will absolutely depend on them. When I moved back from my 2021 R1 to my old 2021. I had a real shock. I had no idea how dependent on traction control I’d become! How blasé about mashing the throttle, and hanging the rear end out I’d become. I got on my 2021. and started scaring myself a bit.So, the aids can definitely make you lazy and complacent. They allow you to let your discipline and skills lapse. They can also make you contemptuous of the risks the road offers. You don’t realise how much closer to the absolute limits of the bike you are riding at‡ you dive into a corner at much closer to the limits of the tyres and tarmac’s abilities, and the computer electro-magically fixes it.When something does go wrong though, where is your safety margin? There is none. You’ve used it all up. The electronics have masked all the warning signs you’d be getting on the way to the limit, until there’s absolutely nothing those aids, you, or anything else can do. And because you’re dependent on those aids, and you’re complacent, lazy, and shit, well‡ someone’s gonna get a-hurt, real bad.The other thing to take into account is, these are electronic aids. Electronics, well‡ fail. water, shock, vibration, dust, wear, whatever, there is always a chance they’ll malfunction. It might be a small chance, but, if you at least have learned the skills the ‘old fashioned‡ way, if they fail, you got those skills to draw on.That’s my take anyway.
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