cornerstone Posted July 30, 2006 Author Report Share Posted July 30, 2006 UNDERGROUND? Ooh yeah! WINNER! In the course of constructing a pyramid, a large stone cube was being transported across the desert on logs. All of the logs were two metres in circumference. How far did the stone cube move in relation to the ground, with each complete revolution of the logs? Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 30, 2006 Author Report Share Posted July 30, 2006 Okay, that sent everyone running! Here's a non-maths one for those that aren't into that sort of thing... If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle? (I call this game 'spot the wino'! ) Quote Link to comment Share on other sites More sharing options...
Pugwash Posted July 30, 2006 Report Share Posted July 30, 2006 Okay, that sent everyone running! Here's a non-maths one for those that aren't into that sort of thing... If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle? (I call this game 'spot the wino'! ) You gerra fork and ... hic ... pushshsh tha cork inna bottle witha handle and ... heh ... DRINK!!!! Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 30, 2006 Author Report Share Posted July 30, 2006 You gerra fork and ... hic ... pushshsh tha cork inna bottle witha handle and ... heh ... DRINK!!!! Yeah, you're right....but I'm stone cold sober. WINNER! Remember, this question is still 'live', as is the blood one for those that haven't surrendered on it: In the course of constructing a pyramid, a large stone cube was being transported across the desert on logs. All of the logs were two metres in circumference. How far did the stone cube move in relation to the ground, with each complete revolution of the logs? Enjoy! Quote Link to comment Share on other sites More sharing options...
KB Posted July 30, 2006 Report Share Posted July 30, 2006 Ok this sounds to obvious but...........................2 metres? Quote Link to comment Share on other sites More sharing options...
Pugwash Posted July 30, 2006 Report Share Posted July 30, 2006 In the course of constructing a pyramid, a large stone cube was being transported across the desert on logs. All of the logs were two metres in circumference. How far did the stone cube move in relation to the ground, with each complete revolution of the logs? Four Metres Quote Link to comment Share on other sites More sharing options...
KB Posted July 30, 2006 Report Share Posted July 30, 2006 Four Metres I'm sure you're right and I'm also sure there is a mathematical equation to prove it, but it's beyond me Ken Quote Link to comment Share on other sites More sharing options...
Pugwash Posted July 30, 2006 Report Share Posted July 30, 2006 I'm sure you're right and I'm also sure there is a mathematical equation to prove it, but it's beyond me If you imagine the log isn't moving, the ground moves 2 metres one way and the stone moves 2 metres the other. Quote Link to comment Share on other sites More sharing options...
KB Posted July 30, 2006 Report Share Posted July 30, 2006 Of course! Ken Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 30, 2006 Author Report Share Posted July 30, 2006 Aye, it was four metres. Just a quick dash in with a new question!! There are two ships of equal size and equal strength. One is made of wood and the other of steel. Can you explain which is heavier? Quote Link to comment Share on other sites More sharing options...
melvin.x Posted July 31, 2006 Report Share Posted July 31, 2006 There are two ships of equal size and equal strength. One is made of wood and the other of steel. Can you explain which is heavier? If they have the same strength the one made of wood must be heavier because you need a lot more wood to build a ship that has the same strength as a steel made one... And now I go to bed... Quote Link to comment Share on other sites More sharing options...
KB Posted July 31, 2006 Report Share Posted July 31, 2006 Yeah 'equal strength' is the kicker in this one Ken Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 31, 2006 Author Report Share Posted July 31, 2006 If they have the same strength the one made of wood must be heavier because you need a lot more wood to build a ship that has the same strength as a steel made one... And now I go to bed... Goal Melvin!! That's exactly right. And now time for.... SCOTTISH QUESTION OF THE DAY Assuming that you are paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time? (It doesn't depend on how much popcorn they eat!) Quote Link to comment Share on other sites More sharing options...
KB Posted July 31, 2006 Report Share Posted July 31, 2006 It's cheaper to that both at the same time (fuel cost) but only a tight Scot would think of that Ken Quote Link to comment Share on other sites More sharing options...
melvin.x Posted July 31, 2006 Report Share Posted July 31, 2006 It's cheaper to that both at the same time (fuel cost) but only a tight Scot would think of that Ken That´s also a correct answer, but the main reason is that when you go twice you have to pay 4 tickets and when you go once you have to pay only 3. Don´t forget your own ticket... Quote Link to comment Share on other sites More sharing options...
Pugwash Posted July 31, 2006 Report Share Posted July 31, 2006 It's cheaper to that both at the same time (fuel cost) but only a tight Scot would think of that Ken A true Scot would walk to Shug's Big Cinema (SBC). Melvin got it right with the pay for yourself thingy. Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 31, 2006 Author Report Share Posted July 31, 2006 That´s also a correct answer, but the main reason is that when you go twice you have to pay 4 tickets and when you go once you have to pay only 3. Don´t forget your own ticket... Correct! WINNER! For the rest of the day, in honour you will now have the skills of an international Scotland player. This may require you tying your boot laces together! Okay this is a bit easy, but hey... Two mothers and two daughters were fishing. They managed to catch one big fish, one small fish, and one fat fish. Since only three fish were caught, how was it possible that they each took home a fish? Quote Link to comment Share on other sites More sharing options...
melvin.x Posted July 31, 2006 Report Share Posted July 31, 2006 Two mothers and two daughters were fishing. They managed to catch one big fish, one small fish, and one fat fish. Since only three fish were caught, how was it possible that they each took home a fish? Granny, mother and daughter were fishing... Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 31, 2006 Author Report Share Posted July 31, 2006 Granny, mother and daughter were fishing... How many three cent stamps are in a dozen? Quote Link to comment Share on other sites More sharing options...
jonthebhoy Posted July 31, 2006 Report Share Posted July 31, 2006 How many three cent stamps are in a dozen? ......eh...........12! Quote Link to comment Share on other sites More sharing options...
KB Posted July 31, 2006 Report Share Posted July 31, 2006 An application of the calculator thought experiment (CTE) Ý tells us that x sin x is a product; y = (x)(sin x). Therefore, by the product rule, dy dx = (1)(sin x) + (x)(cos x) = sin x + x cos x Recall from Section 2 that y = cosec x = 1 sin x . Therefore, by the quotient rule, dy dx = (0)(sin x) (1)(cos x) sin2x (recall that sin2x is just (sin x)2) = cos x sin2x = cos x sin x . 1 sin x = cotan x cosec x. (from the identities in Section 2) Notice that we have just obtained the derivative of one of the remaining five trigonometric functions. Four to go... © Since the given function is a quotient, dy dx = (2x+1)(sin x) (x2+x)(cos x) sin2x , and let us just leave it like that (there is no easy simplification of the answer). (d) Here, an application of the CTEÝ tells us that y is the sine of a quantity. Since d dx sin x = cos x, the chain rule (press the pearl to go to the topic summary for a quick review) tells us that d dx sin u = cos u du dx so that d dx sin (3x21) = cos (3x21) d dx (3x21) = 6x cos(3x21) So.......ahh........12 Ken Edit.......see what happens I give you my working out like every good boy should and jtb beats me Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 31, 2006 Author Report Share Posted July 31, 2006 Extra points for working it out! TWO WINNERS!! In the 'Strange' family, each daughter has the same number of brothers as she has sisters. Each son has twice as many sisters as he has brothers. How many sons and daughters are in the family? An application of the calculator thought experiment (CTE) Ý tells us that x sin x is a product; y = (x)(sin x). Therefore, by the product rule, dy dx = (1)(sin x) + (x)(cos x) = sin x + x cos x Recall from Section 2 that y = cosec x = 1 sin x . Therefore, by the quotient rule, dy dx = (0)(sin x) (1)(cos x) sin2x (recall that sin2x is just (sin x)2) = cos x sin2x = cos x sin x . 1 sin x = cotan x cosec x. (from the identities in Section 2) Notice that we have just obtained the derivative of one of the remaining five trigonometric functions. Four to go... © Since the given function is a quotient, dy dx = (2x+1)(sin x) (x2+x)(cos x) sin2x , and let us just leave it like that (there is no easy simplification of the answer). (d) Here, an application of the CTEÝ tells us that y is the sine of a quantity. Since d dx sin x = cos x, the chain rule (press the pearl to go to the topic summary for a quick review) tells us that d dx sin u = cos u du dx so that d dx sin (3x21) = cos (3x21) d dx (3x21) = 6x cos(3x21) So.......ahh........12 Ken Edit.......see what happens I give you my working out like every good boy should and jtb beats me Quote Link to comment Share on other sites More sharing options...
jonthebhoy Posted July 31, 2006 Report Share Posted July 31, 2006 Extra points for working it out! TWO WINNERS!! In the 'Strange' family, each daughter has the same number of brothers as she has sisters. Each son has twice as many sisters as he has brothers. How many sons and daughters are in the family? 3 sons and 4 daughters. Quote Link to comment Share on other sites More sharing options...
cornerstone Posted July 31, 2006 Author Report Share Posted July 31, 2006 3 sons and 4 daughters. Ach, so fast!! WINNER! What is the value of one-half of two-thirds of three-quarters of four-fifths of five-sixths of six-sevenths of seven-eighths of eight-ninths of nine-tenths of one thousand? Quote Link to comment Share on other sites More sharing options...
jonthebhoy Posted July 31, 2006 Report Share Posted July 31, 2006 Ach, so fast!! WINNER! What is the value of one-half of two-thirds of three-quarters of four-fifths of five-sixths of six-sevenths of seven-eighths of eight-ninths of nine-tenths of one thousand? 100 Quote Link to comment Share on other sites More sharing options...
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