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Two circles are drawn with five inches between the centers. A line is drawn tangent to the bottom of one circle and the top of the other. The circumference of one circle is 6.28 inches. The area of the other circle is 12.56 inches squared, Angle x is formed by the tangent line and the line between the centers. Determine angle x. (assume that pi = 3.14)
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Guest Message by DevFuse
#332455 Tangent to two circles
Posted by
on 22 May 2013 - 11:26 PM
#332418 How Low can U go?
Posted by
on 21 May 2013 - 04:42 AM
Spoiler for We'll go with...
i found an error in my calculation using 189/18 = 10.5 oops nice work!
#332415 number maze
Posted by
on 21 May 2013 - 02:01 AM
#332404 Classic Sam Loyd Tongue Twister on Multiplication (perplexed professor)
Posted by
on 20 May 2013 - 11:26 PM
Tommy muttonhead propounds to his teacher the perplexing query: "If five times six were 33, what would the half of 20 be?" The other pupils solved the problem redily, but Tommy could not see how a thing that was not what they said it was had anything to do with something else that is not what they say it is.
#332402 Making Ice
Posted by
on 20 May 2013 - 10:52 PM
I think one of the problems with this problem is that we are missing the assumption that standard ice trays hold 12 ice cubes
#332401 Coin Triplets
Posted by
on 20 May 2013 - 10:49 PM
Two players play the following game with a fair coin. Player 1 chooses (and announces) a triplet (HHH, HHT, HTH, HTT, THH, THT, TTH, or TTT) that might result from three successive tosses of the coin. Player 2 then chooses a different triplet. The players toss the coin until one of the two named triplets appears. The triplets may appear in any three consecutive tosses: (1st, 2nd, 3rd), (2nd, 3rd, 4th), and so on. The winner is the player whose triplet appears first.
What is the optimal strategy for each player? With best play, who is most likely to win?
Suppose the triplets were chosen in secret? What then would be the optimal strategy?
What would be the optimal strategy against a randomly selected triplet?
#332388 How Low can U go?
Posted by
on 20 May 2013 - 07:19 PM
suppose there is a three digit number M where 100*a + 10*b +1*c = M where a, b, and c are digits
What is the minimum value that can be found from M/(a+b+c)?
#332387 At the Snack Shack
Posted by
on 20 May 2013 - 07:14 PM
When Jack went back for a late-night snack, he bought three items off the rack. Zack rang up the snacks and said "5.70, Jack." "Wait, Zack, you multiplied the prices instead of adding!" "Multiply, add; it still comes out the same. Pay up." What were the prices of Jack's three items?
#332386 A swimmer loses their cap.
Posted by
on 20 May 2013 - 07:09 PM
As a swimmer jumps off a small bridge and begins to swim upstream, her swim cap comes off and floats downstream. Ten minutes later she turns around, swimming downstream with the same effort, past her original bridge. At the next bridge, 1000 meters away from the first, she catches the cap. What was the speed of the current? Of the swimmer?
#332384 Ridiculous Inverse
Posted by
on 20 May 2013 - 07:04 PM
Many of my algebra and precalculus students think the 'inverse function' of f(x), often written f^(-1)(x), is the same as the reciprocal 1/f(x) (mistaking the -1 for an exponent). This (as I am obliged to remind them) is almost always false. But can you find at least one function whose inverse is also its reciprocal? Tiebreaker: Find as many as you can!
#332378 An ungrateful award
Posted by
on 20 May 2013 - 04:36 PM
King Chester awarded a triangular piece of land to his favorite court jester. The three sides measured 150 2/3 yards, 195 3/4 yards, and 45 yards 3 inches. His wife had long been asking him to have a piece of land where she could build a home, a garden, and a temple in each corner. The jester told his wife the good news but was surprised that shew as unhappy. Can you tell why she was unhappy?
#332377 Breaking through the circle
Posted by
on 20 May 2013 - 04:18 PM
Prem was doing his homework. With a radius of 20cm he drew a circle. He then drew 7 lines inside the circle with the help of a foot-rule. Can you tell in how many minimum and maximum divisions was the circle divided by these lines?
#332367 PowerCo
Posted by
on 20 May 2013 - 05:21 AM
PowerCo has three plants that must provide enough electricity to four cities. Shipping to each city from the various plants costs varying amounts. Moreover each plant has a set supply of energy that it can send to the various cities. The specifics of this information are outlined in the chart below:
From City 1 City 2 city 3 city 4 Supply
Plant 1 $8 $6 $10 $9 35
Plant 2 $9 $12 $13 $7 50
Plant 3 $14 $9 $16 $5 40
Demand 45 20 30 30
How can PowerCo best minimize its costs?
#332339 What time is it?
Posted by
on 19 May 2013 - 02:28 AM
"What time is it, Rory?" asked Cory one lazy day. "When I checked my watch this morning, the hour hand was where the minute hand is now, and the minute hand was one minute before where the hour hand now sits. I notice both hands are now at exact minute divisions." What is the time now? When did Rory check this morning?
#332338 Tessellated Pictures
Posted by
on 19 May 2013 - 02:24 AM
I have lots of photo prints, in two sizes: (a) 4 x 6 inches, and (b) 5 x 7 inches. I put photos up on the wall, each one can be vertical or horizontal, so that they tile into a big rectangle (with no overlapping or cutting, of course).
i) Prove I can't make a 19 x 19-inch "photo-square."
II) Show me how to tile the 29 x 29 photo-square.
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