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Guest Message by DevFuse
 

BMAD

Member Since 18 Feb 2013
Offline Last Active Today, 01:32 PM
*****

#337644 Circles to make a pentagon

Posted by BMAD on 01 March 2014 - 04:15 PM

Spoiler for pentagon solution

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#337634 Circles to make a pentagon

Posted by BMAD on 28 February 2014 - 04:34 PM

tslf, you have me worried.  For I have done it much the same way.  Let me re-examine my own solution as well.


  • -1


#337586 scheme

Posted by BMAD on 27 February 2014 - 03:14 PM

Dear friend,
Do you want to get rich quick? Just follow the instructions carefully below and you
may never need to work again:
1. At the bottom of this email there are 8 names and addresses.
 Send $5 to the name at the top of this list.
2. Delete that name and add your own name and address at the bottom of the list.
3. Send this email to 5 new friends.
 
 
If the process goes as planned, how much money would you make?

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#337544 Complex numbers

Posted by BMAD on 26 February 2014 - 05:26 PM

Consider computing the product of two complex numbers (a + bi) and (c + di). By foiling the polynomials as we learned in grade school. We get:
 
 
 
       a   + bi 
       c   + di  
     ---------- 
       adi - bd 
ca + cbi 
---------------- 
(ca - bd) + (ad + cb)i   
 
 
Note that this standard method uses 4 multiplications and 2 additions to compute the product. (The plus sign in between (ca - bd) and (ad + cb)i does not count as an addition. Think of a complex number as simply a 2-tuple.)
 
It is actually possible to compute this complex product using only 3 multiplications and 3 additions. From a logic design perspective, this is preferable since multiplications are more expensive to implement than additions. Can you figure out how to do this?

  • -1


#337502 Spin the bottle

Posted by BMAD on 25 February 2014 - 05:55 PM

6 friends are sitting in a circle whom you have been observing playing the game called 'spin the bottle'.  They invite you to play as well.  Being a good sport, you agree to play.  You happen to notice however that it is HIlga's turn and you would rather not kiss Hilga.  You have also noticed that the bottle when spun with the left hand has a tendency to stop on a person an even distance away (e.g. the second, fourth, sixth person from her) and when spun with the right hand will land on a multiple of 3 distance away from HIlga.  Currently the bottle is pointing directly across from Hilga but if it were to land on herself she would immediately spin it again from that position, switching hands in the process.  You have no idea which hand she will use first nor do you know which way rotation she will place on the bottle [clockwise or counter-clockwise]. 

 

Where should you sit?


  • -1


#337241 area and perimeter

Posted by BMAD on 24 January 2014 - 07:12 AM

Carter fenced in a rectangular plot of land and then divided it into two halves by putting another fence along the main diagonal. This diagonal fence measured 41 metres exactly.

Martindale also fenced in a rectangular plot of land in a similar way (including the diagonal fence) but his rectangle was one-third greater in area than Carter's plot and used less fencing.

In both plots all the the dimensions (lengths, widths and diagonals) were a whole number of metres.
How much more fencing did Carter use than Martindale?
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#337016 For the holidays

Posted by BMAD on 16 December 2013 - 04:12 PM

Find the value of h.

Attached Images

  • tree.gif

  • -1


#337014 Area of a crescent

Posted by BMAD on 16 December 2013 - 03:23 PM

The blue crescent is made up of a semicircle and a quarter circle (of a larger circle). If the width of the figure (diameter of the semicircle) is 1, what is the area of the crescent?

 

crescent.gif


  • -1


#336988 Couple Candy Shopping

Posted by BMAD on 13 December 2013 - 12:39 AM

  1. Three couples bought candy at a candy store. Each person paid as many cents per candy as pieces of candy he or she bought, and everyone bought a different number of pieces (no one was empty handed.) When they compared their bills, they found that the difference between the amounts paid by each husband and wife was the same. What is the smallest number of candies purchased? Show the amounts for the difference and for each person/couple.
  2. What if there were two couples?
  3. Four couples?
  4. Five couples?
  5. Can a method be extended for M couples?
  6. If the difference between each husband's and wife's amount is less than 500 cents, what was the largest number of couples possible in the store?

  • -1


#336888 Infinite Flips

Posted by BMAD on 04 December 2013 - 02:24 AM

Given a coin with probability p of landing on heads after a flip, what is the probability that the number of heads will ever equal the number of tails assuming an infinite number of flips?


  • -1


#336859 perfect powers

Posted by BMAD on 02 December 2013 - 02:36 AM

@PerhapsCheckITAgain

 

I see no requirement that the numbers be square numbers just that i square three numbers


  • -1


#336840 perfect powers

Posted by BMAD on 29 November 2013 - 06:48 PM

Spoiler for strictly zero

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#336838 perfect powers

Posted by BMAD on 29 November 2013 - 06:45 PM

Spoiler for the answer is actually a lot smaller than this but


  • -1


#336593 algebraic continuity theorem

Posted by BMAD on 12 November 2013 - 11:30 PM

I am helping a friend in introductory real analysis, someone please help me finish, I am stuck.

Want to show that f(x)/g(x) is continuous as x goes to c given that g© is not 0.

|f(x)/g(x) - f©/g©| = |1/(g(x)g©)||f(x)g©-f©g(x)| = |1/(g(x)g©)||f(x)g©-f©g(x)-f(x)g(x) + f(x)g(x)| <= |1/(g(x)g©)||f(x)||g(x)-g©| + |g(x)||f(x)- f©|

Then I draw a Blank.
  • -1


#336565 How many taxis are there?

Posted by BMAD on 10 November 2013 - 05:58 PM

I arrive at a small town.  Leaving the airport i see five taxis out front.  The city sponsors the taxis.  Each taxicab has a unique number on it.  The largest number on the taxicab was 90.  How many taxis are there in the city?


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