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Harder Problems of the Week 1. Draw the graph of the function for different values of a. What does this graph
 

Summary: Harder Problems of the Week
Due May 21
1. Draw the graph of the function for different values of a. What does this graph
look like?
2. In the game "World of Goo" you build structures out of goo balls. If I make a tower like this:
And each layer is 1.3 meters tall, how tall can my tower be if I use 297 goos (say each goo
contributes 1 edge, so there are 3 in the first picture, and 9 in the second.)
3. Laura takes her dog for a walk. Laura walks at 4 miles per hour, but her dog runs at 10 miles
an hour. Walking along a path, the dog runs away from her to the end of the path, and back to
her. How much farther does the dog run that Laura for a path of length n miles?
4. A weird number is a number that is the product of two consecutive primes, such as 7x11=77 .
What is the least common multiple of the 6 smallest weird numbers?
5. Consider the following pattern:
sqrt( 1+ 1*2*3*4) = 5
sqrt( 1+ 2*3*4*5) = 11
sqrt( 1+ 3*4*5*6) = 19
sqrt( 1+ 4*5*6*7) = 29
sqrt( 1+ 5*6*7*8) = 41
Determine sqrt( 1+ 79*80*81*82) using the pattern above. Why does this pattern hold?

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics