Subcategories

• Week 1

  Algebra Tricks, Number Algebra, Simplifying Expressions, Finding the Unknown

  Day 1

  Day 2

  Day 3

  Day 4
  13
  Topics
  57
  Posts

  K

  It is still supposed to be a=b=4.
  The reason is because if "a" and "b" are both 4, then a shorter way of writing it is a=b=4.

  $${4+4 \over 2}=4 $$

  where the first is "a" and second is "b"

• Week 2

  Sum Patterns, Squares and Roots, Fractional Powers, Decimals to Fractions

  Day 5

  Day 6

  Day 7

  Day 8
  15
  Topics
  37
  Posts

  

  @the-blade-dancer So sorry for the late response! Basically, the sentence explains why we think that 162 * r^8 = 32/81. It's essentially an educated guess...

  As the solution says, the denominator of 32/81 is 3^4. This is the same thing as saying the number has a factor of 3^-4 (because 32/81 = 32 * 1/81 = 32 * (1/3^4) = 32 * 3^-4). On the other hand, 162 has a factor of 3^4 = 81. So to get from 162 to 32/81, thinking purely in terms of the powers of 3, we are trying to get from

  3^4 * something to 3^(-4) * something

  Well, to do that, we have to divide by 3^8. We just found that the ratio is sqrt(2)/3, so we want to multiply by the ratio 8 times: this gives (sqrt(2))^8 / 3^8 so it's like dividing by 3^8, which is what we want.

  I hope that makes sense!

• Week 3

  Two Variables, Many Variables, Factoring Quadratics, Quadratic Formula

  Day 9

  Day 10

  Day 11

  Day 12
  16
  Topics
  32
  Posts

  W

  On the miniproblem from Challenge Explanation 5 for Day 10, I think there might be a mistake. The solution says to add the equations and I got 4a+4b+4c+4d+4e, however, the solution gets 3a+3b+3c+3d+3e. Can anyone check or confirm?

• Week 4

  Coordinating Locations, Intersecting Lines, Coordinate Geometry, Slope of a Curve

  Day 13

  Day 14

  Day 15

  Day 16
  14
  Topics
  33
  Posts

  K

  You can see that with graph paper that B is slightly longer.