this table of sailing records shows the year and speed of each yacht in its transatlantic journey. each yacht sailed from the ambrose light tower in new york to lizard point in england for a total of 3364 statute miles.
1) a yacht’s speed is measured in knots or nautical miles per hour. what was the average speed in knots or nautical miles per hour for the atlantic and the playstation?
2)use the table of unit conversions and convert the nautical miles per hour you obtained from the previous question to statute miles per hour for the atlantic and the playstation
3)first, divide 3364 statute miles by the statute miles per hour you obtained from the previous question for the atlantic and playstation. this will find the number of hours it took each yacht to traverse the atlantic ocean. then answer this question: what was the time difference by which the playstation beat the atlantic?
4)there are 360 degrees of longitude at the equator. the length of a nautical mile initially represented 1/60 degree of longitude at the equator, and is quite close to that measurement today. about how many nautical miles is the circumference of the earth at the equator?

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.