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How many times in a twelve hour period does the sum of the digits on a digital clock equal six and prove it?
notation: natural numbers = 0,1, 2, 3, 4, 5, ....., (some define it without the zero, though) <= means smaller than or equal to, {} is set notation and means a set of numbers : (such that) then some condition. For example {x: x is not a duck} is the set of all things not a duck. Our goal is to prove that there are 21 different times. let x1 = hours, x2 = tens of minutes, x3 = minutes. We are going to prove the statement about the set {x1, x2,x3: 1<=x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6}. It will be taken by assumption that this set is the set of digital clock combinations that add up to 6. So then, we must prove that there are unique 21 elements in the set {x1 + x2 + x3 : 1<= x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6}. {x1 , x2 , x3 : 1<= x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6} = {x1 , x2 , x3 : 1<= x1 <= 6, 0<= x2<=5, 0<=x3 <= 5, x1 + x2 + x3 = 6} because x3<=6, and because if x1 >=1, then x2 + x3 <=5, and x3, x2 >= 0 , so surely x3, x2 <= x5. Either x1 = 1, 2, 3, 4, 5, or 6. Next, x1 + x2 + x3 = 6, so x2 + x3 = 6 - x1. There are n+1 natural numbers between 0 and n (I'm being lazy and not proving this, but the proof would be so much longer if I proved it), and since 0 <= x2 <= 5 <= 6-x1, there are at most 6-x1+1 values of x2 for each value of x1. When x1 = 1, there are a maximum of 6, when x1 = 2, there are 6-2+1 = 5, when x1 = 3, there are 6-3+1 = 4, when x1 = 3, there are 3, then 2, and then 1. Summing this up gives us a maximum of 21. So it is at most 21 and at least 21, so exactly 21.
How do you factor x3 plus 12x2-5x?
x3 + 12x2 - 5x = x(x2 + 12x - 5) = x(x + 6 - √41)(x + 6 + √41)
X3 64 343?
The math problem X3 times 64/334 equals 4/7. Getting this answer you will first have to find the value of X.
What is the degree of 4x6 - 2x3 x - 3 x3?
the answer is 6
How do you simplify 81?
Multiply and simplify 3^-2 x3^6
What does -x3 equals -6 equal to?
9
Is 6 plus 6 plus 6 an expression of 6 x3?
Yes.
What kind of transmission does the 2007 BMW X3 have?
The 2007 BMW X3 has a 6-speed manual.
What size engine does the 2009 BMW X3 have?
The 2009 BMW X3 has an inline 6 engine.
What size engine does the 2006 BMW X3 have?
The 2006 BMW X3 has an inline 6 engine.
What size engine does the 2008 BMW X3 have?
The 2008 BMW X3 has an inline 6 engine.
What size engine does the 2011 BMW X3 have?
The 2011 BMW X3 has an inline 6 engine.
What kind of transmission does the 2010 BMW X3 have?
The 2010 BMW X3 has a 6-speed manual.
What size engine does the 2007 BMW X3 have?
The 2007 BMW X3 has an inline 6 engine.
What kind of transmission does the 2005 BMW X3 have?
The 2005 BMW X3 has a 6-speed manual.
What kind of transmission does the 2004 BMW X3 have?
The 2004 BMW X3 has a 6-speed manual.
What kind of transmission does the 2009 BMW X3 have?
The 2009 BMW X3 has a 6-speed manual.
