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  1. M

    Determine the remainders when dividing their squares by four

    (2n + 1)^2 is not 4n^2 + 1. And I think he was more concerned with the remainder you get when you divide by 4, not the expression in terms of fractions.
  2. M

    Solving a trig equation

    It's fine because you know that an x where cos(x) is zero can't possibly be a solution (otherwise you have 4 - sqrt(3) = 0).
  3. M

    Finding the angel between two vectors

    It can't be 90. That would imply the dot product is zero (see the formula mentioned)
  4. M

    Question 19 - quadratic probility problem

    You're getting there. What's the problem with n being 10.5. Look at your original assumptions. What are you tacitly assuming about the original n balls?
  5. M

    Question 19 - quadratic probility problem

    Look, you're essentially supposed to say, "Suppose Bill is right. Suppose 7/(n + 7) = 2/5. Then such and such would follow." Why would the conclusion be a problem?
  6. M

    Question 19 - quadratic probility problem

    Alternatively, you can note that you have 35/(2n + 14) = 1. 35 is odd. 2n + 14 is even. Strange, isn't it?
  7. M

    Question 19 - quadratic probility problem're leaving out the equality part of the equation. Solve for n.