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  1. arpon

    Number of n-length "words"

    First, consider this problem : How many words of length ##n## contains ##2k## ##0##s? There are ##^nC_{2k}## ways to choose the ##2k## places for ##2k## ##0##s. After setting ##0##s, we have ##n-2k## places to be filled up by ##1##s and ##2##s. We can use as many ##1##s and ##2##s as we like...
  2. arpon

    Estimated Instantaneous Rate Of Change

    The question does not ask for the point where "##f(x)##" is positive, negative and zero, rather it asks for where "the instantaneous rate of change" is positive, negative and zero. If ##f(x)## is zero, it does not mean that the instantaneous rate of change is also zero. For example, consider the...
  3. arpon

    Linear Algebra Problem

    Homework Statement Under what restrictions on ##c, d, e##, will the combinations ##c\vec u + d\vec v + e\vec w## fill in the dashed triangle? Homework Equations The Attempt at a Solution Clearly, ##\vec w + a (\vec v - \vec w) + b(\vec u - \vec v)## will be in the triangle when ##0 \leq b...
  4. arpon

    Angle between two straight lines

    No, there is no explanation about ##\theta## & ##\alpha##. And the equation I wrote is exactly the same as in the problem.
  5. arpon

    Angle between two straight lines

    Thanks for your reply. This also gives me same kind of equation.
  6. arpon

    Angle between two straight lines

    Homework Statement Find the angle between the straight lines: ##(x^2+y^2)(\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta})=(x \tan{\theta} - y \sin{\alpha})^2## Homework Equations [Not applicable] The Attempt at a Solution Dividing by ##x^2##, ## (1+(\frac{y}{x})^2)(\cos^2{\theta}...
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