# Search results for query: *

1. ### 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. ### 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. ### 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. ### 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. ### Angle between two straight lines

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