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...
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...
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...
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}...