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May
1
revised How to find the full Taylor expansion of the following:
added 27 characters in body
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, you claimed it's a proof -- before we show that, it's not really a proof, is it?
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, if $\vec{a} = a_x \hat{i} + a_y \hat{j}$, by definition, $$\left| \vec{a} \right| = \vec{a} \cdot \vec{a} = a_x^2 + a_y^2.$$
May
1
comment How to find the full Taylor expansion of the following:
@Frumpy partial fractions should reduce denominator to degree 1
May
1
answered How to find the full Taylor expansion of the following:
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
I don't understand why this is a proof of geometric and algebraic equivalence. Algebraically, you argued $$\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y.$$ Geometrically, you argued that $$\vec{a} \cdot \vec{b} = \left| \vec{a} \right| \cdot \left| \vec{b} \right| \cos \theta = \sqrt{a_x^2 + a_y^2} \sqrt{b_x^2 + b_y^2} \cos \theta. $$ Why are they the same???
May
1
revised Geometric and algebraic definitions of the dot product , proof of equivalence?
added 213 characters in body
Apr
30
comment Ball Probability help
@user3335209 from (B) you found $\mathbb{P}[\text{same color}] = 14/45$. They must be either same or different, so $$\mathbb{P}[\text{same color}] + \mathbb{P}[\text{different color}] = 1$$
Apr
30
answered Finding values $a$ and $b$ which transforms a differential equation
Apr
30
answered Ball Probability help
Apr
30
revised Ball Probability help
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Apr
28
revised Simple linear regression prove variables are uncorrelated:
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Apr
28
comment A linear growth model with immigration
@Danny yes, $o(h)$ includes any constant factor...
Apr
28
comment A linear growth model with immigration
@Danny $o(h)$ and $-o(h)$ is the same thing.
Apr
28
answered A linear growth model with immigration
Apr
28
revised What does “Formulate the system of equations for a finite difference discretisation of the problem” mean?
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Apr
28
comment What does “Formulate the system of equations for a finite difference discretisation of the problem” mean?
What is meant by the question is, find the set of linear equations one would need to solve to get the numerical approximation to the problem you described via the method of finite differences.
Apr
24
comment Complicated but easy problem solving?
For the purpose of this problem, 03 is a more convenient representation than plain 3
Apr
24
comment Complicated but easy problem solving?
@AndréNicolas misread the problem, was counting numbers with 3 not actual occurrences. Fixed now.
Apr
24
comment Complicated but easy problem solving?
@gnasher729 fixed, thanks