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Jun
17
comment Is there a questionned ordering symbol like the questionned equality?
Is $\overset{?}{\text{better}}$ really better?
Jun
17
comment Find the value of a so that the 2 x 2 matrix A is invertible
Yes, using the determinant is a good idea, particularly for a $2\times 2$ where computation is simple.
Jun
17
comment dividing 40 players into pairs
Once we choose the rooms to be occupied by the offense, we must assign offensive players to rooms and bunks. What we need to do is make sure that in numerator and denominator we are counting the same sort of thing. Since I am using $40!$ (all permutations) in the denominator, I must have all "favourable" permutations on top. We took a counting approach since that's the sort of thing you were using. But note that Ross Millikan's direct solution is in my opinion better.
Jun
17
comment Prove some number is algebraic over a field
I noticed that I used $5$ and $2$ instead of $5$ and $3$. That changes the hint to $\frac{2}{\sqrt{5}+\sqrt{3}}=\sqrt{5}-\sqrt{3}$.
Jun
17
comment Prove some number is algebraic over a field
@user157243: You are welcome. There are plenty of answers already, I just wanted to give you a start.
Jun
17
answered dividing 40 players into pairs
Jun
17
comment Prove some number is algebraic over a field
For the equality, clearly $\mathbb{Q}(\sqrt{2}+\sqrt{5})\subseteq \mathbb{Q}(\sqrt{2},\sqrt{5})$. For the other direction, note that $\frac{3}{\sqrt{5}+\sqrt{2}}=\sqrt{5}-\sqrt{2}$.
Jun
17
comment Analysis of how-many-squares and rectangles are are there on a chess board?
Do you mean how do we prove that $1^2+2^2+\cdots+n^2=\frac{(n)(n+1)(2n+1)}{6}$? Many ways. Induction is one. Exploiting the fact that $(k+1)^3-k^3=3k^2+3k+1$ is another. Must have been done many times in many ways on MSE.
Jun
17
comment How to get the number of ways of getting a five card hand that is a straight flush from a standard deck of cards
Note that definitions can differ. Wikipedia in its definition section includes the Royal flush among the straight flushes. That gives $40$. But someone else could be using a different definition.
Jun
17
comment Combinatorics and Probability Problem Concerning Poker Hands
In a straight, the low card takes on any one of $10$ values, Ace, 2, 3, 4, 5, 6, 7, 8, 9, or 10. The highest possible low value is 10, because that gives 10, Jack, Queen, King, Ace.
Jun
17
comment Cardinality of all inverse functions (bijections) defined on: $\mathbb{R}\rightarrow \mathbb{R}$
There are many others that would work. I was trying to get a sort of "indicator" (yes/no) function. Don't flip if yes, flip if no sounded like a good idea.
Jun
17
answered Cardinality of all inverse functions (bijections) defined on: $\mathbb{R}\rightarrow \mathbb{R}$
Jun
17
comment Probability- What percentage answered ‘Yes’?
Hint: How many percent replied no to both? How many percent replied yes to both? If the answers are not clear, draw a Venn diagram.
Jun
17
comment what is inverse of $y = 5 ^ {\ln x }$
Do not use logs to base $5$. Write $\ln y=(\ln x)(\ln 5)$, solve for $\ln x$, then take the exponential.
Jun
17
comment instantaneous velocity
Yes, you then went on to try to find the average velocity, which is not correctly done. The average velocity is the change in displacement divided by the change in time. But you already had the instantaneous velocity.
Jun
17
comment statements about summation
I assumed that OP saw that one needed $\sum_1^\infty (\cos(k\theta)+i\sin(k\theta))$, and worried about separating into two sums. But the wording is definitely not clear enough for this to be anything more than speculation.
Jun
17
comment instantaneous velocity
It asked for instantaneous velocity. That's $f'(1.8)$.
Jun
17
comment Undecidable sentence in Godel's incompleteness theorem
The result about Hilbert's 10th problem is proved via an elaborate translation into "Diophantine" language of undecidability results obtained via diagonalization.
Jun
17
answered Need an example of piece wise function continuous but not differentiable
Jun
17
comment The prime elements of the ring $ \mathbb{Z} \! \left[ \dfrac{i \sqrt{3} - 1}{2} \right] $.
For information and references, please see this Wikipedia article on Eisenstein primes.