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awarded  Caucus
Oct
12
comment Find the length of the arc of the curve $x= y^5/5 + 1/(12y^3)$ over $[2,4]$
I think you may want the square of dx/dy instead of dy/dx in your second equation.
Oct
7
comment Blue eyes: a logic puzzle
I think this is the correct insight. The impetus the guru provides is synchronizing the system. This is not well covered in the usual formulation of the problem however. The common knowledge thread of this problem seems like a bit of a red herring: even before the guru it is reasonable to assume of I know that you know etc already is in place.
Jan
24
awarded  Nice Answer
May
14
comment Finding a square root by division method
or... he needs no more plants if he plants 31x31
May
13
awarded  Caucus
May
10
awarded  Commentator
May
10
comment How to find a point on the tangent line whos length is 1?
$(x,y)=(\cos\alpha-t\sin\alpha, \sin\alpha+t\cos\alpha)$. For $\alpha=0$ that is $(x,y)=(1,t)$ - a vertical line centered at $(1,0)$ for $t=0$ (measuring the line $\pm\frac{1}{2}$ around that point). Still, your $0.9$ corresponds to $t=-0.4$, so $(x,y)=(1,-0.4)$. Hope this helps.
May
10
awarded  Yearling
May
10
comment How to find a point on the tangent line whos length is 1?
... or for 0.9 (which corresponds to $t=-0.4$ in this formulation): $(x,y)\approx (0.99, 0.42)$.
May
10
comment How to find a point on the tangent line whos length is 1?
Might be worth your while to plot that function somehow to get a feel for it. If we use your figure as an example so that $\alpha=\frac{\pi}{4}$ we get $(x,y)=\frac{1}{\sqrt{2}}\{(1,1)+t*(-1,1)\}$. So, at $t=0$ you get the point where the tangent touches the circle, at $t=0.5$ you get (since $|\vec s|=1$) $(x,y)=\frac{1}{\sqrt{2}}(\frac{3}{2},\frac{1}{2})$.
May
10
answered How to find a point on the tangent line whos length is 1?
May
10
comment Finding probability that a person gets $7$ when rolling a pair of dice
They are almost complementary except for the fact that rolling 7 in the first try is a win. As you can see $p+q=1+\frac{1}{6}$.
May
10
comment Finding probability that a person gets $7$ when rolling a pair of dice
It is similar to this problem - you want to generate uniform random integers in the range 1-4. If you don't have a four sided die on hand, just roll a 6-sided one and ignore all fives and sixes (just re-roll until you get something in the range you are interested in). Try to convince yourself that this procedure produces a uniform distribution of integers 1 to 4, then go back to the comment before this one...
May
10
comment Finding probability that a person gets $7$ when rolling a pair of dice
You could branch the tree to infinity if you do it that way but you don't have to. For instance, first roll is that 2, then you have a long stretch of 3s or anything other than 2 or 7. They don't matter for the outcome, only a 2 or 7 will terminate the sequence - that's why I consider the relative chance of those outcomes.
May
9
comment Partial derivatives.
"Where f is a function as shown above." suggests that $f$ is defined before "Suppose", maybe in a previous discussion in a textbook?
May
9
comment Finding probability that a person gets $7$ when rolling a pair of dice
"... winning at that point..." in my comment really should be "... winning in that branch..."
May
9
comment Finding probability that a person gets $7$ when rolling a pair of dice
Once you have rolled that two you only have to consider rolls of 2 or 7 to terminate the game. The relative chance of that is 1:6, so the chance of winning at that point is $\frac{1}{36}\times\frac{1}{7}$
May
9
awarded  Editor
May
9
revised Finding probability that a person gets $7$ when rolling a pair of dice
Corrected numerical mistake