# arbautjc

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bio website location Besancon, France age 33 member for 7 months seen 15 hours ago profile views 189

 May18 comment What is a perimeter of a sector?@Jawad. Because the sector has also two sides equal to radius. May18 comment What is a perimeter of a sector?@Jawad. Just a question of convention (in the same vein: for area of a cylinder, do you count the two disks?), but it appears the usual convention is counting the radius (see here for example). Anyway it would be useless to have another name for arc length. May14 comment Trigonometry Addition Thereom With Only one exact value?Given that $150=180-30$, it should be easy. May14 comment Solve a cubic polynomial (given one root is four times a second root)?I already answered this. Use the first two equations of Hagen to get a trinomial. May14 comment Integral of $\int^1_0 \frac{dx}{1+e^{2x}}$Then expand in partial fraction, and it's ok. May14 comment Solve a cubic polynomial (given one root is four times a second root)?And where do you think Vieta's formulas come from? May14 comment Solve a cubic polynomial (given one root is four times a second root)?Just expand $10(x-a)(x-4a)(x-b)$ and say it's equal to $10x^3+23x^2+5x-2$. Then isolate $b$ from the first equation given by Hagen, put it in the second, and you have an equation of degree 2 to solve. May12 comment prove that the unit circle $x^2+y^2=1$ is a closed set@Jyrki, no, Brian Scott is right, it's all about rotating the origin to eliminate the case where angles jump from $0$ to $2\pi$. Of course it's not very difficult to overcome, though a bit tricky. May12 comment prove that the unit circle $x^2+y^2=1$ is a closed setIt's ok, except for sequences oscillating around 0: there may be values near $0$ and values near $2\pi$, thus the sequence $\theta_n$ is not convergent. May12 comment Classify the abelian groups of order 81, 144 and 216For references in english, I think Lang or Dummit & Foote would have this, and much more. May12 comment Line equation - parametric and canonicalAh, ok. You find this by isolating $t$ from the parametric equations. May11 comment How to find prime numbersFor formulas (bad approach, but funny), have a look at this and that. @rondo9, there is a formula for next prime number, but probably not what you would expect. May10 comment $\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$?@Inceptio. If you don't understand area, it's liquely you won't understand $pi$ and $\sqrt{2}$ either. May10 comment How to find prime numbersThere are actually formulas, but they are all equivalent to some searching algorithm. May10 comment Solve a cubic polynomial?Then the simplest who be to develop $5(x-a)^2(x-b)$ and identify coefficients. May10 comment Solve a cubic polynomial?Hint: if two roots are equal to $a$, then the derivative of your polynomial has $a$ as a root. To see why, just write $P=(x-a)^2 Q$ and differentiate. Hence, you have only an equation of degree 2 to solve. Apr15 comment Prove the inequality $4S \sqrt{3}\le a^2+b^2+c^2$+1, very nice proof Apr15 comment Coefficient of Taylor Series of $\sqrt{1+x}$What is the coefficient of $x^n$ in the Taylor series? Hint: there is $f^{(n)}(a)$ in factor. Now, can you differentiate $\sqrt{1+x}$ three times? Apr13 comment Why the SVD is named so…@S.P I know, but it's to be found in history of mathematics. Apr13 comment Why the SVD is named so…en.wikipedia.org/wiki/Singular_value_decomposition#History