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Proof by contradiction in Discrete Mathematics
Ok, so my college book is the worst book ever and I can only survive from this site and youtube. Could someone please explain the answer below? I really d...
Apr 13, 2026
Archive: News
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Arc Length of an Astroid
I want to find the arc length of the equation: $ x^{2/3} + y^{2/3} = 4 $ My steps follow as: $ y= f(x) = (4-x^{2/3})^{3/2} $ $ f'(x)= -x^{-1/3}(4-x^{...
Apr 13, 2026
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Parametric equation of a circle given starting point.
Find the parametric equations of a circle with radius of $5$ where you start at point $(5,0)$ at $v=0$ and you travel clockwise with a period of $3$. So, ...
Apr 13, 2026
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surface area using formula and double integrals
The prompt here is to find the surface area using double integrals. $$f(x) = 2\sqrt{xy}$$ with the vertices (1,1) (1,2) (2,2) (2,1). From resources the fo...
Apr 13, 2026
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Derivative of squared Frobenius norm of a matrix
In linear regression, the loss function is expressed as $$\frac1N \left\|XW-Y\right\|_{\text{F}}^2$$ where $X, W, Y$ are matrices. Taking derivative w.r.t...
Apr 13, 2026
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How to derive demand function from a utility function without any knowledge of Lagrange Multipliers?
How do I derive the demand function for a utility function of, say, $U(x,y)=\sqrt{11x+11y}$ for goods X and Y in terms of $P_x$, $P_y$, and income $I$, wi...
Apr 13, 2026
![How to find the exact value of $ \cos(36^\circ) $? [duplicate]](https://news.conceivablytech.com/uploads/how-to-find-the-exact-value-of-cos-36-circ-duplicate_720.jpg)
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How to find the exact value of $ \cos(36^\circ) $? [duplicate]
The problem reads as follows: Noting that $t=\frac{\pi}{5}$ satisfies $3t=\pi-2t$, find the exact value of $$\cos(36^\circ)$$ it says that you may find us...
Apr 13, 2026
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How to prove that a $3 \times 3$ Magic Square must have $5$ in its middle cell?
A Magic Square of order $n$ is an arrangement of $n^2$ numbers, usually distinct integers, in a square, such that the $n$ numbers in all rows, all columns...
Apr 13, 2026
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Cauchy Integral Formula for z outside disc
If $ f(z) $ is analytic for $ |z| \geq 1 $, and $ f(z) $ is bounded as $ z $ approaches infinity, then how can I derive an equivalent of Cauchy' Inte...
Apr 13, 2026
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number between 17 and 18, and has a rational square root
"number between 17 and 18, and has a rational square root" Is there even one? They all keep coming up irrational for me
Apr 13, 2026
