# Tagged Questions

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### What is a French curve, as mentioned by Feynman?

I'm reading "Surely You're Joking, Mr. Feynman!", he says: I often liked to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve (a ...
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### Optimisation: Maximum of a rectangle with semi circles at each end

A field is being built in the form of a rectangle with semi circles at each end. A $400$m racetract to is be built around the playing field. a) What Radius of the semicircular end would give the ...
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### Upper bound on optimal multinomial logit

Let $[N]={1,...,N}$ denote a set of items, item $i$ has a unit revenue of $r_i>0$ and a utility $u_i>0$. Items have to be assorted in $N$ slots with sampling probabilities $v_k>0$. Let ...
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### Optimization with contraint

Given the value K with constraint x+y = K, what can be the maximum value of x*y be? How did they derive this answer? It is equivalent to finding the maximum value of x*(K-x), which will happen when x ...
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### Determine the maximum cross‐sectional area.

The client wants to maximise the volume of a materials store to be constructed next to a 3 metre high stone wall (shown as OA in the cross section in the diagram). The roof (AB) and front (BC) are ...
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### determine the maximum cross‐sectional area.

The client wants to maximise the volume of a materials store to be constructed next to a 3  metre high stone wall (shown as OA in the cross section in the diagram). The roof (AB) and  front (BC) are ...
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### find the minimum value of $x^2-6x+9+ \dfrac{64}{x^2}$

Looking for an elegant solution. I can do by brute force, that is finding derivative and double derivative. All Ideas will be appreciated and tried by me.
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### Nearest and farthest point from a function to another [closed]

Find the nearest and farthest point from the ellipse $x^2 + 3y^2 =3$ to the segment made by $x+y = 3$ in the first quadrant. Found in a multivariable calculus course. So I have to find the ...
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### By looking at a graph of a function, how do I find the maxima/minima of its curvature function. [closed]

All Ideas are appreciated. I could think of some intuitive ideas, but could not back them by solid clean reasoning. thanks, I will post If i find anything
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### Minimization of two variables

(General) How can I find $$\min\limits_{\phi\leq x\leq \alpha , \ \beta \leq y \leq \delta}\{a+bx,c+dy\}$$ given values of $a,b,c,d,\phi, \alpha, \beta, \delta \in \mathbb{R}?$ (Specific) How can I ...
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### fence a circular land and a square land.

With a wire mesh of 1000 mts divided into two parts , we want to fence a circular land and a square land. a)Calculate the lengths of each of the parties such that the total area enclosed is ...
### Find f with A plane curve whose equation is $y - f (x) = 0$ passes through the origin.
A plane curve whose equation is $y - f (x) = 0$ passes through the origin.Consider the rectangle $R_x$ formed by the coordinate axes and lines parallel to the axis passing through the point \$(x, f ...