2
votes
Matching pair of socks question
Your error comes from assuming the zero of the derivative is a minimum, whereas it is a maximum. If he could buy $1.25$ packs of black socks he would have $18$ of each color and there would be $324$ ...
- 379k
1
vote
Accepted
Bike turning angle "through what angle". Wordtrick?
The turn angle is measured with respect to the forward direction of the bike. This makes sense because if you go straight on your bike, you are not turning at all, so your turn should be 0 degrees. ...
- 34.6k
1
vote
Accepted
Problem 3-40 in "Calculus on Manifolds" by Spivak. Show that we can write $g=g_n\circ\cdots\circ g_1$ if and only if $g'(x)$ is a diagonal matrix.
Unforunately, Spivak's formulation of the problem is false. Consider
$$g(x,y)=(x+y,x)$$
and pick any $(x_1,y_1)$. Then
$$g'(x_1,y_1)=g'(x,y)=\begin{bmatrix}1&1\\1&0\end{bmatrix}$$
with $\det g'...
- 348
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