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Jun
12
comment Curve fitting to connect certain points
What is the significance of the blue curve? Why are the interpolation points represented as triangles? How do they affect/constrain the black curve?
May
22
comment How to calculate per unit costs for multiple items
Does 'x' represent a variable or multiplication?
May
22
comment Time-varying frequency waveform
A couple of things to consider. First you should make sure that the requested frequency is no more than 1/2 of the signal sample frequency to avoid aliasing. Second, what you are trying to do here is frequency modulation. If you read the Wikipedia article, you will see that it generates higher frequencies than expected. Third, depending on how the wave is synthesized, you need to adjust the phase of the signal to make sure it is continuous. I am not sure if your method does that.
May
19
comment Laplace transform of unit step function
By definition: $f(t) = \begin{cases} t, & \text{$0 \le t \le 1 $} \\ 0, & \text{$1 \lt t \lt \infty$} \\ \end{cases}$
May
19
comment Laplace transform of unit step function
The function is zero for $t>1$. You don't need to integrate it.
May
19
comment Laplace transform of unit step function
Can you use a Laplace transform table? The function above is only useful if you are using a table. Otherwise just integrate from 0 to 1, i.e. $F(s)= \int_0^1e^{-st}tdt$.
May
19
comment Laplace transform of unit step function
The function you want to use is $f(t)=t(u(t)-u(t-1))$.
May
14
comment Gaining Linear Algebra Intuition — Subspaces
This set of lectures helped me a lot: ocw.mit.edu/courses/mathematics/….
May
7
comment Show that exist a rotation $r$ such that $r(u)=v$
Hint: You need the axis-angle representation of a rotation (see: en.wikipedia.org/wiki/Axis_angle). You can use the dot product to find the angle and the cross product to find the axis.
Feb
26
comment Are orthogonal spaces exhaustive, i.e. is every vector in either the column space or its orthogonal complement?
@Ethan, Yes, you are correct that the union (in the formal sense) between the two subspaces is zero. I took the sense of your question at the end of the first paragraph "are there some vectors in $R^n$ which are in neither?" I thought that by using the term union, you intended span.
Feb
26
comment Are orthogonal spaces exhaustive, i.e. is every vector in either the column space or its orthogonal complement?
Yes, see this: en.wikipedia.org/wiki/Fundamental_theorem_of_linear_algebra
Feb
25
comment How To Generate Random Points on the Positive Side of a Plane in 3-D
See my second edit.
Feb
25
comment How To Generate Random Points on the Positive Side of a Plane in 3-D
This link tells you how to do it.
Feb
21
comment Integral of $e^{\overline{z}}$
Try using separate integrals over the top and bottom halves of the unit circle. I.e. one integral from $0$ to $\pi$ and another from $\pi$ to $2\pi$.
Feb
20
comment Double integral of a region.
You have the right thought. See my second edit coming shortly....
Feb
20
comment Double integral of a region.
I don't think that your solution for shape 2 is correct. Note that although the shape is symmetrical, there is no indication that the function is.
Feb
13
comment Unreachable rubik cube positions.
The OP explicitly stated "by applying standard moves", so moving stickers doesn't count. This answer does not address the intent of the OP.
Feb
12
comment Linear Algebra - Show that $M$ is not a vector space
So $\begin{bmatrix}0&b\\c&d\end{bmatrix}$ and $\begin{bmatrix}a&b\\c&0\end{bmatrix}$ are in the set. Is their sum in the set?
Feb
12
comment Linear Algebra - Show that $M$ is not a vector space
Is the set closed under addition?
Feb
9
comment a and b are integers where gcd(a,b)=p which is a prime. find gcd(a^2,b^2).
By squaring a and b, you do not introduce any additional prime factors.