hypothetical 4 dimensional vector space
Before I start asking the question, I want to apologize for my illiteracy in latex maths and the abstraction of my question. My question is, is it possibl...
Category: General
Computing the surface integral of the octant of a sphere with polar coordinate substitution
Let me first describe where I start: $$\iint_Sz^2\,dS$$ We want to compute the surface integral of the octant of a sphere $S$. The radius = 1. The sphere ...
Birthday Paradox: why permutations and not combinations?
The Birthday Problem: given $n$ people (typically $n<365$), what is the probability that some pair of them share a birthday (omitting Feb 29th, for sim...
Determining a basis for Col($A$) and a dimension for the null space of $A$
Let $A = \begin{bmatrix}1&-1&1&0&-2&1\\1&-1&1&1&0&0\\-1&1&-1&2&5&-1\end{bmatrix}$ a) Determine...
Find the rational canonical form of $A=\left(\begin{smallmatrix} -1 & -2 & 6 \\ -1 & 0 & 3\\ -1 & -1 &4 \end{smallmatrix}\right)$
Attempt First, the characteristic polynomial of $A$ is $\chi_A=(t-1)^3$ and the minimum polynomial is $\mu_A=(t-1)^2$. Since the degree of the minimum pol...
The Derivative of $\cos(x-2)$
I would think that the solution would be $-\sin(x-2)$, but when i use WolframAlpha it says that the answer is $\sin(2-x)$. Are these $2$ answers equivalen...
Does the line connecting the centers of two externally tangent circles contain the point of tangency?
In the picture below, the two circles are externally tangent at point $O$; $BC$ is tangent to both circles; the radius of the large circle is $25$ and the...
How to round $ 0.03446$ to three decimal places?
What is $ 0.03446 $ rounded to three decimal places? I think it is $0.035$ but someone told me that it should be $0.034$. I think $0.035$ because the $6$ ...
Does calculating d/dt of someething mean the same as calculating the derivative?
Probably a dumb question but I missed college for a week due to sickness. The exercise I have to do is: d/dt eight root of t^7. Does this simply mean I ha...
Is coNP closed under Kleene star?
Is coNP closed under Kleene star operation? I have the answers, in which they say it is possible to build a graph that describes all possible divisions of...
