general
Boundary of any Open Ball
Is it true that for any open ball $B(x;r)$, its boundary must be the sphere, $S(x;r)=\{y \in X : d(x,y)=r\}$? So I am trying to go about this with initial...
Apr 19, 2026
Archive: General
general
Solve the differential equation in the case where there is no resonance.
Problem: $$y'' + 20y = 100sin(wt)$$ Initial Condition: $$y=0$$ when $$t=0$$ Attempt: I know $w = 2\sqrt{5}$ when resonance occurs. But what do y...
Apr 19, 2026
general
Finding the number of standard deviations from the mean, only given $P(X<55) = 0.7$
The continuous random variable, $X$, is normally distributed with $P(X<55) = 0.7$ a) How many standard deviations from the mean is a score of $55$? b) ...
Apr 19, 2026
general
Proof that the matrix multiplication is associative – is commutativity of the elements necessary?
This is a picture of the proof, we assume that the elements of the matrix are elements of a ring: I don't know how the associativity is proved here w...
Apr 19, 2026
general
Range of absolute value function $g(x) = |4 - x|$
A function $g$ is defined as $g(x)=|4-x|$, find the range of $g$ if its domain is $-3\leq x \leq 6$. My attempt: I substitute $-3$ and $6$ into the functi...
Apr 19, 2026
general
Non-singular matrix, determinants
I should find the values x for which the matrix is non-singular. I already know that the matrix is singular when det(A) is 0. So basically the matrix will...
Apr 19, 2026
general
How to calculate the volume obtained by rotating the following around the x axis?
The original problem is: "Find the volume of the solid obtained by rotating about the x axis the region enclosed by the curves $y = \frac{9}{x^2 + 9},y=0,...
Apr 19, 2026
general
Confused about the definition of a random sample, statistics and estimators/estimates
I'm currently studying basic statistics, and I don't really understand the definition of random sample in the book I'm reading (Introductio...
Apr 19, 2026
general
Why do you use n-1 in Standard error of the mean but n in hypothesis testing
When you divide in hypothesis testing you use the formula: $$ \frac{\bar X-\mu}{s/\sqrt n} $$ but the standard error of the mean is: $$ \frac s{\sqrt {n-1...
Apr 19, 2026
general
Spring constant $K$
A mass $m_1$ with initial velocity $V_0$ collides with a spring attached to mass $m_2$ initially resting on a frictionless surface according to the figure...
Apr 19, 2026
