Calculating error tolerance for approximate values
If $a$ and $b$ are nearly equal,show that $$ \frac{a+b}{2}-\frac{(a-b)^2}{4(a+b)}$$ is the approximate value of $\sqrt{ab}$ with an error in excess less t...
Apr 14, 2026 1 VIEWS
Topic: General
5104 Articles 
how to calculate the phase angle
When we transform $a\sin x+b\cos x=c$ into $a\sin x+b\cos x=R\sin(x+k)$, we calculate the $k$ angle by $k=\tan(b/a)$. By using calculator, we get a positi...
Apr 14, 2026 2 VIEWS
Inverse Laplace transform - using the table
I am trying to find the inverse Laplace transform $(g(t))$ of $$ G(s) = \frac{2s}{(s+1)^2+4}$$ I know about the inverse transforms $e^{a t}\cos(\omega t)$...
Apr 14, 2026 2 VIEWS
General equation of a cone
What is the general equation of a cone in $\mathbb{R}^3$ space? There should be no assumptions about the location of the vertex, direction of the axis or ...
Apr 14, 2026 1 VIEWS
Writing a composite transformation as a matrix multiplication
I am confused about a question on matrix multiplication of a transformation. I have two matrices, P and Q as follows: $$P = \begin{pmatrix}\frac{1}{2} &am...
Apr 14, 2026 1 VIEWS
Beginner's text for Algebraic Number Theory
What's a good book for learning Algebraic Number Theory with minimum prerequisites? Assume that the reader has done a basic abstract algebra course.
Apr 14, 2026 2 VIEWS
Is every integer a rational number? [closed]
Why is this the case? $0$ is an integer and it can't be divided by $0$... It's on my textbook, as it says We conclude that every integer is a ra...
Apr 14, 2026 2 VIEWS
Unique solution vs. exactly one solution for a linear system
On one problem I'm doing right now, the problem states that the linear system has a "unique solution". Does that mean it has exactly one solution, or...
Apr 14, 2026 1 VIEWS
Solving differential equation $xdy + ydx = 0$
Solve following equation $$xdy + ydx = 0$$ My process: group variables $$xdy = -ydx \ \ \ ; \ \ \ \frac{x}{dx} = -\frac{y}{dy}$$ Integrate $$\int{\frac{dx...
Apr 14, 2026 1 VIEWS
Amount of NaHCO3 needed to neutralize HCl [closed]
With the equation: HCl + NaHCO3 --> NaCl + CO2 + H2O Find the number of grams of NaHCO3, to three significant figures, required to neutralize 75 mililitre...
Apr 14, 2026 1 VIEWS
Volume of Truncated Octagonal Prism
I was looking for the volume of this octagonal prism shown below. It looks like this: It seems that I couldn't think of a formula that could give a v...
Apr 14, 2026 2 VIEWS
Existence of d-regular graphs
It is well known that if $0<d<n$ and $d\cdot n$ is even then there exist $d$-regular graphs on $n$ vertices. My question is: What is the easiest way...
Apr 14, 2026 1 VIEWS