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• Today, 10:41
Here is this week's POTW: A charge $-q_1$ is located at the origin of a $y$-axis and a charge $-q_2$ is located at $y=d$. At what point along...
0 replies | 9 view(s)
• Today, 10:40
Congratulations to the following members for their correct submission: kaliprasad My solution is as follows: For the entire system...
1 replies | 50 view(s)
• Yesterday, 15:53
mathmari replied to a thread Open cover in Analysis
I think that it holds that there is for every $n \in \mathbb{N}$ an $0 < x < 1$ such that $\frac{1}{n} \in \left(\frac{x}{2},\frac{3x}{2}\right)$,...
3 replies | 48 view(s)
• Yesterday, 15:42
Hello and welcome to MHB! :D We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This...
1 replies | 59 view(s)
• Yesterday, 14:43
mathmari started a thread Open cover in Analysis
Hey!! :o Let $\mathbb{R}$ provided with the metric $d(x,y)=|x-y|$. I want to check if the collections of sets $$S_1=\left \{\left (\frac{x}{2},... 3 replies | 48 view(s) • Yesterday, 09:31 I like Serena replied to a thread Right triangle. in Geometry Google translates triangle as sankakkei. And searching for sankakkei shows that this word is also used for a three dimensional puzzle of triangles.... 19 replies | 193 view(s) • April 24th, 2018, 06:54 My own best guess was to look at the differences: \frac 13, \frac 16, \frac 1{10}. The next difference might be \frac 1{15}, although it does... 9 replies | 141 view(s) • April 23rd, 2018, 15:52 I like Serena replied to a thread Special Relativity in Physics It's the other way around. 11 replies | 135 view(s) • April 23rd, 2018, 15:26 I like Serena replied to a thread Right triangle. in Geometry For the record, something like that is called a sangaku. A drawing that exhibits a proof, without any words, expressions, or symbols. Admittedly my... 19 replies | 193 view(s) • April 23rd, 2018, 15:04 I like Serena replied to a thread Right triangle. in Geometry You mean just drawings? (Wondering) Something like this: \begin{tikzpicture} %preamble \usetikzlibrary{arrows} \def\a{sqrt(17)} ... 19 replies | 193 view(s) • April 23rd, 2018, 13:37 I like Serena replied to a thread Right triangle. in Geometry To be honest, I only used trigonometry because it means I have to use fewer words to explain those ratios! (Rofl) 19 replies | 193 view(s) • April 23rd, 2018, 13:20 I like Serena replied to a thread Right triangle. in Geometry Trigonometry is only used in the first step. We can replace it with non-trigonometry by observing that triangles ABC and ACD are similar, meaning... 19 replies | 193 view(s) • April 23rd, 2018, 12:55 I like Serena replied to a thread Right triangle. in Geometry Let's make a drawing: \begin{tikzpicture} %preamble \usetikzlibrary{arrows} \def\a{sqrt(17)} \def\b{sqrt(68)} \def\c{sqrt(85)} ... 19 replies | 193 view(s) • April 23rd, 2018, 09:13 I like Serena replied to a thread Special Relativity in Physics Indeed, the distance travelled is v\Delta t' = 240\text{ lightyear}. So we have \Delta t' = \frac{240\text{ lightyear}}{v} and \Delta t =... 11 replies | 135 view(s) • April 22nd, 2018, 17:50 mathmari replied to a thread Banach space in Analysis I understand!! Thank you very much!! (Smile) 6 replies | 87 view(s) • April 22nd, 2018, 12:30 Let me throw in another XKCD: I do hope that no one drops our people table! (Worried) 19 replies | 522 view(s) • April 22nd, 2018, 11:32 I like Serena replied to a thread Optics: Lenses in Physics Normally the object and image are at different sides of the lense, meaning their distances add up. However, it is possible that we have a virtual... 6 replies | 89 view(s) • April 22nd, 2018, 10:17 MarkFL replied to a thread Olinguito in Introductions Hello, and welcome to MHB! (Wave) 8 replies | 106 view(s) • April 22nd, 2018, 09:31 Good! (Happy) We have:$$\epsilon = -\d \Phi t = -\d {(B_i A_i + B_o A_o)} t\approx -A_i\d {B_i} t  where $A_i$ is the cross sectional area...
9 replies | 125 view(s)
• April 22nd, 2018, 09:17
mathmari replied to a thread Banach space in Analysis
I got stuck right now. I haven't really understood that part. (Thinking) I thought that the Cauchy sequence should be in $Y$ but its limit...
6 replies | 87 view(s)
• April 22nd, 2018, 08:59
I like Serena replied to a thread Banach space in Analysis
$C(\mathbb{R})$ means that $\forall t\in \mathbb R: \lim_{h\to 0} f(t+h)=f(t)$. Will that be true if $f$ is the absolute converging limit of a...
6 replies | 87 view(s)
• April 22nd, 2018, 08:47
How about not letting ourselves be stopped by that, but just do the math?
9 replies | 125 view(s)
• April 22nd, 2018, 08:45
I like Serena replied to a thread Optics: Lenses in Physics
Good! It means that we have the set of equations: \begin{cases} d_o+d_i=2.4 \text{ m} \\ f = 0.55 \text{ m}\\ \frac 1{d_o} + \frac 1 {d_i} = \frac...
6 replies | 89 view(s)
• April 22nd, 2018, 08:29
We have $\varepsilon = -\d \Phi t$. This applies to all of the magnetic field that passes through the loop. And that includes the magnetic field that...
9 replies | 125 view(s)
• April 22nd, 2018, 08:05
mathmari replied to a thread Banach space in Analysis
Great!! (Yes) How could we justify that $C(\mathbb{R})$ is a Banach space? (Wondering) Do we have to show that $\frac{\sin^2\left... 6 replies | 87 view(s) • April 22nd, 2018, 07:58 I like Serena replied to a thread Banach space in Analysis Hey mathmari!! (Wave) What you have is correct. So$X$is indeed complete and therefore a Banach space. And$Y\$ has a Cauchy sequence that shows...
6 replies | 87 view(s)
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