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Today, 10:41

MarkFL started a thread Problem Of The Week #311 Apr 26th, 2018 in POTW for Secondary School/High School Students

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...

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0 replies | 9 view(s)
Today, 10:40

MarkFL replied to a thread Problem Of The Week #310 Apr 20th, 2018 in POTW for Secondary School/High School Students

Congratulations to the following members for their correct submission: kaliprasad My solution is as follows: For the entire system...

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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 $\frac{1}{n} \in \left(\frac{x}{2},\frac{3x}{2}\right)$,...

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3 replies | 48 view(s)
Yesterday, 15:42

MarkFL replied to a thread Construct the 99% confidence interval estimate in Basic Probability and Statistics

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...

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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},...

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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....

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19 replies | 193 view(s)
April 24th, 2018, 06:54

I like Serena replied to a thread nth term with fractions in Pre-Algebra and Algebra

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...

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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.

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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...

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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)} ...

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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)

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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...

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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)} ...

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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 =...

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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)

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6 replies | 87 view(s)
April 22nd, 2018, 12:30

I like Serena replied to a thread Error 502, bad gateway in Questions, Comments, and Feedback

Let me throw in another XKCD: I do hope that no one drops our people table! (Worried)

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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...

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6 replies | 89 view(s)
April 22nd, 2018, 10:17

MarkFL replied to a thread Olinguito in Introductions

Hello, and welcome to MHB! (Wave)

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8 replies | 106 view(s)
April 22nd, 2018, 09:31

I like Serena replied to a thread Electromagnetic Induction in Physics

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...

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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...

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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...

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6 replies | 87 view(s)
April 22nd, 2018, 08:47

I like Serena replied to a thread Electromagnetic Induction in Physics

How about not letting ourselves be stopped by that, but just do the math?

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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...

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6 replies | 89 view(s)
April 22nd, 2018, 08:29

I like Serena replied to a thread Electromagnetic Induction in Physics

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...

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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...

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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...

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6 replies | 87 view(s)

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