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Today,
04:42
MarkFL
replied to a thread
BBCode For Username HTML Markup
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1 replies | 45 view(s)
Yesterday,
22:53
MarkFL
replied to a thread
Prove a number is divisible by a number?
in
Number Theory
Another approach would be to use the binomial theorem: 7^n-1=(6+1)^n-1=6\sum_{k=1}^{n}\left({n \choose k}6^{k-1}\right)
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7 replies | 81 view(s)
Yesterday,
14:51
MarkFL
replied to a thread
AlphaZero Crushes Chess
in
Chat Room
That's amazing! (Yes)
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2 replies | 38 view(s)
Yesterday,
14:38
MarkFL
replied to a thread
limit of a series
in
Calculus
As suggested, I would continue on your current path, but I wanted to show how I would approach the problem... I would begin by expressing the...
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3 replies | 44 view(s)
Yesterday,
11:59
MarkFL
replied to a thread
Need help with reversal of a calculation involving gravitational constant.
in
Pre-Algebra and Algebra
It's actually: G=\frac{rV_e^2}{2M}
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6 replies | 67 view(s)
Yesterday,
01:55
MarkFL
replied to a thread
Revenue and Cost and Profit Problem
in
Business Mathematics
To follow up: The axis of symmetry is: x=-\frac{48}{2(-2)}=12 We see that the profit function opens downward, and so the vertex is the...
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3 replies | 44 view(s)
December 10th, 2017,
18:13
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
It seems that $O\left(\frac{\log{N}}{\log{\log{N}}}\right)$ is a known upper bound for the number of distince prime divisors of $N$, but I haven't...
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85 replies | 877 view(s)
December 10th, 2017,
12:30
MarkFL
replied to a thread
Revenue and Cost and Profit Problem
in
Business Mathematics
Another approach would be to express your profit function in vertex form: P(x)=-a(x-h)^2+k where: P_{\max}=k
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3 replies | 44 view(s)
December 10th, 2017,
00:57
MarkFL
replied to a thread
Revenue and Cost and Profit Problem
in
Business Mathematics
Your profit function is correct: P(x)=-2x^2+48x-108 Now, what I would do is find the axis of symmetry (since the vertex lies on this...
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3 replies | 44 view(s)
December 9th, 2017,
17:06
MarkFL
replied to a thread
m2215b.14 Find the limiting velocity
in
Calculus
If the hyperbolic tangent factor goes to 1, then the terminal velocity $v_T$ must be: v_T=\sqrt{\frac{mg}{k}} Dimensional analysis shows that...
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13 replies | 165 view(s)
December 9th, 2017,
15:05
MarkFL
replied to a thread
m2215b.14 Find the limiting velocity
in
Calculus
Yes, and so what does this tell you about the terminal velocity?
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13 replies | 165 view(s)
December 9th, 2017,
08:12
MarkFL
replied to a thread
Need help with reversal of a calculation involving gravitational constant.
in
Pre-Algebra and Algebra
Hello, and welcome to MHB, Edwin! (Wave) We are given: V_e=\sqrt{\frac{2GM}{r}} What do we get if we square both sides of the equation?
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6 replies | 67 view(s)
December 8th, 2017,
20:08
MarkFL
replied to a thread
m2215b.14 Find the limiting velocity
in
Calculus
Yes, so what's the limit: \lim_{u\to\infty}\tanh(u)\,?
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13 replies | 165 view(s)
December 8th, 2017,
19:39
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
Don't we have that $k \leq \pi(\mathit \Pi)$ and so $k=O{\left( \frac{\mathit \Pi}{\log{ \mathit \Pi}}\right)}$ ? Or am I wrong? (Thinking)
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85 replies | 877 view(s)
December 8th, 2017,
19:12
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
The last inequality holds when $\frac{1}{2}(x^{\frac{1}{3}}-2)^2>\frac{1}{3}x^{\frac{2}{3}} \Rightarrow...
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85 replies | 877 view(s)
December 8th, 2017,
14:48
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
How else could we get the lower bound? (Thinking)
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85 replies | 877 view(s)
December 8th, 2017,
13:22
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
Yes, right... Doesn't $n^{\frac 12 X(X-1)} > n^{\frac 13 X^2}$ only hold when $\frac{1}{2}X^2-\frac{1}{2}X>\frac{1}{3}X^2 \Rightarrow X>3$ ?...
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85 replies | 877 view(s)
December 8th, 2017,
11:07
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
So we have that $n^i-1>n^{i-1}$ only if $n-n^{-(i-1)}>1$. And taking into consideration that $n \geq 2$ and $-(i-1) \leq 0$, we get that...
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85 replies | 877 view(s)
December 8th, 2017,
06:08
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
So is it as follows? $$\log{8}+3 \log{(\lceil \log{n}\rceil)}+3 \log{(\log{\log{n}})} \leq \log{(\log{n})}+3 \log{(\log{n}+1)}+3 \log{(\log{n})}...
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85 replies | 877 view(s)
December 8th, 2017,
02:39
MarkFL
replied to a thread [SOLVED]
M2215b.08 Find the volume of the solid (shell meithod)
in
Calculus
Let's check your result using the washer method: V=\pi\left(\int_0^{\sin\left(\frac{\pi^2}{4}\right)}...
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8 replies | 97 view(s)
December 7th, 2017,
22:14
MarkFL
replied to a thread [SOLVED]
M2215b.08 Find the volume of the solid (shell meithod)
in
Calculus
You originally had the integrand correct, but when you corrected the limits, you changed the integrand such that the integral was still incorrect...
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8 replies | 97 view(s)
December 7th, 2017,
19:23
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
This holds when $\lceil \log{n}\rceil \geq \frac{(\log{\log{n}})^3}{8}$, right? If so, how can we easily prove this? Do we use induction? Then we...
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85 replies | 877 view(s)
December 7th, 2017,
17:54
MarkFL
replied to a thread [SOLVED]
M2215b.08 Find the volume of the solid (shell meithod)
in
Calculus
Now, reverse the change you made to the integrand...
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8 replies | 97 view(s)
December 7th, 2017,
17:49
MarkFL
replied to a thread [SOLVED]
M2215b.08 Find the volume of the solid (shell meithod)
in
Calculus
Examine your limits of integration more closely...:)
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8 replies | 97 view(s)
December 7th, 2017,
14:50
evinda
replied to a thread
Test whether the integer is a prime
in
Number Theory
Then we check how many times the while-loop is executed. There is the following lemma. First of all, how do we get that...
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85 replies | 877 view(s)
December 7th, 2017,
14:28
MarkFL
replied to a thread
m2215b.14 Find the limiting velocity
in
Calculus
No, I was thinking more along the lines of: \tanh(u)\equiv\frac{e^{u}-e^{-u}}{e^{u}+e^{-u}} What happens if you multiply that by: ...
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13 replies | 165 view(s)
December 7th, 2017,
13:44
MarkFL
replied to a thread
m2215b.14 Find the limiting velocity
in
Calculus
Okay, now the given velocity function is dimensionally consistent, given that $k$ has units of mass per length (can you demonstrate this?). In...
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13 replies | 165 view(s)
December 7th, 2017,
13:29
MarkFL
replied to a thread
Require Edit Reason
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Update - Version 1.3: Add ability to exempt all usergroups from being required to edit, to allow for the setting of pre-defined edit reasons...
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1 replies | 65 view(s)
December 6th, 2017,
21:13
MarkFL
replied to a thread
m2215b.14 Find the limiting velocity
in
Calculus
You've given a constant velocity here...
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13 replies | 165 view(s)
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November 27th, 2017
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Peter
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Re: Antisymmetric Relations ... and Partial Orderings of Sets - H&J, Section 5, Ch.2 ... ...
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can you think of a good...
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Re: Antisymmetric Relations ... and Partial Orderings of Sets - H&J, Section 5, Ch.2 ... ...
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In the above text from...
November 25th, 2017
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