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HallsofIvy
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Today,
13:15
MarkFL
replied to a thread
high school inequality 3
in
Challenge Questions and Puzzles
It will be interesting to see the OP's solution. :)
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5 replies | 108 view(s)
Today,
12:12
MarkFL
replied to a thread
Factor By Grouping
in
Pre-Calculus
Think of it like this: ...
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3 replies | 23 view(s)
Today,
12:07
MarkFL
replied to a thread
Difference of Cubes?
in
Pre-Calculus
I applied the exponential property: x^ny^n=(xy)^n Since $8=2^3$, we can write: 8c^3=2^3c^3=(2c)^3
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3 replies | 28 view(s)
Today,
12:02
MarkFL
replied to a thread
Factoring Fractional Expression
in
Pre-Calculus
It can be factored further, as there is both a sum and difference of cubes there. Bear in mind I only dealt with the numerator. :D
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3 replies | 29 view(s)
Today,
00:51
MarkFL
replied to a thread
Factoring Fractional Expression
in
Pre-Calculus
Yes, in fact: ...
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3 replies | 29 view(s)
Today,
00:45
MarkFL
replied to a thread
Factor Fractional Expression
in
Pre-Calculus
I would write the expression as the difference of squares: ...
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2 replies | 22 view(s)
Today,
00:40
MarkFL
replied to a thread
Difference of Cubes?
in
Pre-Calculus
I would begin by writing the expression as the difference of cubes: (a+b)^3-8c^3=(a+b)^3-(2c)^3 Now apply the difference of cubes formula...:D
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3 replies | 28 view(s)
Today,
00:37
MarkFL
replied to a thread
Factor By Grouping
in
Pre-Calculus
I would factor as follows: 8a^3+27b^3+2a+3b=(2a)^2+(3b)^3+2a+3b=(2a+3b)\left(4a^2-6ab+9b^2\right)+(2a+3b)=(2a+3b)\left(4a^2-6ab+9b^2+1\right) ...
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3 replies | 23 view(s)
Today,
00:28
MarkFL
replied to a thread
Factor p^4 + 4
in
Pre-Calculus
If we allow for complex factors, then we can state: p^4+4=\left(p^2+2i\right)\left(p^2-2i\right) However, over the reals, the sum of two...
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4 replies | 42 view(s)
May 20th, 2017,
22:05
MarkFL
replied to a thread
4 Element by 4 Element Multiplication Table ...
in
LaTeX Help and Discussion
You need to wrap any $\LaTeX$ in dollar-sign delimiters, however then an error regarding the matrix m being unrecognized crops up, and I don't see...
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14 replies | 158 view(s)
May 20th, 2017,
21:31
MarkFL
replied to a thread
242.17.8 Solve the given equation by variation of parameters.
in
Differential Equations
Let's first solve this ODE using the method of undetermined coefficients. We know the homogeneous solution is: y_h(x)=c_1e^{5x}+c_2xe^{5x} And...
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2 replies | 43 view(s)
May 20th, 2017,
19:16
MarkFL
replied to a thread
242.17.8 Solve the given equation by variation of parameters.
in
Differential Equations
Your fundamental solution set for the corresponding homogeneous equation is: \left\{e^{5x},xe^{5x}\right\} So now we take as our particular...
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2 replies | 43 view(s)
May 20th, 2017,
16:42
HallsofIvy
replied to a thread
Apples
in
Basic Probability and Statistics
If it is possible that some of the people get no apples, then there are 5 choices who to give the first apple to, 5 choices who to give the second...
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4 replies | 82 view(s)
May 20th, 2017,
13:49
HallsofIvy
replied to a thread
Power series and uniform convergence.
in
Analysis
It is fairly standard to use the "ratio test" or "root test" to determine convergence of a power series. And I presume you know that "if a series...
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1 replies | 39 view(s)
May 20th, 2017,
08:43
HallsofIvy
replied to a thread
Probability of Turning into a Bird
in
Basic Probability and Statistics
If "the time" has not yet come, why are you posting so many questions like these?
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5 replies | 91 view(s)
May 20th, 2017,
08:35
HallsofIvy
replied to a thread
Total Price Per Ticket
in
Pre-Calculus
If you divide 25 tickets by 0.75 dollars you will have "tickets per dollar" when you want "dollars per ticket". But, anyway, the "75 cents each" is...
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4 replies | 89 view(s)
May 20th, 2017,
03:38
MarkFL
replied to a thread
4 Element by 4 Element Multiplication Table ...
in
LaTeX Help and Discussion
I do agree that would be better, but I honestly don't know how to get MathJax to do that. :D
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14 replies | 158 view(s)
May 20th, 2017,
01:56
MarkFL
replied to a thread
4 Element by 4 Element Multiplication Table ...
in
LaTeX Help and Discussion
Do you mean something like this? \begin{array}{|c|c|c|c|c|} \hline & 1 & 2 & 3 & 4 \\ \hline 1 & 1 & 2 & 3 & 4 \\ \hline 2 & 2 & 4 & 6 & 8 \\...
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14 replies | 158 view(s)
May 19th, 2017,
21:08
MarkFL
replied to a thread [SOLVED]
639.7.6.97 write an equivalent polar equation
in
Pre-Calculus
Looks good to me. (Yes) edit: On second thought...there is an issue...$2y=2r\sin(\theta)$...:D
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2 replies | 65 view(s)
May 19th, 2017,
15:23
MarkFL
posted a
visitor message
on
Whitefang23's
profile
Hello! I would recommend you post in that thread, show what progress you've made so far, and hopefully someone can help. :)
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May 19th, 2017,
15:14
MarkFL
replied to a thread
Review of Calculus 1
in
Calculus
I say whatever works best for you is fine by me. :) To save time, I would likely only review the sections pertaining to the problems I missed.
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10 replies | 144 view(s)
May 19th, 2017,
14:05
MarkFL
replied to a thread
Review of Calculus 1
in
Calculus
Plugging in, we obtain \d{V}{t}=4\pi(2t+1)^2(2)=8\pi(2t+1)^2 Hence, in \frac{\text{cm}^3}{\text{s}}, we have: ...
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10 replies | 144 view(s)
May 19th, 2017,
13:02
MarkFL
replied to a thread
Review of Calculus 1
in
Calculus
No, just plug in for $r$ and \d{r}{t} in the expression for the time rate of change of volume. :D
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10 replies | 144 view(s)
May 19th, 2017,
12:44
MarkFL
replied to a thread
Review of Calculus 2
in
Calculus
In post #6, I gave two different anti-derivatives...how can we show both are correct?
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10 replies | 146 view(s)
May 19th, 2017,
12:35
MarkFL
replied to a thread
Review of Calculus 1
in
Calculus
If we assume the balloon is spherical, then we can begin with the volume of a sphere: V=\frac{4}{3}\pi r^3 Differentiating w.r.t time $t$, we...
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10 replies | 144 view(s)
May 19th, 2017,
12:19
MarkFL
replied to a thread
Review of Calculus 2
in
Calculus
Well, yes differentiating both forms gets us back to the original integrand, but how do we "justify" that both are correct?
see more
10 replies | 146 view(s)
May 19th, 2017,
07:57
HallsofIvy
replied to a thread
Probability of Turning into a Bird
in
Basic Probability and Statistics
It looks to me like a large part of your problem with probability is that you keep telling yourself this.
see more
5 replies | 91 view(s)
May 19th, 2017,
01:29
MarkFL
replied to a thread
Probability: Replacement & Without Replacement
in
Basic Probability and Statistics
Cohen might be a good source for problems, however, for development of the theory, there are likely much better texts dedicated to the topic...that's...
see more
12 replies | 160 view(s)
May 19th, 2017,
01:18
MarkFL
replied to a thread
Probability: Replacement & Without Replacement
in
Basic Probability and Statistics
Those who are both interested in probability and who may have a recommendation will likely read this thread. While I know several people here who...
see more
12 replies | 160 view(s)
May 19th, 2017,
01:06
MarkFL
replied to a thread
Probability: Replacement & Without Replacement
in
Basic Probability and Statistics
No, I don't have a good recommendation...I would try your local library first. :D
see more
12 replies | 160 view(s)
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May 22nd, 2017
00:13 -
RTCNTC
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Re: Total Price Per Ticket
by
HallsofIvy
Tickets at a fair cost...
May 20th, 2017
17:33 -
RTCNTC
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Re: Apples
by
HallsofIvy
If it is possible that...
May 19th, 2017
08:52 -
RTCNTC
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Re: Probability of Turning into a Bird
by
HallsofIvy
I can see that...
May 17th, 2017
16:10 -
RTCNTC
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Re: More Factoring
by
HallsofIvy
Because it was...
May 16th, 2017
00:46 -
karush
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Re: 17.2.9 Solve the given equation by the method of undetermined coefficients
by
HallsofIvy
ok going to see if i can...
May 14th, 2017
23:16 -
RTCNTC
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Re: Square Root vs Cube Root
by
HallsofIvy
The product of two...
23:03 -
RTCNTC
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Re: Approximation for π and sqrt{2}
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HallsofIvy
Say whether each...
22:33 -
MarkFL
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Re: Square Root vs Cube Root
by
HallsofIvy
The product of two...
May 13th, 2017
16:09 -
MarkFL
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Re: Volume of Shipping Box
by
HallsofIvy
I'm sure that MarkFL is...
May 12th, 2017
19:17 -
Harpazo
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Re: Mass and Center of Mass
by
HallsofIvy
To find the mass (using...
08:53 -
Ackbach
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Re: Mass and Center of Mass
by
HallsofIvy
To find the mass (using...
May 11th, 2017
21:09 -
Harpazo
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Re: Mass and Center of Mass
by
HallsofIvy
You don't need to...
15:39 -
evinda
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Re: Is the solution unique?
by
HallsofIvy
What you have isn't "of...
May 10th, 2017
23:57 -
Harpazo
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Re: Find Mass & Center of Mass
by
HallsofIvy
Surely, you realized...
09:39 -
MarkFL
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Re: Differentiation of infinite series
by
HallsofIvy
Find derivative of...
May 9th, 2017
17:19 -
evinda
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Re: Method of seperation of variables
by
HallsofIvy
Hello!!! (Wave) I...
May 7th, 2017
12:46 -
MarkFL
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Re: Radius of Gyration
by
HallsofIvy
Yes, it is. The "radius...
12:46 -
MarkFL
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Re: Center of Mass
by
HallsofIvy
Imagine being able to...
11:01 -
Harpazo
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Re: Center of Mass
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HallsofIvy
Imagine being able to...
11:00 -
Harpazo
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Re: Radius of Gyration
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HallsofIvy
Yes, it is. The "radius...
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