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karush
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Yesterday,
21:30
MarkFL
replied to a thread
attachment an image in line
in
Questions, Comments, and Feedback
Attaching an image inline has nothing to do with using $\LaTeX$. To attach an image inline, follow these steps: 1.) Click the "Insert Image"...
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2 replies  29 view(s)
April 24th, 2017,
19:09
MarkFL
replied to a thread
Range of Rational Inequality
in
PreCalculus
Aw...shucks. (Blush)(Worried)
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10 replies  213 view(s)
April 24th, 2017,
15:22
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
Yes, and I would write this as: a_n=\frac{\left(1+\sqrt{5}\right)^n\left(1\sqrt{5}\right)^n}{\sqrt{5}} For this, I would observe that we...
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22 replies  277 view(s)
April 24th, 2017,
14:44
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
Yes, that's what I got as well. (Yes) As a followup question, using your result and the relationship between this sequence and the Fibonacci...
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22 replies  277 view(s)
April 24th, 2017,
14:42
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
What you actually get is: c_1=c_2 This is what you get if you consider the case where $n=0$...which is $a_0=0$. So, using $a_1$, we then...
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22 replies  277 view(s)
April 24th, 2017,
14:15
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
I get different values...please post your work so I can see where we differ. :)
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22 replies  277 view(s)
April 24th, 2017,
13:34
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
If $F_n$ is the $n$th Fibonacci number, then I considered: a_{n}=2^nF_{n}\implies F_n=2^{n}a_{n} But, we know: F_{n+1}=F_{n}+F_{n1} And...
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22 replies  277 view(s)
April 24th, 2017,
12:59
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
Based on the reasoning in the link posted, and extending it to tiles of two colors, I would posit the recurrence: a_{n+1}=2a_{n}+4a_{n1} where...
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22 replies  277 view(s)
April 24th, 2017,
12:25
MarkFL
replied to a thread
search and swap
in
PreAlgebra and Algebra
I didn't intend for my post(s) to be taken as any kind of proof, just my musings on the explanations given by others. :D
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11 replies  230 view(s)
April 23rd, 2017,
13:38
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
Well, let's see...the characteristic equation is: r2=0\implies r=2 And thus, the closed form will take the form: a_k=c_12^k Now, we must...
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22 replies  277 view(s)
April 23rd, 2017,
13:13
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
Typically, when you solve a recurrence relation (difference equation), you turn the relationship between successive values of the recurrence into a...
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22 replies  277 view(s)
April 23rd, 2017,
13:04
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
I agree that: a_k=2a_{k1} My reasoning would be: a_k=(\text{number of color choices})\cdot a_{k1} Each time we add a tile, we have 2...
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22 replies  277 view(s)
April 23rd, 2017,
12:50
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
If we assume the dominoes are 1 X 2, and we assume there will be no blank spaces (i.e. the chart is completely filled), then we must assume $n$ is...
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22 replies  277 view(s)
April 23rd, 2017,
11:53
MarkFL
replied to a thread
Recurrence equation
in
Discrete Mathematics, Set Theory, and Logic
In my opinion, this is the most poorly constructed problem I've seen in quite some time (shame on whoever assigned this to students). Why were...
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22 replies  277 view(s)
April 23rd, 2017,
00:16
MarkFL
replied to a thread
search and swap
in
PreAlgebra and Algebra
Yes, now it makes sense to me the think of the "worst case scenario" for $n$ cards (let's call this $W_n$) to be: ...
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11 replies  230 view(s)
April 22nd, 2017,
21:09
MarkFL
replied to a thread [SOLVED]
17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
in
Differential Equations
Only when the roots of the characteristic equation are imaginary do you typically express the homogeneous solution as a sinusoid. For example, if the...
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5 replies  175 view(s)
April 22nd, 2017,
20:13
karush
replied to a thread [SOLVED]
17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
in
Differential Equations
wow thank you I did the very last problem and got the "fantastic" robot reply but I followed your example to get it anyway I need to do...
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5 replies  175 view(s)
April 22nd, 2017,
19:59
MarkFL
replied to a thread [SOLVED]
17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
in
Differential Equations
What I used to like to do as a student, when presented with a batch of similar problems, is to generalize to get a formula I could use. Suppose we...
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5 replies  175 view(s)
April 22nd, 2017,
19:01
MarkFL
replied to a thread [SOLVED]
17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
in
Differential Equations
This problem is almost identical to the previous. What is your homogeneous solution $y_h$?
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5 replies  175 view(s)
April 22nd, 2017,
17:18
karush
started a thread [SOLVED]
17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
in
Differential Equations
the function y_p is a particular solution to the specified nonhomogeneous equation. Find the unique solution satisfying the equation and the given...
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5 replies  175 view(s)
April 22nd, 2017,
16:22
karush
replied to a thread [SOLVED]
17.2.10 y_p is a particular solution
in
Differential Equations
that was very helpful:cool:, The example I was looking was really hard to follow I'll post another similar one and see if can get thru it ...
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7 replies  131 view(s)
April 22nd, 2017,
16:22
MarkFL
replied to a thread
Normal Distribution: Percentiles
in
Basic Probability and Statistics
Hello and welcome to MHB! (Wave) Using a thread title of "probability and statistics" in our forum titled "Basic Probability and Statistics" is...
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1 replies  48 view(s)
April 22nd, 2017,
16:01
MarkFL
replied to a thread [SOLVED]
17.2.10 y_p is a particular solution
in
Differential Equations
I didn't notice before, but your characteristic roots are incorrect...we actually have: r\in\{2,0\} And so the general solution is: ...
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7 replies  131 view(s)
April 22nd, 2017,
15:55
karush
replied to a thread [SOLVED]
17.2.10 y_p is a particular solution
in
Differential Equations
$\textrm{set $y=0$ and $x=0$}$ $$0=c_2 \sin(\sqrt{2}(0)) +c_1\cos(\sqrt{2}(0)) +\frac{3(0)}{2}$$ $$0=c_2\sqrt{2}\cos(\sqrt{2}(0))...
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7 replies  131 view(s)
April 22nd, 2017,
15:06
karush
replied to a thread [SOLVED]
17.2.10 y_p is a particular solution
in
Differential Equations
$\textrm{Differtial equation solution}$ $$y=c_2 \sin(\sqrt{2}x)+c_1\cos(\sqrt{2}x) +\frac{3x}{2}$$ $$y'=\sqrt{2}\sqrt{2}\cos(\sqrt{2}x)...
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7 replies  131 view(s)
April 22nd, 2017,
13:29
MarkFL
replied to a thread
Volume Of Rectangular Prism
in
PreAlgebra and Algebra
The dimensions are length $\ell$, width $w$ and height $h$. Suppose we know $\ell$ and $w$ to be 6 and 2 respectively. A rectangular prism (cuboid)...
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3 replies  95 view(s)
April 22nd, 2017,
12:32
MarkFL
replied to a thread
Value of K
in
Basic Probability and Statistics
I also thought that might be the intended problem. :D
see more
7 replies  169 view(s)
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karush
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Sudharaka

November 24th, 2015
08:50
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Happy Birthday karush!
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About karush
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November 24, 1944 (72)
About karush
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Wahiawa, Hawaii
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retired from Architecture and Surveying
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April 24th, 2017
15:38 
karush
clicked Thanks for this post:
Re: 17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
by
HallsofIvy
With characteristic...
14:37 
karush
clicked Thanks for this post:
Re: 17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
by
MarkFL
wow thank you I did...
April 22nd, 2017
21:11 
MarkFL
clicked Thanks for this post:
Re: 17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
by
karush
wow thank you I did...
20:13 
karush
clicked Thanks for this post:
Re: 17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
by
MarkFL
the function y_p is a...
20:13 
karush
clicked Thanks for this post:
Re: 17.2.53 Find the unique solution satisfying the equation and the given initial conditions.
by
MarkFL
What I used to like to...
16:24 
MarkFL
clicked Thanks for this post:
Re: 17.2.10 y_p is a particular solution
by
karush
that was very...
16:16 
karush
clicked Thanks for this post:
Re: 17.2.10 y_p is a particular solution
by
MarkFL
I didn't notice before,...
15:33 
karush
clicked Thanks for this post:
Re: 17.2.10 y_p is a particular solution
by
HallsofIvy
Okay, that was the next...
15:33 
karush
clicked Thanks for this post:
Re: 17.2.10 y_p is a particular solution
by
MarkFL
I added the y= to the OP...
April 21st, 2017
19:30 
MarkFL
clicked Thanks for this post:
Re: 17.2.10 y_p is a particular solution
by
karush
I added the y= to the OP...
April 13th, 2017
22:58 
karush
clicked Thanks for this post:
Re: 242.tr.05 Use the integral test to determine if a series converges.
by
MarkFL
I would define: ...
22:58 
karush
clicked Thanks for this post:
Re: 242.tr.05 Use the integral test to determine if a series converges.
by
greg1313
$$\int_0^\infty\frac{1}{\...
April 12th, 2017
11:59 
greg1313
clicked Thanks for this post:
Re: 10.r.19 is this telescoping
by
karush
big Mahalo again .........
April 11th, 2017
19:46 
MarkFL
clicked Thanks for this post:
Re: 10.r.19 is this telescoping
by
karush
big Mahalo again .........
19:33 
karush
clicked Thanks for this post:
Re: 10.r.19 is this telescoping
by
MarkFL
Using partial fraction...