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• Today, 13:13
$d=\sqrt{R^2-2Rr}$
1 replies | 85 view(s)
• Today, 12:22
my solution: the area of the 1st square=$2R^2$ the area of the 2nd square=$R^2$ the area of the 3rd square=$\dfrac {R^2}{2}$ the area of the...
3 replies | 72 view(s)
• Yesterday, 12:24
Just to follow up, here is the completed table: Sum $S$ Probability of $S$: $P(S)$ Net Gain/Loss (in dollars) $G$ Product $G\cdot P(S)$
2 replies | 79 view(s)
• March 26th, 2017, 22:32
That is the radius of the circle after it has been increased by $a$ units. If I tell you that my weight increased by 20 lbs., then you know my...
4 replies | 84 view(s)
• March 26th, 2017, 21:35
Let's let $0<a$ be the number units the radius must be increased. And so the change in area we can write as: \Delta A=\pi(r+a)^2-\pi r^2=b Now...
4 replies | 84 view(s)
• March 25th, 2017, 21:53
MarkFL replied to a thread The Distance Across in Geometry
\overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)}=\sqrt{2(50)}=\sqrt{100}=10 :D
8 replies | 91 view(s)
• March 25th, 2017, 21:07
MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
I arbitrarily chose another point on the constraint, so that we could do a comparison like I mentioned just now in the other thread. :D
9 replies | 90 view(s)
• March 25th, 2017, 21:04
MarkFL replied to a thread Lagrange Multipliers in Calculus
I chose the point as it is on the constraint. Using that point, we can determine if our one critical point is a maximum or a minimum. If the...
9 replies | 75 view(s)
• March 25th, 2017, 19:21
MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
I agree that the point $(2,2)$, is the only one that meets all criteria. Now we need to compare the value of $f$ at another point on the constraint,...
9 replies | 90 view(s)
• March 25th, 2017, 19:08
MarkFL replied to a thread Lagrange Multipliers in Calculus
I agree that of the 3 critical points, $(1,1)$ is the only one in quadrant I. Now, we know this is either a maximum or a minimum, and to determine...
9 replies | 75 view(s)
• March 25th, 2017, 11:15
MarkFL replied to a thread Factoring...6 in Pre-Calculus
It might be more clear to state something like the following: The difference of cubes formula states: p^3-q^3=(p-q)\left(p^2+pq+q^2\right) ...
5 replies | 77 view(s)
• March 25th, 2017, 10:47
MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
Consider: e^u=0 What do you get when solving for $u$? Okay, you correctly found $x^2=y^2$...what do you get when you substitute for...
9 replies | 90 view(s)
• March 25th, 2017, 10:39
MarkFL replied to a thread Lagrange Multipliers in Calculus
What I would do is use the constraint to determine $y=2-x$. Now substitute for $y$ in both equations you mentioned, and solve for $x$, then your...
9 replies | 75 view(s)
• March 25th, 2017, 02:30
This is a calculus question...please don't continue to post calculus questions in other forums. If given: ...
3 replies | 87 view(s)
• March 24th, 2017, 23:12
MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
If you solve both equations for $\lambda$ and then equate the results, you obtain: \frac{ye^{xy}}{2x}=\frac{xe^{xy}}{2y} Multiply through by 2:...
9 replies | 90 view(s)
• March 24th, 2017, 21:24
MarkFL replied to a thread Lagrange Multipliers in Calculus
Okay, so what this implies is: \frac{x}{\sqrt{6-x^2-y^2}}=\frac{y}{\sqrt{6-x^2-y^2}} Cross-multiply: x\sqrt{6-x^2-y^2}=y\sqrt{6-x^2-y^2} ...
9 replies | 75 view(s)
• March 24th, 2017, 16:18
MarkFL replied to a thread The Distance Across in Geometry
Using the Pythagorean theorem, we find: \overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)} Now, we know that...
8 replies | 91 view(s)
• March 24th, 2017, 06:10
MarkFL replied to a thread [SOLVED] Minimum of function under constraint in Calculus
I would use W|A: W|A - optimize 2x+y subject to xy=18
8 replies | 262 view(s)
• March 24th, 2017, 04:29
The objective function is linear, so it describes a plane, and so I don't believe there will be any saddle points, or in fact any critical points...
4 replies | 63 view(s)
• March 24th, 2017, 04:04
MarkFL replied to a thread Boat direction in Calculus
Is this a calculus-based physics course?
6 replies | 100 view(s)
• March 24th, 2017, 01:37
What I would do is observe that we have cyclical symmetry, that is we may interchange $x_1$ and $x_2$ with no change in either the objective function...
4 replies | 63 view(s)
• March 24th, 2017, 01:25
MarkFL replied to a thread The Distance Across in Geometry
Not quite...it would be \sqrt{2}a and \sqrt{2}b...so what would the diagonal of the rectangle be?
8 replies | 91 view(s)
• March 23rd, 2017, 21:17
MarkFL replied to a thread The Distance Across in Geometry
I would let $a$ be the length (in cm) of the segments with 1 tick mark, and $b$ be the length (in cm) of the segments with 2 tick marks. And so,...
8 replies | 91 view(s)
• March 23rd, 2017, 19:30
MarkFL replied to a thread Boat direction in Calculus
Being that it is an optimization problem, on a function in two variables, the way I worked it using the calculus is the most straightforward way I...
6 replies | 100 view(s)
• March 23rd, 2017, 12:53
MarkFL replied to a thread Boat direction in Calculus
I think what I would do is orient a coordinate system such that south is up and west is to the right. At time $t=0$, have boat A at the origin, and...
6 replies | 100 view(s)
• March 23rd, 2017, 11:28
There are online calculators that will spit out the answer to this question, however if you want genuine help, we need to know what you've tried, or...
3 replies | 106 view(s)
• March 23rd, 2017, 03:19
MarkFL replied to a thread Factoring...3 in Pre-Calculus
Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.
6 replies | 81 view(s)
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### 16 Visitor Messages

1. Hi Albert,

I was meant to reply to the PM but it seems to me your account here has exceeded your stored private messages quota and hence you cannot receive new message(s).

Anyway, I just wanted to thank you for reply and guess what, I just solved that challenge! Hurray! Haha...

Best,

anemone
2. Hi Albert,

I am aware that to editing our own post of less than 24 hours old (which I think is a good thing rather than keep adding responses by posting new follow-up posts to make mess of the look of one particular thread) is encouraged and not frowned upon, but I wanted to also let you know I have come to realize of your latest edit/update to my latest challenge only when I was about to reply to it. If by any chance I missed reading it, that would be unfair to you because your newest edited post deserves a credit, imho.

Thus in the future if you want to do a major edit to your previous post, I would recommend you to instead add another reply beneath your previous post, does that sound good to you, Albert?

Best wishes,

anemone
3. Hi Albert, congratulations on winning the MHB Challenges Award!
4. Hi Albert,

I wanted to say that I like your profile .sig, Little Prince was a story I read almost 2 years ago but it still touches my heart. It was the best story I ever have read in my life.

Best Regards,
Balarka
.
5. Hello, me again Albert!

Here is what our administrator Jameson has said regarding the issue:

"Ok, when that happens all he needs to do is reload the page. It should eventually render correctly. There's no need for more info. This happens for me periodically as well and I just reload the page. The only issue would be if after reloading many times he still couldn't see Latex."

So, when it happens again, try reloading the page, and if after several times the error still occurs, capture a screen shot and email the image to me.

Best Regards,

Mark.
6. Hello again Albert,

The staff here would really like to help, and it would be informative for use if you could get a screen shot of the error and email it to me, and I will forward it to the staff so we can see exactly what the error looks like at your end.

Best Regards,

Mark.
7. Hello Albert,

I have reported your problem to the staff here, and I can assure you they are a very knowledgeable and involved team of administrators whose primary goal is that our member's problems get addressed promptly.

Best Regards,

Mark
8. Hello Albert,

First I wanted to ask you if the issue you had yesterday was resolved...I waited for your email of the problem description but never got it. I want to help you get to the bottom of the problem if I can.

Second, I edited your latest post of the solution to the minimization problem. We try not to link to other math forums unless we are showing where a problem comes from if posted by someone else, to give credit to the OP. Since this problem is yours, you should post the solution at both places rather than at one, and then linking to that at the other.

Best Regards,

Mark.

1) http://www.mathhelpboards.com/f28/fi...equation-3193/ (Original title: please find n)

2) http://www.mathhelpboards.com/f28/bi...-squares-3198/ (Original title: mission impossible)
10. Hi again! You have asked in your thread >>here<< how to move a thread if you accidentally posted in a wrong sub-forum. The answer is you can't do that. However you can report the post by clicking on the little triangle (shown below) and writing down your request. I have moved your thread to the Challenge Questions and Puzzles sub-forum.

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