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  • MarkFL's Avatar
    Today, 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 | 63 view(s)
  • MarkFL's Avatar
    Yesterday, 22:32
    MarkFL replied to a thread Radius of Circle in Pre-Calculus
    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 | 58 view(s)
  • MarkFL's Avatar
    Yesterday, 21:35
    MarkFL replied to a thread Radius of Circle in Pre-Calculus
    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 | 58 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 72 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 72 view(s)
  • MarkFL's Avatar
    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 | 73 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 72 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 72 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 254 view(s)
  • MarkFL's Avatar
    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 | 62 view(s)
  • MarkFL's Avatar
    March 24th, 2017, 04:04
    MarkFL replied to a thread Boat direction in Calculus
    Is this a calculus-based physics course?
    6 replies | 92 view(s)
  • MarkFL's Avatar
    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 | 62 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 84 view(s)
  • MarkFL's Avatar
    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 | 92 view(s)
  • MarkFL's Avatar
    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 | 92 view(s)
  • MarkFL's Avatar
    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 | 103 view(s)
  • MarkFL's Avatar
    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 | 79 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:50
    MarkFL replied to a thread Factoring...3 in Pre-Calculus
    I would say division is the inverse of multiplication, but factoring is certainly related to division. For example, we know: ...
    6 replies | 79 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:42
    MarkFL replied to a thread Factoring...4 in Pre-Calculus
    Looks good. (Yes)
    2 replies | 36 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:32
    MarkFL replied to a thread Factoring...3 in Pre-Calculus
    Perfect. (Yes)
    6 replies | 79 view(s)
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    Hello by0young0math! Happy Birthday!
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    Hello and welcome back to MHB, bw0young0math!

    We are happy to see that you have returned, and we look forward to your continued participation here!

    On Behalf Of MHB's Staff,

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    Hello and welcome back to MHB, bw0young0math!

    We are happy to see that you have returned, and we look forward to your continued participation here!

    On Behalf Of MHB's Staff,

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    Hey Young,

    I do spend a gret deal of time online, particularly here at MHB, but I do sleep and eat. I hardly ever manually log off and this may make it appear that I am online more than I actually am too.

    Best Regards,

    Mark.
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    Hello Young,

    First let me say I am very happy you found MHB. I wish you the best in becoming a teacher, and I have great respect for educators. I feel teachers make one of the most profound impacts on society in general.

    While I participate on several math help sites, and am a global moderator on two of them and an administrator on a third, MHB is my favorite for many reasons. MHB has a truly dedicated team of administrators who are always looking for ways to make MHB even better. They take each and every comment/suggestion made by the members very seriously. They make certain to let those who are contributing know that it is appreciated.

    I simply enjoy trying to help students gain a better understanding of mathematics. I find it very gratifying. I think mathematics is a universe full of so many wonderful concepts that give us deep insights into the world in which we live. I want to help people to see some of these things.

    Best Regards,

    Mark.
  6. Reply/View Conversation
    " ..,I study complex analyis, but it is as difficult as I study real analysis."

    Would you believe that I learnt complex analysis without any knowledge of real analysis . Yes , I faced some difficulties but it is the most interesting mathematical subject for me .


    " special function.. I heard that word at first from you. "

    They are not taught in university you can learn them yourself . Some might be given as side notes or exericises in complex analysis or differential equations like bessel functions Legendre polynomials , gamma functions ...

    "If I'm not rude, could I ask you how long you study math? If so long, what do you think about math's attraction?"

    For around one year . Most of it is just self-study . I don't quite understand your question .
  7. Reply/View Conversation
    Hi Young

    I am Zaid , nice to meet you !

    I am interested in complex analysis , special functions and integration here .
    I guess we are +3 GMT , in here .

    Analysis is a big subject , I guess you are discussing Real analysis at the moment . I agree it is an attractive area .
  8. Reply/View Conversation
    Hello,

    One of our administrators is going to see about correcting this issue, but it may take several weeks to do so. We appreciate you bringing up this issue as we do want to get it corrected.

    Best Regards,

    Mark.
  9. Reply/View Conversation
    You should watch "Dong Yi", take my word, it's equally beautiful as "DaeJangGeum".

    Nice to hear you like analysis topics. Analysis is a bit difficult at first but as you get hold of it, things will become easier. In any case do PM(private message) me or any other staff member if you have any questions regarding the site. I know you have a problem with your profile picture, but it will be solved soon, the administrators are already looking into it.

    A nice day to you too.....
  10. Reply/View Conversation
    Hello again,

    I have raised the issue with the staff concerning profile pictures and it seems there is a problem with the displaying of these pictures, most probably because of the extensive custom design work the admins have done to give MHB a unique look and feel. At the moment we are deciding what action we should take. I just wanted to keep you updated.

    I am very happy that you like MHB and wish to both ask and answer questions. Please feel free to do both; we encourage your participation.

    Best Regards,

    Mark.
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