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  • 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)
  • I like Serena's Avatar
    Yesterday, 12:05
    I like Serena replied to a thread ideal gas in Other Topics
    Hi markosheehan, Yes, there are Van der Waals forces in all cases. However, Helium is the only one that is electrically neutral. That's because...
    1 replies | 46 view(s)
  • I like Serena's Avatar
    Yesterday, 11:52
    I like Serena replied to a thread copper(2) oxide in Other Topics
    Yes, there are exceptions. Most elements have a stable bonding with a full outer shell, but they typically also have alternative stable bondings....
    5 replies | 76 view(s)
  • Rido12's Avatar
    Yesterday, 11:46
    Rido12 replied to a thread copper(2) oxide in Other Topics
    There are many exceptions. I remember back in my first year chemistry course, my professor criticized the textbook for providing incorrect...
    5 replies | 76 view(s)
  • I like Serena's Avatar
    Yesterday, 09:08
    I like Serena replied to a thread copper(2) oxide in Other Topics
    Hi markosheehan, I'm assuming EC stands for Electron Configuration? Before the bonding Copper has the configuration 2-8-18-1 (there are 18...
    5 replies | 76 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)
  • I like Serena's Avatar
    March 25th, 2017, 06:59
    Hey evinda!! (Smile) I haven't figured it out yet. :( However, I can see a couple of approaches... According to Euler we have: $$a^{\phi(pq)}...
    1 replies | 57 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)
  • I like Serena's Avatar
    March 24th, 2017, 17:47
    Actually, f(n)=2n is not a bijection, since for instance 1 does not have an original. But it does free up all the odd rooms, so that a new arrival...
    1 replies | 46 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)
  • evinda's Avatar
    March 23rd, 2017, 16:08
    evinda started a thread Show equivalence in Number Theory
    Hello!!! (Wave) Suppose that $p,q$ are two distinct primes , $n=pq$ and $d=gcd(p-1,q-1)$. I want to show that if $a^{n-1} \equiv 1 \pmod{n}$ for...
    1 replies | 57 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)
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