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• 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
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 | 84 view(s)
• March 26th, 2017, 22:19
Hi tmt, (Wave) For the quoted part in bold, should this read "If all cars are reserved for the day..."? I think there are two events here,...
1 replies | 49 view(s)
• March 26th, 2017, 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 | 84 view(s)
• March 26th, 2017, 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 | 78 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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13 Visitor Messages

1. Happy Birthday, Bacterius!! I hope you have a nice celebration with your close ones. . Thank you for being an active part of MHB!
2. Hey Bacterius, really liked the number theory challenge of yours. I wonder if that's an Olympiad problem. (PS : I have produced somewhat of a solution, but I am not sure if it's correct)
3. Hey, Happy Birthday! Here in the U.S., the 21st birthday in really the last milestone of youth, because that's the legal drinking age.
4. I hope that today is the beginning of a great year for you...Happy Birthday!
5. For what it's worth, you come across on the forums as someone with wisdom and maturity far beyond your years.
6. Happy Birthday!

You are no longer a teenager...it's all downhill from here.
7. Happy Birthday, mate!!
8. Happy birthday!
9. Hey Bacterius!

I thought your post in the sequence challenge was very enlightening and well-written! Excellent job!
10. Hey,

Just wanted to say that your post explaining the Taylor series was very well written! Marvelous job!
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