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• Yesterday, 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 | 48 view(s)
• Yesterday, 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 | 45 view(s)
• Yesterday, 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 | 48 view(s)
• Yesterday, 20:41
Looks good. -Dan
2 replies | 29 view(s)
• Yesterday, 15:14
I am so sorry, that I have posted a challenge, the solution of which, I am not certain. My problem is the use of the Rearrangement Inequality in the...
1 replies | 88 view(s)
• 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 | 74 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 | 83 view(s)
• March 25th, 2017, 21:31
At a guess you are forgetting about the cross term. (a + b)^2 \neq a^2 + b^2. It is (a + b)^2 = a^2 + 2ab + b^2. You are going to end up having to...
4 replies | 56 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 | 82 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 | 70 view(s)
• March 25th, 2017, 20:52
Rewrite as $\sqrt{2t+5}+\sqrt{2t+8}=\sqrt{8t+25}$. What do you get when you square both sides?
4 replies | 56 view(s)
• March 25th, 2017, 20:02
Here is this week's POTW: ----- Let $f$ be a real function with a continuous third derivative such that $f(x),f'(x), f''(x), f'''(x)$ are...
0 replies | 27 view(s)
• March 25th, 2017, 20:00
We first note that \ Subtracting $S$ from this gives two sums, one of which is \ and the other of which sums to $xy^3/$. Therefore...
1 replies | 66 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 | 82 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 | 70 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 | 73 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 | 82 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 | 70 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 | 84 view(s)
• March 24th, 2017, 23:17
greg1313 replied to a thread Factoring...8 in Pre-Calculus
1. Correct. 2. Correct. 3. Yes, apply the sum of cubes formula to $8a^3+27b^3$. Be careful with your variable names. $a$ does not necessarily...
2 replies | 39 view(s)
• March 24th, 2017, 23:16
topsquark replied to a thread Factoring...7 in Pre-Calculus
I mentioned this in another thread. Don't set the LHS of "a = a + b" It's too confusing. -Dan
3 replies | 48 view(s)
• March 24th, 2017, 23:13
topsquark replied to a thread Factoring...6 in Pre-Calculus
You need to clarify your variables. "b = (a - b)" isn't right. Pick a variable name, say, p... Anything but that b on the LHS.... Then you have p...
5 replies | 73 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 | 82 view(s)
• March 24th, 2017, 22:57
greg1313 replied to a thread Factoring...7 in Pre-Calculus
$$(a-b)^3=a^3-3a^2b+3ab^2-b^3$$ Rearrange: \begin{align*}a^3-b^3&=(a-b)^3+3a^2b-3ab^2 \\ &=(a-b)^3+3ab(a-b) \\ &=(a-b) \\...
3 replies | 48 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 | 70 view(s)
• March 24th, 2017, 21:05
topsquark replied to a thread Factoring...5 in Pre-Calculus
Yeppers! -Dan
2 replies | 33 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 | 83 view(s)
• March 24th, 2017, 13:33
Is the angle contained by $a$ and $b$ equal to $90^\circ$? For that matter, what is the complete problem?
2 replies | 67 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 | 254 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 | 62 view(s)
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### 21 Visitor Messages

1. Have a wonderful, happy, healthy birthday now and forever!
2. Happy Birthday, topsquark!!!
3. Hey Topsquark! Think you could check my quantum physics question? Thanks!
4. so he just kept posting the same thing over and over??? dam. ban him and say it was a mistake. like you did with nycmath. that one was sooo funny lol because i always thought he was annoying
5. i was reading the thread by alexchan on mhf "I'm sorry for before action. Hopefully, we can continue to discuss." did u delete the original thread? because now I HAVE TO know what he got in trouble for. tell meeeee dan pleeeeaaase.
6. hiiiiiiiiiii a few of us have been talking about it since yesterday. come to mathhelpboards.com/chat/ that place needs ur funnyness!!!!
7. The last ten digit is 8000000018 but not 6795421006 because $44!+9= 2658271574788448768043625811014615890319638528000000018 \ne 2658271574788448768043625811014615890319638526795421006$.
8. Hey Dan, so, you are now 44! (44 factorial + 9 days) old? Hehehe...
9. Happy Birthday Dan!!
10. Hey Dan...Happy Birthday, you crusty old curmudgeon!
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