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• Today, 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,...
6 replies | 47 view(s)
• Today, 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...
6 replies | 40 view(s)
• Today, 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) ...
4 replies | 56 view(s)
• Today, 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...
6 replies | 47 view(s)
• Today, 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...
6 replies | 40 view(s)
• Today, 02:30
This is a calculus question...please don't continue to post calculus questions in other forums. If given: ...
3 replies | 78 view(s)
• Yesterday, 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 | 38 view(s)
• Yesterday, 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...
4 replies | 56 view(s)
• Yesterday, 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:...
6 replies | 47 view(s)
• Yesterday, 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} ...
6 replies | 40 view(s)
• Yesterday, 21:05
topsquark replied to a thread Factoring...5 in Pre-Calculus
Yeppers! -Dan
2 replies | 27 view(s)
• Yesterday, 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...
6 replies | 63 view(s)
• Yesterday, 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 | 249 view(s)
• Yesterday, 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 | 60 view(s)
• Yesterday, 04:04
MarkFL replied to a thread Boat direction in Calculus
Is this a calculus-based physics course?
6 replies | 91 view(s)
• Yesterday, 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 | 60 view(s)
• Yesterday, 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?
6 replies | 63 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,...
6 replies | 63 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 | 91 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 | 91 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 | 102 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 | 74 view(s)
• 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 | 74 view(s)
• March 23rd, 2017, 02:42
MarkFL replied to a thread Factoring...4 in Pre-Calculus
Looks good. (Yes)
2 replies | 34 view(s)
• March 23rd, 2017, 02:32
MarkFL replied to a thread Factoring...3 in Pre-Calculus
Perfect. (Yes)
6 replies | 74 view(s)
• March 23rd, 2017, 02:24
MarkFL replied to a thread Factoring...2 in Pre-Calculus
I was just rewriting that term as a perfect square: 9(ab+c)^2=3^2(ab+c)^2=(3(ab+c))^2
4 replies | 47 view(s)
• March 23rd, 2017, 02:16
MarkFL replied to a thread Factoring...2 in Pre-Calculus
I would first write the expression as: (2ab)^2-(3(ab+c))^2 Now, factor as the difference of squares, and simplify. :D
4 replies | 47 view(s)
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