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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)

March 25th, 2017, 21:53
\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, 21:07
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
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, 20:02
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
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
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
It might be more clear to state something like the following:
The difference of cubes formula states:
p^3q^3=(pq)\left(p^2+pq+q^2\right)
...
5 replies  73 view(s)

March 25th, 2017, 10:47
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
What I would do is use the constraint to determine $y=2x$. 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, 23:12
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, 21:24
Okay, so what this implies is:
\frac{x}{\sqrt{6x^2y^2}}=\frac{y}{\sqrt{6x^2y^2}}
Crossmultiply:
x\sqrt{6x^2y^2}=y\sqrt{6x^2y^2}
...
9 replies  70 view(s)

March 24th, 2017, 16:18
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, 06:10
I would use WA:
WA  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)

March 24th, 2017, 04:04
Is this a calculusbased physics course?
6 replies  92 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  62 view(s)

March 24th, 2017, 01:25
Not quite...it would be \sqrt{2}a and \sqrt{2}b...so what would the diagonal of the rectangle be?
8 replies  83 view(s)

March 23rd, 2017, 21:17
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  83 view(s)

March 23rd, 2017, 19:30
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)

March 23rd, 2017, 12:53
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)

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)

March 23rd, 2017, 03:19
Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.
6 replies  78 view(s)
 Date of Birth
 September 6
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 BS Mathematics, East Tennessee State University
BS Computer Science, East Tennessee State University
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