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Wilmer
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August 17th, 2017,
02:10
MarkFL
replied to a thread
231.12.3.65 Determine the smallest distance between a point and a line
in
Calculus
Small quibble...axis of symmetry is: t=-\frac{1}{105} So, since the parabola opens up, the vertex is a minimum, so the minimum distance will be...
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8 replies | 155 view(s)
August 17th, 2017,
00:59
MarkFL
replied to a thread
231.12.3.65 Determine the smallest distance between a point and a line
in
Calculus
For a parabola of the form: f(x)=ax^2+bx+c We know the axis of symmetry is at: x=-\frac{b}{2a} So, for:
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8 replies | 155 view(s)
August 16th, 2017,
21:58
MarkFL
replied to a thread
231.12.3.63 Determine the smallest distance between point and line
in
Calculus
Isn't this question a duplicate of the following? 231.12.3.65 Determine the smallest distance between a point and a line
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1 replies | 37 view(s)
August 14th, 2017,
01:09
MarkFL
replied to a thread
Solar Eclipse 2017
in
Chat Room
I was just reading about how tree leaves can form "pinhole cameras" and the eclipse can be seen in their shadows:
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4 replies | 162 view(s)
August 13th, 2017,
14:03
MarkFL
replied to a thread [SOLVED]
12 DeMoivre's theorem
in
Trigonometry
In case you're wondering how I obtained the following factorizations: 1+3i=(1+i)(2+i) 2-2i=-(1+i)^3 What I did for the first was to write: ...
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13 replies | 237 view(s)
August 13th, 2017,
10:15
MarkFL
replied to a thread [SOLVED]
12 DeMoivre's theorem
in
Trigonometry
What definition for "complex form" were you given? That was the confusing issue for me. I am aware of rectangular, polar and exponential forms for...
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13 replies | 237 view(s)
August 12th, 2017,
22:07
MarkFL
replied to a thread [SOLVED]
12 DeMoivre's theorem
in
Trigonometry
I'm wondering if what we're supposed to do here is: 1+3i=(1+i)(2+i) 2-2i=-(1+i)^3 And so the product is: ...
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13 replies | 237 view(s)
August 8th, 2017,
19:10
MarkFL
replied to a thread
231.13.3.75 top vertex of a regular tetrahedron
in
Calculus
The following post may give you some insight: Tetrahedral stack of spheres
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2 replies | 74 view(s)
August 7th, 2017,
15:38
MarkFL
replied to a thread
Find the minimal value
in
Challenge Questions and Puzzles
My solution: By cyclic symmetry, we know the critical value is at the point: \left(x_1,\cdots,x_{2017}\right)=(2016,\cdots,2016) And the...
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2 replies | 88 view(s)
August 4th, 2017,
10:51
MarkFL
replied to a thread
Negative numbers with fraction problem
in
Pre-Algebra and Algebra
Canceling is the process of simplifying a fraction by dividing out any factors common to the numerator and denominator. A fraction in its simplest...
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9 replies | 214 view(s)
August 3rd, 2017,
15:06
MarkFL
replied to a thread [SOLVED]
S.8.5.41 sin(a + b) =
in
Trigonometry
If we have: \sin(\alpha)=\frac{1}{3} But, we want the angle between the terminal side of $\alpha$ and \frac{\pi}{2}...that is we want the...
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5 replies | 143 view(s)
August 3rd, 2017,
11:48
MarkFL
replied to a thread
Negative numbers with fraction problem
in
Pre-Algebra and Algebra
We are given to simplify: \frac{3}{4}\left(\frac{5}{6}\left(-\frac{18}{25}\right)+\frac{1}{2}\right) The first thing I would do is use the...
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9 replies | 214 view(s)
August 3rd, 2017,
00:24
MarkFL
replied to a thread [SOLVED]
S.8.5.41 sin(a + b) =
in
Trigonometry
I'm assuming you are to solve for $\theta$...in which case I would observe that there are solutions in quadrant I and quadrant II, and they are...
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5 replies | 143 view(s)
August 2nd, 2017,
19:21
MarkFL
replied to a thread [SOLVED]
S.8.5.41 sin(a + b) =
in
Trigonometry
From the graph on the left, we have: 2\sin(\alpha)=1\implies \sin(\alpha)=\frac{1}{2}- Hence: ...
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5 replies | 143 view(s)
August 1st, 2017,
12:29
MarkFL
replied to a thread
Combination of a Smile and a Frown ...
in
LaTeX Help and Discussion
I'm thinking it would be cool to put a button somewhere in our editor that opens that page in a popup window. (Yes)
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6 replies | 160 view(s)
August 1st, 2017,
07:58
MarkFL
replied to a thread
Combination of a Smile and a Frown ...
in
LaTeX Help and Discussion
This is what I meant:
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6 replies | 160 view(s)
August 1st, 2017,
02:38
MarkFL
replied to a thread
Combination of a Smile and a Frown ...
in
LaTeX Help and Discussion
We have it as a symbol in our Quick $\LaTeX$ element, in the Algebra section, with the toolltip "Asymptotic To"...the code is: \asymp which...
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6 replies | 160 view(s)
July 31st, 2017,
19:14
MarkFL
replied to a thread
Find cos(x) and sin(x) if angle x has these properties...
in
Trigonometry
Hello and welcome to MHB, Sirmeris! (Wave) I agree with your reasoning, and your conclusion. (Yes)
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1 replies | 97 view(s)
July 31st, 2017,
19:05
MarkFL
replied to a thread [SOLVED]
w.8.8.19 Integration of 2 to \infty
in
Calculus
Yes. An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more...
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7 replies | 185 view(s)
July 31st, 2017,
16:36
MarkFL
replied to a thread [SOLVED]
w.8.8.19 Integration of 2 to \infty
in
Calculus
Yes, I think the way I would handle it is: I=\lim_{t\to0}\left(\int_t^{\frac{1}{2}} \cos(\pi...
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7 replies | 185 view(s)
July 31st, 2017,
16:18
MarkFL
replied to a thread
integration
in
Calculus
Let me know where the confusion lies, and I'll try to explain. :)
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6 replies | 137 view(s)
July 31st, 2017,
15:35
MarkFL
replied to a thread [SOLVED]
w.8.8.19 Integration of 2 to \infty
in
Calculus
We need to change the limits as well in accordance with the substitution, so we would have: I=\lim_{t\to0}\left(\int_t^{\frac{1}{2}} \cos(\pi...
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7 replies | 185 view(s)
July 31st, 2017,
14:59
MarkFL
replied to a thread [SOLVED]
w.8.8.19 Integration of 2 to \infty
in
Calculus
I would begin by writing: I=\lim_{t\to\infty}\left(\int_2^t \frac{\cos\left(\frac{\pi}{x}\right)}{x^2}\,dx\right) Next, I would use the...
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7 replies | 185 view(s)
July 31st, 2017,
11:25
MarkFL
replied to a thread
integration
in
Calculus
A simpler approach would be to add via integration all of the circumferences of the concentric circles from radius 0 to radius r: A=\int_0^r (2\pi...
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6 replies | 137 view(s)
July 31st, 2017,
10:45
MarkFL
replied to a thread
integration
in
Calculus
This is just a substitution: x=r\sin(\theta) And via differentiation, we obtain: dx=r\cos(\theta)\,d\theta This takes care of the...
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6 replies | 137 view(s)
July 31st, 2017,
10:27
MarkFL
replied to a thread
integration
in
Calculus
Okay, so what you want using this approach is: A=4\int_0^r \sqrt{r^2-x^2}\,dx We need to multiply by 4 since we are integrating over just 1 of...
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6 replies | 137 view(s)
July 30th, 2017,
22:43
MarkFL
replied to a thread
Any one who can solve this?
in
Differential Equations
Note: This was done by taking the solution given by W|A and essentially "working backwards." We are given to solve: ...
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6 replies | 234 view(s)
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