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suluclac
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January 20th, 2017,
11:54
MarkFL
replied to a thread
Differentiation challenge
in
Challenge Questions and Puzzles
We appreciate challenge problems of virtually any level of difficulty. My advice to everyone is that if you find a posted problem "too easy" to...
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7 replies | 183 view(s)
January 19th, 2017,
10:19
MarkFL
replied to a thread
Minimum of function under constraint
in
Calculus
Yes, the function as a whole is not bounded from below or from above. Let's look at this using Lagrange Multipliers... We have the objective...
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6 replies | 85 view(s)
January 18th, 2017,
22:47
MarkFL
replied to a thread
Minimum of function under constraint
in
Calculus
You also need to check the boundaries of the function, one of which is $x=0$, at which the function is discontinuous. Another way to find the range...
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6 replies | 85 view(s)
January 18th, 2017,
20:13
MarkFL
replied to a thread
Minimum of function under constraint
in
Calculus
The function: f(x)=\frac{36}{x}+x has 2 local extrema, but we need to also look at the range, which is $(-\infty,-6]\,\cup\,[6,\infty)$. You...
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6 replies | 85 view(s)
January 17th, 2017,
17:35
MarkFL
replied to a thread [SOLVED]
231.12.3.63 Determine the smallest distance between point P and the line L through the origin
in
Calculus
The square of the distance is: D^2=(x+8)^2+(6x-4)^2=37x^2-32x+80 Critical value is from: 74x-32=0\implies x=\frac{16}{37} ...
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2 replies | 60 view(s)
January 16th, 2017,
19:00
greg1313
replied to a thread [SOLVED]
231.12.3.19 angle between vectors
in
Calculus
Your answer looks good to me. What are the zeros for? Cross-product is 3-d. What you have here appears to be 2-d and you've used the dot product.
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3 replies | 71 view(s)
January 16th, 2017,
18:23
greg1313
replied to a thread
Parabola question
in
Pre-Algebra and Algebra
That's correct. Alternatively, we have $$b=5(a)^2+a(a)+b\implies a=0$$ Substituting $-\frac{a}{10}=0$ for $x$ into $y=5x^2+ax+b$ gives...
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5 replies | 99 view(s)
January 16th, 2017,
17:17
MarkFL
replied to a thread
Parabola question
in
Pre-Algebra and Algebra
Yes, that's what I got too. (Yes) So then, what is $y_{\min}$?
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5 replies | 99 view(s)
January 16th, 2017,
16:04
MarkFL
replied to a thread
Parabola question
in
Pre-Algebra and Algebra
We know the axis of symmetry for the general quadratic: f(x)=ax^2+bx+c is the line: x=-\frac{b}{2a} And so for the given function:
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5 replies | 99 view(s)
January 15th, 2017,
15:39
greg1313
replied to a thread
Smilie Tabs: Easier Access To Smilies
in
Announcements
Cool. :cool:(Cool)(Malthe) Thanks MarkFL and MHB!
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3 replies | 115 view(s)
January 15th, 2017,
15:03
MarkFL
started a thread
Smilie Tabs: Easier Access To Smilies
in
Announcements
Hello MHB Community! (Wave) We have just installed a new feature that will make adding smilies to your posts easier and more efficient. When you...
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3 replies | 115 view(s)
January 15th, 2017,
10:59
MarkFL
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
We could use Lagrange Multipliers...consider the objective function: f(x,y)=\sin(x)-\sin(y) Subject to the constraint: ...
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11 replies | 294 view(s)
January 15th, 2017,
09:39
greg1313
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
Yes; quite right. My apologies for my blunder. :o
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11 replies | 294 view(s)
January 14th, 2017,
21:29
greg1313
replied to a thread [SOLVED]
206.08.05.44 partial fraction decomposition
in
Calculus
Differentiate $3/u$. What is $\frac{\sin(\theta)\cos(\theta)}{2}+\frac{\theta}{2}$ in terms of $x$?
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6 replies | 154 view(s)
January 14th, 2017,
17:13
greg1313
replied to a thread [SOLVED]
206.08.05.44 partial fraction decomposition
in
Calculus
First one's ok. You've made a sign error on the second one and haven't completed the back-sub. For the third, you should be integrating with respect...
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6 replies | 154 view(s)
January 14th, 2017,
13:40
greg1313
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
Your proof is ok, it's your conclusion that needs work. See vidyarth's post (post #2). As an alternative, write $\sin(x)-\cos(x)$ as...
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11 replies | 294 view(s)
January 13th, 2017,
03:57
greg1313
replied to a thread
Prove that sin(x)+cos(x) is equal or larger than 1
in
Trigonometry
Your conclusion only shows that the original statement must be true at $x=\frac{\pi}{2}$. What about the remainder of the interval? Does your...
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11 replies | 294 view(s)
January 13th, 2017,
03:18
greg1313
replied to a thread
Limits with the natural logarithm
in
Calculus
Ok, so we're given $\lim_{x\to0}\frac{\log(1+x)}{x}=1$ and we have ...
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3 replies | 95 view(s)
January 13th, 2017,
01:56
greg1313
replied to a thread [SOLVED]
206.08.05.44 partial fraction decomposition
in
Calculus
Good! Suggestions: Write as $$\int\frac{4}{x^2+16}\text{ d}x$$ $$3\int\frac{2x}{(x^2+16)^2}\text{ d}x$$
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6 replies | 154 view(s)
January 12th, 2017,
23:20
MarkFL
replied to a thread
Site upgrade and planned downtime Wed, Jan 11
in
Announcements
Yes, when I got in tonight, I found Jameson had sent me the cure for the thanks issue. (Dance)
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12 replies | 310 view(s)
January 12th, 2017,
22:41
MarkFL
replied to a thread
Site upgrade and planned downtime Wed, Jan 11
in
Announcements
After an upgrade to the latest version of our thanks product, that is now functioning again. (Yes)
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12 replies | 310 view(s)
January 12th, 2017,
21:32
greg1313
replied to a thread
Limit with square root
in
Calculus
Multiply by $\frac{\sqrt{x^2+3}-x}{\sqrt{x^2+3}-x}$.
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2 replies | 90 view(s)
January 12th, 2017,
16:33
MarkFL
replied to a thread
cone
in
Calculus
The vessel into which the water is flowing has a radius that is one half the height. Any "cone of water" partially or completely filling the vessel...
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3 replies | 90 view(s)
January 12th, 2017,
16:11
MarkFL
replied to a thread
cone
in
Calculus
At any point in time, how are the radius and height of the "cone of water" within the conical vessel related?
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3 replies | 90 view(s)
January 12th, 2017,
11:24
MarkFL
replied to a thread
Hello
in
Introductions
Hello and welcome to MHB, MC! (Wave) Sorry for the late reply...I've been busy with the site upgrade. It's good to see you here! (Yes)
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5 replies | 215 view(s)
January 12th, 2017,
05:53
MarkFL
replied to a thread
Site upgrade and planned downtime Wed, Jan 11
in
Announcements
The upgrade is now complete, but we had to disable the post thanking feature for now until we can figure out how to restore this feature. Hopefully...
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12 replies | 310 view(s)
January 11th, 2017,
02:36
MarkFL
replied to a thread
Site upgrade and planned downtime Wed, Jan 11
in
Announcements
Most likely somewhere around 10 pm EST...but could be later, not likely to be earlier.
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12 replies | 310 view(s)
January 10th, 2017,
22:03
greg1313
replied to a thread
206.07.05.88 Int rational expression
in
Calculus
Nope. You're ok up until $$\int\frac{1}{u\sqrt{u^2+1}}\text{ d}u$$ That should be $$\int\frac{1}{u\sqrt{u^2-1}}\text{ d}u$$ ...
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6 replies | 156 view(s)
January 9th, 2017,
21:55
greg1313
replied to a thread
Find x and y if x, y are members of real numbers and: (x+i)(3-iy)=1+13i
in
Pre-Algebra and Algebra
Your approach and posted work are ok. To continue, $$3x+y=1\implies y=1-3x$$ $$3-xy=13\implies xy=-10$$ $$x(1-3x)=-10$$
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1 replies | 71 view(s)
January 9th, 2017,
01:27
MarkFL
replied to a thread
ACT problem
in
Pre-Algebra and Algebra
Let: f(x)=2x^2-4x-z Now, if $x-4$ is a factor of $f$, then we must have: f(4)=0 So, this allows us to write:
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2 replies | 103 view(s)
January 9th, 2017,
00:05
greg1313
replied to a thread [SOLVED]
w8.5.1 integral expansion
in
Calculus
No, it's not fine. The '16' is not applied to $x^2+4$ as the notation used implies. Sorry to nitpick but clean notation helps to avoid errors and...
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8 replies | 319 view(s)
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