I am thinking of purchasing this little fella  and (also) using it as an external monitor to my MacBook Pro (mid 2014).   Is it possible?
I have a MacBook Pro with Mini DisplayPort and I want to use target display mode to use a Thunderbolt iMac as an external display. If this works, would I need a Mini DisplayPort cable or a Thunderbolt cable?
Prove that $||x|-|y||\le |x-y|$ I've seen the full proof of the Triangle Inequality  \begin{equation*} |x+y|\le|x|+|y|.  \end{equation*} However, I haven't seen the proof of the reverse triangle inequality:  \begin{equation*} ||x|-|y||\le|x-y|. \end{equation*} Would you please prove this using only the Triangle Inequality above?  Thank you very much. I am using &lt;a&gt; tags for links on a web page. How do I disable the Tab key from selecting either of them? Run a program without administrative privileges in Windows 7 My account in Windows 7 is an administrator account. When I open the Run box (WinKey + R), I am warned, "This task will be created with administrative privileges."    Is there any way to run programs as myself, but without administrative privileges when logged in as an administrator? I can't find a definitive answer for this. As far as I know, you can't have multiple __init__ functions in a Python class. So how do I solve this problem? Suppose I have a class called Cheese with the number_of_holes property. How can I have two ways of creating cheese objects...  One that takes a number of holes like this: parmesan = Cheese(num_holes = 15) And one that takes no arguments and just randomizes the number_of_holes property: gouda = Cheese()  I can think of only one way to do this, but this seems clunky: class Cheese():     def __init__(self, num_holes = 0):         if (num_holes == 0):             # Randomize number_of_holes         else:             number_of_holes = num_holes  What do you say? Is there another way? I am rendering my scene with only one sample but all the renders of the same picture have a different seed value. How can I combine them correctly? I wrote a java-program that loads all the images and takes the average pixel color for each pixel of the images. Is that a correct way of combining the images? It doesn't reduce the noise very much so I am not happy with it. What can I do? How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ How to show  $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ How are Anonymous inner classes used in Java? What is the use of anonymous classes in Java? Can we say that usage of anonymous class is one of the advantages of Java? In linguistics, is there a term describing this phenomenon, i.e., when the syllables of two words are slurred together in the spoken language?  They are not contractions. While contractions are acceptable in any register, this combination of words is very informal and hardly ever found in formal writing.  kinda (kind of)   sorta (sort of)   coulda (could have)   shoulda (should have)   lotta (lot of)   oughta (ought to)   betcha (bet you)   lemme (let me)   tseasy (it's easy)   willya (will you)  Inasmuch as English Language speakers (just like the speakers of any natural language) have a tendency to join word sounds in speech, examples abound and a complete list would be hard to produce. I’m looking for a word or phrase describing this linguistic phenomenon as it occurs in speech. $ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $, prove $ab + bc + ca \le 3$ If $a,b,c$ real numbers such that $$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $$,  prove that $ab + bc + ca \le 3$.     Attempt:  Assume that $a,b,c &gt; 0$.   $$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1  $$ $$ \implies  (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1) + (a^{2} + b^{2} + 1)(a^{2}+c^{2}+1) +  (a^{2} + c^{2} + 1)(b^{2}+c^{2}+1) \ge (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1)$$  $$ \implies  ((ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 b^{2} + c^{2} + b^{4} + 1) + ((ab)^{2} + (ac)^{2} + (bc)^{2} + b^{2} + 2 a^{2} + c^{2} + a^{4} + 1) + ((ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 c^{2} + b^{2} + c^{4} + 1) \ge (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1)$$  $$ \implies  3((ab)^{2} + (ac)^{2} + (bc)^{2}) + 4(a^{2} + b^{2} + c^{2}) + (a^{4}+b^{4}+c^{4}) + 3  \ge (a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1)$$  Next, notice  $$(a^{2} + b^{2} + 1)(b^{2}+c^{2}+1)(c^{2} + a^{2} + 1) = ((ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 b^{2} + c^{2} + b^{4} + 1)(c^{2} + a^{2} + 1) $$ $$ = (abc)^{2} + a^{2}c^{4} + b^{2}c^{4} + (ac)^{2} + 2(bc)^{2} + c^{4} + b^{4}c^{2} + c^{2} + a^{4} b^{2} + a^{4}c^{2} + (abc)^{2} + a^{4}  + 2(ab)^{2} + (ac)^{2} + b^{4}a^{2} + a^{2} +  (ab)^{2} + (ac)^{2} + (bc)^{2} + a^{2} + 2 b^{2} + c^{2} + b^{4} + 1 $$ $$ = 2(abc)^{2} + 3(ac)^{2} + 3(bc)^{2} + 3(ab)^{2} + c^{4}a^{2} + c^{4} b^{2} + b^{4}a^{2} + b^{4} c^{2} + a^{4}b^{2} + a^{4} c^{2} + a^{4} + b^{4} + c^{4} + 2(a^{2} + b^{2} + c^{2}) + 1  $$  So we have  $$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $$ $$ \implies  2(a^{2} + b^{2} + c^{2}) +  3  \ge 2(abc)^{2}  + c^{4}a^{2} + c^{4} b^{2} + b^{4}a^{2} + b^{4} c^{2} + a^{4}b^{2} + a^{4} c^{2} + 1 $$ How find this $x^3-5x+10=2^y$ let $x,y$ is positive integer,and such $$x^3-5x+10=2^y$$ find all $x,y$.  since $$x=1\Longrightarrow 1^3-5+10=6$$ can't $$x=2,2^3-5\cdot 2+10=8=2^3$$ so $x=2,y=3$  $$x=3,LHS=27-15+10=22$$ $$x=4,LHS=64-20+10=54$$ $$x=5,LHS=125-25+10=110$$ $$x=6,LHS=216-30+10=236$$ $$\cdots$$  I find $$(x,y)=(2,3)$$  I only find $x\le 7$ this solution.  maybe this have other solution.and This problem is from Mathematical olympiad problems Thank you Material setings in properties window is missing I have added a sphere and I was able to add material and give it a color. Now when I add a second sphere (separate object), the material panel is just blank. What does (obj.length === +obj.length) compare? I am new to linux, but had a question. I am getting in the business of buying old computers, putting Linux on them, then donating them to students who don't have their own computer at home. I have gone through and installed Xubuntu on my system, installed/uninstalled all the software that I want/need, and now want to know if there is a way that I could make an ISO of my system, and put it onto ANOTHER computer, and still have all of my tweaks, and programs ready to go after the ISO has installed. That way I don't need to go through and spend an hour or two on every computer.   What programs would you recommend for creating an ISO like this?   Thanks, Tobin Why have a letter in a word when it’s silent in pronunciation, like the b in debt?  Can anyone please clarify my uncertainty here? No, actually I didn't, but that was a close call and I'm really curious how would one go about that one.  On my third or fourth visit to the Nether, I still didn't realize the risk, and didn't place marks that would help me get back to the origin (currently I like to use flint and iron to create big flaming arrows towards the exit, visible from afar.) I wandered past one hill, and then I couldn't locate the place I came from. I wisened up and started placing marks in form of torches, towers of netherrack with glowstones on top etc. The bunch of wood I had in my stash has proven invaluable as I ran out of steaks, and had to craft a bowl and start making mushroom soup. I realized the fastest way back would be to simply die, but since I had no clue where I was, that would mean losing my quite precious equipment, which cost me a lot of time and effort to gather and enchant, for that trip specifically. I also knew I had traveled rather far from the portal before starting placing marks, so the chances of finding it again by going in any random direction were rather slim.  By sheer luck I found one of the caverns I had explored before, and found my way back, but that was really a close call and I'd prefer to know any hints what to do in Nether if you're already lost (no Obsidian to build a new portal, not willing to die and forgot the direction to the exit.) Including the interaction but not the main effects in a model Is it ever valid to include a two-way interaction in a model without including the main effects?  What if your hypothesis is only about the interaction, do you still need to include the main effects? Short way for upper triangularization $a_1 a_1', a_2 a_2', ..., a_n a_n'$ is not a reduced modulo system $\mod p$. If $a_1, a_2, ..., a_n$ is a reduced residue system $\mod p$ and $a_1', a_2', ..., a_n'$ is another reduced residue system $\mod p$ then $a_1 a_1', a_2 a_2', ..., a_n a_n'$  is not a reduced modulo system $\mod p$.  Not able to show a counter to it. Help Needed. I have a simple skull model, to which I applied the subdivision modifier. For the most part everything works as expected, except I keep getting these weird sharp vertices and I can't seem to figure out how to flatten them.    I'm using Blender 2.8. Is this some kind of feature I can disable/enable for particular vertices? The distance between the sharp vertices and the gray outline differ.    Any suggestions please? Thank you!  EDIT: I also tried selecting as both - vertexes and edges and then applied Edge->Clear Sharp, but nothing changed. What is the value of lim$_{n\to \infty} a_n$ if $\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}$? Let $\{a_n\}$ be a sequence of real numbers such that $$\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}.$$  What is the value of $\lim_{n\to \infty} a_n$?