What is the purpose of using both past participle and past tense?
When is the present perfect tense used instead of the past tense?
Power Supply Capacity Formula How do I run .sh scripts? Whenever I open a .sh file, it opens it in gedit instead of the terminal. I can't find any option similar to Right Click → Open With → Other Application... → Terminal.  How do I open this file in the terminal? Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$. After working it out on a number line, I got: $\{4, 5, 6\}$.  As it stands, the expression contains the integers that do not belong to the set $B$ that cross into $C$. This would result in $4, 5, 6$. Number $7$ would not be included because of the soft brackets surrounding $C = (2, 7)$. Is this correct? Presently, how much information can a quantum computer store, in how many qubits? What restrictions are there and how does it vary across realizations (efficiency of data storage, ease of reading and writing, etc)? Auto-sort column Google Spreadsheet on incoming Google Form response How can I get the Google Spreadsheet to automatically order the incoming form responses alphabetically (2nd column)?   I know how to do this manually or by going in and editing a cell, but cannot get it to do this as an onevent for incoming response. Why $¬¬\bot \not\in PROP$? I'm reading Dalen's Logic and Structure.  He gives the definition of the set $PROP$:     Definition $\bf2.1.2$ The set $PROP$ of propositions is the smallest set $X$ with the properties       $\begin{array}{rl} \rm(i)&amp;p_i\in X(i\in N),\bot\in X,\\ \rm(ii)&amp;\varphi,\psi\in X\Rightarrow(\varphi\wedge\psi),(\varphi\vee\psi),(\varphi\to\psi),(\varphi\leftrightarrow\psi)\in X,\\ \rm(iii)&amp;\varphi\in X\Rightarrow(\neg\varphi)\in X.\\ \end{array}$   Then there are some examples:        And he says that $¬¬\bot \not\in PROP$, but I don't understand it. Isn't $¬¬  \bot=\bot$ due to the property of double negation? Considering this is true, $\bot\in PROP$. Of course, in this question, I'm pressuposing some kind of evaluation, that $¬¬ \bot$ becomes $\bot$ due to the law of the double negation, but perhaps it should be hold in an unevaluated form.  Ex:. $1+1=2$ because we presupose the $1$ merges with $1$ and then becomes two. If the merge (evaluation) does not happen, then I guess:  $$1+1=1+1$$ $$2=2$$ $$2\neq 1+1$$ $$1+1\neq 2$$  Perhaps it's something like that, I took the idea from Mathematica. Sometimes it does treats things as different in the absence of full evaluation. What is a word/idiom for 'unable to decide'? Let's say I have an important decision to make and I can't decide between two competing things (like break up with a girl or not break up with her). What would be a word/idiom to express that? What is an English adjective that means "able to learn new things quickly"? I want to install the latest Firefox on my Ubuntu (64bit) box.  What is the best way to do this? Is there a specific update site or should I download the binaries manually? If doing manually, in which directory should I put the files? In my home directory, or is there a better place? How can I display keyboard shortcuts as I press them? Regarding the `book`, `report`, and `article` document classes: what are the main differences? $\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists? Let $F$ be a field. $(x-c)|(p(x)-p(c))$.   So if $x-c|p(x)=q(x)-\frac{r}{x-c}$ so for $x-c|p(x)-p(c)=s(x-c)-\frac{r}{x-c}$. Is that correct? Or is there a different way to go about proving this? I have proved that $x-c|p(x)$ has a remainder of $p(c)$ so It wuld make sense that $p(x)-p(c)$ would be $x-c$. I unlocked the 'Files' button/icon from my unity launcher and now it disappearead and I cannot restore it or get it back I unlocked the 'Files' button for the Ubuntu file manager from the unity launcher and I cannot get it back.   When I run the file manager from the dash, the icon does not appear on the launcher like it does for all other applications while they are running. I wanted to have an empty launcher when no applications are running, and just have the icons of those I am actively using there.  Any idea why I don't see it in the launcher when its running or how to lock it back? What resolution should a large format artwork for print be? Finding critical points (extrema) directly without using eigenvalues If we have a function $f: \mathbb R^3\rightarrow \mathbb R$ of the form:  $$f(x)=(a_1x_1^2+a_2x_2^2+a_3x_3^2)e^{-x_1^2-x_2^2-x_3^2}$$  where $a_1&gt;a_2&gt;a_3&gt;0$.   We can find the critical points by:  $$\frac{\partial f}{\partial x_1} =2x_1e^{-x_1^2-x_2^2-x_3^2}(a_1-a_1x_1^2-a_2x_2^2-a_3x_3^2)=0$$  And solving symmetrically for $x_2$ and $x_3$. We get critical points: $(0,0,0) , (\pm 1,0,0) , (0,\pm 1, 0) , (0,0,\pm 1)$   We could determine the nature of them by looking at the eigenvalues of the Hessian, but is there a way to just analyse it directly? Obviously $(0,0,0)$ is a strict global minimum, but I can't quite see that the other points are. Any pointers/hints would be appreciated. Is Iron Man stronger than the Hulk? In Avengers: Endgame, when Hulk initially uses the new Infinity Gauntlet, it takes a tremendous effort from him (in addition to almost burning his entire arm), in order to snap his fingers and restore the world as we knew it. Yet at the end of the movie, when Iron Man uses the Gauntlet, it seems very easy for him to snap his fingers.  How was Tony able to wield the stones with such ease when Hulk was clearly struggling with it? I process all my photos to black and white. Although I use a polariser where possible, I often find myself wanting to drop the luminance of the sky further which I do using a Black and White adjustment layer (in Photoshop). This usually results in a lighter halo following the line of the horizon, where the blues of the sky meet whatever the colour of the land is.  My current solution to this problem is to run a brush along this margin with a colour set to the same as the sky and the blend-mode set to Darken. This effectively paints in the lighter band with the sky colour while not laying down the colour on top of the darker horizon. Whilst this is effective, it is very time consuming.  Is there a better approach to dealing with these halos?  Here is a video that illustrated the Darken solution that I mention: How can I show that if the second fundamental form of a surface is identically equal to zero, then the surface is a plane? This is my question:  Let P be a plane considered as a surface in 3-space. Show that its second fundamental form is zero. Conversely, show that if the second fundamental form of a surface is identically zero then the surface is a plane.  So far I have that the general equation of the plane is $$ax+by+cz+d=0.$$ Then $$M(u,v)=(u,v,\alpha u + \beta v + \gamma),$$ where $a,b,c,d,\alpha,\beta, \gamma$ are all constants and $c\not=0$. Then $M_u=(1,0,\alpha)$ and $M_v=(0,1,\beta)$. I know that $\vec{n} =\frac{M_u \times M_v}{|M_u \times M_v|}$ which gives $$ \vec{n}=\frac{(-\alpha,-\beta, 1)}{\sqrt{\alpha^2+\beta^2+1}}.$$ Hence, the unit norm is a constant. $$ M_{uu}=M_{uv}=M_{vv}=0$$ Hence $l=m=n=0$, so the second fundamental form is $$ ldu^2+mdudv+ndv^2=0.$$  Now I need to show the converse, but I don't know how. Please help :) After upgrading to Firefox 57 Quantum many website have rendering issues, such as empty frames, missing text or fonts, etc. I use Kubuntu 16.04 64 bit.  So far, I've tried:   Restarting Firefox in safe mode Disabling "hardware acceleration"   Wiping out my profile Purging Firefox and reinstalling Running Firefox from a clean user account   But nothing helped so far.  Any tips on how to solve this are much appreciated