Why does an abstract class in Java have a constructor?  What is it constructing, as we can't instantiate an abstract class?  Any thoughts?
Can an abstract class have a constructor?  If so, how can it be used and for what purposes?
Maximum power transfer and Thevenin I am trying to find the thevenin resistance value and the Vth for maximum power transfer. I have tried to find Rth by calculating R3 and R2 as parallel resistance and same for R4 and R5 and then adding them with R1 but I am not sure if I have done it the right way. For Vth I have tried using KVL but I think I have calculated wrong current values using current divider rule. I calculated the total current by diving V1 and R1. I hope someone can help. I have attached the picture of the circuit. I've recently been trying to introduce myself to formal logic, and I've hit a stumbling point:  In the text I'm reading, a valid argument is defined as "an argument in which it is impossible for the premises to be true and at the same time the conclusion false."  The text then later prompts me to declare whether it's possible for an argument to be valid with a contradiction for a conclusion. The answer key then claims that yes, it is in fact possible, but offers no further explanation. I'm also supposed to create an example.  I just can't wrap my head around this one.  Here's the example I've worked up, is this a valid argument?   If grass is green then it is raining.  If water is wet then it is not raining.  Therefore: It is raining and not raining.   My head hurts. Does the curvature of spacetime theory assume gravity? Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form &quot;gravity wells.&quot; Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing? If the quotient group $G/N$ be isomorphic to $G_2$, is $G$ isomorphic to $G_1\times G_2$ where $N$ is isomorphic to $G_1$? Algorithm faster than Newton's for calculating $\sqrt{2}$ I am using ArcMap 10.2 and want to represent a layer in a rotated dataframe with chart (graph) symbology. The problem is that the charts do not rotate with the dataframe:     I thought I could convert to graphics and rotate each chart individually, but   that is very tedious I don't find an option to convert a layer to graphics, works for the legend but not for the actual layer symbology Source Code Margin Comments In the paper "Beautiful Code Compelling Evidence", by J.R. Heard -- Code is formated in a particular way which includes margin comments. I am looking for a way to do this as I think it is a very clear way to comment comment code in a literate programming style. Detecting unused packages in LaTeX document I have quite a bad habit of copy-and-pasting my packages from one LaTeX document to another. Is there any way we can detect unused packages (i.e. \usepackage commands) so that they can be removed from the LaTeX document? How can I use a command to delete all files in Downloads whose dates added are greater than 1 year? I am using a Mac. How can I use a command to delete all files in ~/Downloads whose dates added are greater than 1 year? Why does:   $$ \sum_{k=0}^{n} k \binom nk p^k (1-p)^{n-k} = np $$ ? Taking the derivative of:   $$ \sum_{k=0}^{n}  \binom nk p^k (1-p)^{n-k} = (1 + [1-P])^n = 1 $$   does not seem useful, since you would get zero. And induction hasn't yet worked for me, since – during the inductive step – I am unable to prove that:   $$ \sum_{k=0}^{n+1} k \binom {n+1}{k} p^k (1-p)^{n+1-k} = (n+1)p  $$   assuming that:   $$ \sum_{k=0}^{n} k \binom {n}{k} p^k (1-p)^{n-k} = np  $$ Drupal failed after update Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$ Following my  the book then asks      Use this to determine when the field extension  $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$  is biquadratic (where $a,b\in\mathbb{Q}$)   "this" means what proved in the linked post.  My thoughts: First, I don't know what to say when $a^2-b$ is not a square. When $a^2-b$ is a square I think that the extension is of degree $2$ if $a=b$, this leaves the case $a\neq b$ which I am also having problems with and I don't know what to do (I have some cases like if $m,n$ are different primes then the degree of the extension is $4$, but I don't have something that is general)  Can someone please help my do this exercice  ? ID for Contact portion of Person Account Is it possible to get the ID of a Contact which is part of a Person Account?  I have a custom object which has a custom field referencing the Person Account, though it seems to be referencing the Contact directly. I have created a button which I am using to pass the ID into a Visualforce Page.  With the Insert Field drop-down on the create/edit button page I can put in {!Account.Id} or {!Contact.Id} but neither of these work. The Account ID is placed in the URL but is not the correct ID and the Contact ID is blank, which I assume is because the button is on a Person Account page and not a Contact Page. Word for feeling conflicting emotions simultaneously Run cURL commands from Windows console Is there a way to install cURL in windows in order to run cURL commands from the command prompt? Para 5, , by      If the Lord would show thee but this one   thing, -- that to use "thee" and "thou" to a particular person is   proper language, and Scripture language; and that to say "you," is   improper, and arose from pride, and nourisheth pride, and so is of the   world, and not of the Father; and thou should bow thy spirit to him in   this one thing, thou little thinkest what a work it would make within thee, and how strongly the spirit of darkness would fight against thy   subjection thereto. The Lord lead thee as he seeth good, and give thee   faithfully to follow; for else, if the Lord should lead in any thing,   and thou not follow in that thing, his Spirit would be grieved and   vexed thereby, and thy heart in danger of being hardened by the   deceitfulness of sin.   What is the Lord giving thee faithfully to follow?   The grey claims that the reader thinks little of the significance of stressing 'thee' and 'thou' over 'you'. So I'd guess that the Lord is giving 'thee' this caution? If I'm right, why is there no direct object in the bolded? I recognise grammatical differences in the 1600s, but still want to learn. Non-numerical citation mark like [Str91] [Samar] [Tro77] Are PDO prepared statements sufficient to prevent SQL injection? Let's say I have code like this:  $dbh = new PDO("blahblah");  $stmt = $dbh-&gt;prepare('SELECT * FROM users where username = :username'); $stmt-&gt;execute( array(':username' =&gt; $_REQUEST['username']) );   The PDO documentation says:     The parameters to prepared statements don't need to be quoted; the driver handles it for you.   Is that truly all I need to do to avoid SQL injections?  Is it really that easy?  You can assume MySQL if it makes a difference.  Also, I'm really only curious about the use of prepared statements against SQL injection.  In this context, I don't care about XSS or other possible vulnerabilities. Show that $\phi(n)=\frac{n}{2}$ if and only if $n=2^k$ for some positive integer k. I think I have it figured and would like to see if I am on the right track. Thank you. If $X$ is a Banach space, and $T:X \to X$ is a bounded linear operator with norm &lt; $1$, then $I-T$ has a bounded inverse defined by $(I-T)^{-1} = \sum_{n=0}^\infty T^n$.   Thinking in terms of a converse, if $T$ is any bounded linear operator defined on $X$, then does the existence of a bounded inverse $S=(I-T)^{-1}$ imply that $S$ can be represented as $S=\sum_{n=0}^\infty T^n$?