We know that $-1\le \cos x\le1$ so we if we multiply 3 so we get $-3\le 3\cos x\le 3$ and we also know that $-1\le \sin x\le 1$ and and again we multiply 4 we get $-4\le 4\sin x\le 4$ and we can add these two inequality we get $-7\le 3\cos x - 4\sin x\le 7$ but how in the above inequality is forming i m not able to understand at all.
$$|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$$   I have tried: $$|a\sin x+b \cos x|\leq |a+b|\leq \sqrt{a^2+b^2}$$  enough to prove: $$|a+b|\leq \sqrt{a^2+b^2}$$  But I can find how to continue from here
I want to build a flow to trigger an email when a date in one of the fields is nearing. I have a field named Payment due date. is it possible to trigger an email 2 days prior to the Payment due date. So that I don't miss the payment due date and payment is not delayed. Any kind of assistance is appreciated. Thank you very much in advance! Viruses at this period of time do not fit the current definition of life.   Much of the reasoning behind this is that we currently believe that all life must be made up of cells.  Also, many biologist/scientists say that viruses are not living because all they are is just chemicals carrying out their predefined chemistry.   Has anyone every considered the fact that cells, the supposed building blocks of life, themselves simply only carry out predefined chemical actions? All actions cells carry out are chemically driven, not consciously or spiritually driven. Cells do not make choices, they follow chemical directions present in their DNA and RNA. Viruses act very similarly, following the action transcribed in their DNA or RNA.   How can we really even draw a defined line of what life is? Why is the camera tilting around the z axis when I only specified x and y? My goal is to program a camera to point towards the mouse cursor. I attached the following script to the Main Camera.   using UnityEngine; using System.Collections;  public class CameraController : MonoBehaviour {      public float sensitivity;      // Update is called once per frame     void Update () {         transform.Rotate (Input.GetAxis ("Mouse Y") * -1 * sensitivity, Input.GetAxis ("Mouse X") * sensitivity, 0);     } }   I "told" the camera to rotate around the x and y axes. Whenever it does this, the camera tilts sideways. When I checked the rotation of Main Camera, I saw that the z rotation had changed. Why is it rotating around the z axis when I left it at 0? I have a realm with a few of my friends and i want to play the creeper primed sound at him but i am afraid he will see the command and ignore it  Im using: /playsound minecraft:entity.creeper.primed block  Version: 1.14.2 Title of a book telling about people teleported to a hostile planet while in deep meditation I read it sometime in the 90's but it seemed at least 15 years old at that time. The title might be containing something with 'wolves' or 'wilderness'.  Alert - Spoilers below      The book tells of some (I think) earth cult that dictates the practice of meditation. This cult is somewhat of a scam as When reaching the top level of meditation the meditator is either teleported or his consciousness abducted (I can't remember..) to be used as a calculation machine by the abductors.   Any references would be greatly appreciated. Should I use  tag for icons instead of ? Does a wireless-N (802.11n) network have poor performance when in b/g "mixed" mode? It seems to be an "old" wives tale that, when using a wireless-N router in "mixed mode" to support legacy 802.11b or 802.11g devices, the performance of 802.11n clients will suffer.      claim that when running in mixed-mode, all (some?) N clients run at G speeds.   make the same claim, but say it only happens when a G client is connected.    say N clients run faster, but still run about 30% slower than if the router were in N-only mode, even if there are no legacy B/G clients connected.    claim there is no speed drop for N clients when running on a mixed-mode network.  They say the only issue is that overall network throughput will be lower, because only one client can be transmitting at any time, so some of that transmission time must be shared with the legacy B/G clients running at lower speeds, reducing the overall throughput from what it would be if there were only N clients connected.    So, which is it?  Will running in mixed-mode slow down my network, even if there are no B/G clients?  If I'm running N, will having another client connected at B/G slow me down substantially vs. if they were running N? I would like to open all chapters of my PDF ebooks in the same window but neither evince nor okular seems to be capable of doing that (at least not out-of-the-box).  Is there a way to work this out? Where are the proprietary NVIDIA drivers in 16.04? The proprietary NVIDIA drivers "disappeared" with my latest update:    The option of "Proprietary drivers for devices" is correctly set under the "Ubuntu Software" tab. I have the graphics-driver PPA (ppa:graphics-drivers/ppa) correctly added to my sources.  Any ideas on how to bring the proprietary drivers back?  PS1: I need them because some of the games I play under wine don't work without them, for whatever reason.  PS2: Also, this feels like it should have a straightforward answer, but I've been looking online for a while without luck. How do I get the number of days between two dates in JavaScript? How do I get the number of days between two dates in JavaScript? For example, given two dates in input boxes:  &lt;input id="first" value="1/1/2000"/&gt; &lt;input id="second" value="1/1/2001"/&gt;  &lt;script&gt;   alert(datediff("day", first, second)); // what goes here? &lt;/script&gt; Jewish Law prohibits the  However, butter, a milk product, is a kitchen staple for most cooked emulsions (eg. pan-sauces, sauces béchamels, or roux-based sauces). While I use appropriate cooking fats for making non-dairy versions for meat dishes, this frequently doesn't work.  What is a non-dairy fat which may be used to as an emulsifier or roux ingredient? Can I use Facebook's fb:friend-selector in an iframe? Finitely generated monoids- axiomatization- compactness theorem. Let $V$ be spherically symmetric and $W$ i.i.d. Gaussian. Then $E[V|V+W=t]=g(\|t\|)$ A random vector $V \in \mathbb{R}^n$ is said to be spherically symmetric. If for every orthogonal matrix  $A$   the distribution of $AV$ is the same as the distribution of $V$.   My question: Let $W$ be  i.i.d. zero mean Gaussian random variable.     Can we show that  for a spherically symmetric $V$ the conditional expectation  \begin{align} E[V|V+W=t]=   g(\|t\|).  \end{align}  That is the conditional expectation is only a function of the magnitude.   My attempt:  \begin{align} E[V|V+W=t]= \int  V  \frac{f_W(t-v)}{f_{V+W}(t)} dP_V(v)= \frac{\int  v  f_W(t-v) dP_V(v)}{f_{V+W}(t)}= \frac{E[ V  f_W(t-V) ]}{f_{V+W}(t)} \end{align}  Therefore, we can show that the two functions in the above ratio only depend on $\|t\|$.   Observe that we can write $t= \|t\| u_t$  where $u_t$ is a unit vector. Then, for any orthogonal matrix $A$ \begin{align} f_{V+W}(t)=f_{V+W}(\|t\|, u_t)&amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-AV  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|tA^{-1}-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t A^T-V  \|^2}{2}} ]\\ &amp;= f_{V+W}(tA^T)\\ &amp;= f_{V+W}(\|t\|,  u_t A^T) \end{align}  Since, $A$ was arbitrary  we have that $f_{V+W}(t)=h(\|t\|)$(i.e., only depends on the magnitute).  Now I am not sure how to show that $E[ V  f_W(t-V) ]$ only depends on $\|t\|$? How long do seasons last? In the Kittens Game, how long (in real life minutes) do seasons last? jQuery find events handlers registered with an object Product of path connected spaces is path connected I have a directory that contains the following:  x.pdf y.zip z.mp3 a.pdf   I want to delete all files apart from x.pdf and a.pdf. How do I do this from the terminal? There are no subdirectories so no need for any recursion. Trigger Task Scheduler in Windows 7 when computer wakes up from sleep/hibernate I don't want task scheduler or whatever to wake the computer, but when I open the laptop back up and the machine wakes I'd like that to be the trigger that task scheduler or something uses to run an app. I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position and momentum of the atom. We do know that Heisenberg uncertainty principle holds for microscopic particles in motion. But what then is wrong to consider that all molecular motion ceases at absolute zero? In other words, does the uncertainty principle not hold when there is no motion?  Need some help!