I used more or less non stop my new Macbook Pro M1 for about 7 hours and noticed that at the end of the day the battery was already at 14% despite the fact it was fully charged when I started working. While working I was using a second monitor, a wired keyboard, a wireless mouse and a USB hub. The programs I actively used that day were Safari, Chrome, Sublime Text and iTerm2. Safari, Chrome and Sublime were constantly using more or less 500 MB of RAM. Apple said the new M1 had an autonomy of 20 hours so I'm a bit surprised that after only 7 hours of work it is already at 14%. Is this suppose to be normal? Is it the same for everyone out there? Thank you.
I'm new to the world of Apple, I bought a new Macbook Pro, mid-2020, Intel i7, 16GB RAM. I'm a developer, I run apps like VS Code, Sublime Text, Slack, Chrome (Multiple Windows), I play videos/songs in the background. I have been keeping a track of the energy consumption on my Mac, and it only runs for 4 hours. I have reset my SMC after I upgraded to Big Sur. Is 4 hours normal? or should I go to the service center? Update on 3 Feb 2021: I submitted my Mac to the Apple service center they said they conducted a few tests and the conclusion was that the battery is fine (I don't know what type of test they did). So I guess I'll be using it on AC Update on 12 Feb 2021: Took it to the service center, they didn't find any issues so I started using Safari for work and my battery has improved by 1 hour on Average.
How can analytically be  the ?   I found some extremely synthetic equations which from the  (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's laws, but even if it seemed to be a nice procedure they were too much incomplete. Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$ Let $n$ be a positive natural number, $n\ge 2$. Then $\displaystyle\sum_{k=1}^n \frac{1}{k^2} \lt 2 - \frac{1}{n}.$   The basis step was easy but could someone give me a hint in the right direction as to how to do the induction step?  I tried this:  $\displaystyle\sum_{k=1}^k \frac{1}{k^2} + \frac{1}{(k + 1)^2} \lt 2 - \frac{1}{k + 1}$  But it's getting me nowhere or I am doing something wrong. I am no expert so a clear explanation would be appreciated. Thanks. Calculating half derivative of $x$ using Cauchy's repeated integral formula As far as I know, Cauchy's repeated integral formula is defined as: $$(I^nf)(t)=\frac{1}{\Gamma(n)}\int_a^x (x-t)^{n-1}\space f(t)\space\space dt,\space\space n\notin Z_{\le 0}$$  I know that Gamma function is not defined for negative integers and $0$. I also know that differentiation and integration are inverse operators so I thought of finding $\frac{-1}{2}$th antiderivative of $f(x)=x$ so that I can find the half derivative of $x$. However it seems that it does not work. What is the problem with this? Am I missing something or is it not possible? I know some other ways of finding half derivative of $x$, so what I am asking is the problem about what I tried.  My attempt: $$\frac{1}{\Gamma\left(-\frac{1}{2}\right)} \int^x_0(x-t)^{-\frac{3}{2}}\space t\space dt=\frac{x}{2\sqrt{\pi}}\int^0_x u^{-\frac{3}{2}}\space (x-u)\space du$$  This definite integral is divergent and so I cannot get to a result. Understanding the Basic Context of Trusted Hosts I got the trusted host settings error.      The trusted_host_patterns setting is not configured in settings.php. This can lead to security vulnerabilities. It is highly recommended that you configure this. See Protecting against HTTP HOST Header attacks for more information.    I read the  but I'm not understanding some of the basic context.   Are the "trusted hosts" me and other administrators who want to be able to administer the site remotely?  If so, would I add my PC's domain to the trusted host list? Why does (0 < 5 < 3) return true? I am traveling from Chennai to Atlanta. M first flight is to Frankfurt reaches at 8 30 AM. My second flight is scheduled at 10 45 AM.   Will the two hours transit time enough for boarding my second flight.  What should be my do's and dont's?  Update  Its more than enough. I was able to make it without any tension. What is the difference between a field and a property? I am trying to find ways to quantitatively describe the shapes of various polygons. For my project, these polygons represent lakes, rivers, lagoons, and parks. So they can be almost any shape. One easy metric is to calculate perimeter vs. area, which is at best an only slightly useful metric. But I would also very much like to be able to say something about the 'roundness' of a polygon. Or how 'compact' the shape is on a map.  The only way I can think of doing this easily is to calculate the area of each polygon in relation to a bounding box for that polygon (which I already have). But this seems like a poor solution.  So now I am thinking of something more like this - take the centroid of the polygon, add on a series of buffers of increasing areas (say 50%, 100%, 150%), then compare how much overlap there is between each buffer and the original polygon. A perfect circle will have perfect overlap at 100%, and I can use the 50% and 150% buffers to judge how much and in what way each polygon differs.  But even that feels cumbersome, and like a poor workaround for what somebody else has probably already figured out far better.  For reference, at a minimum I will need to be able to look at the resulting indices for the shape of various polygons, and be able to make an educated guess as to their source (River? Reservoir with dendritic shape? Lake/Lagoon? Park?) Can a 20V 4.51A power supply be used with a computer that requires a 19V 3.42A power supply? `/usr/bin/cd` is not working in mac terminal Why directory with large amounts of entries does not shrink in size after entries are removed? How to retrieve a module's path? Possible Duplicate:          I have tried changing my proxy settings in a terminal as:  export HTTP_PROXY=http://10.1.3.1:8080   and  export http_proxy=http://10.1.3.1:8080   but when I try to install a new package or update apt-get, apt-get starts displaying messages from which it seems it is trying to connect to a previously set proxy:  sudo apt-get update   0% [Connecting to 10.1.2.2 (10.1.2.2)] [Connecting to 10.1.2.2 (10.1.2.2)   I have tried setting the proxy via bashrc file but that din work either. As far as I remember 10.1.2.2 was set using GNOME GUI but I don't have access to the GUI right now so I am trying to set it from terminal. Let $f$ be a nonconstant element of ring $\mathbb Z[x]$. Prove that $\langle f \rangle$ is not maximal in $\mathbb Z[x]$.   Let us assume $\langle f \rangle$ is maximal. Then $\mathbb Z[x] / \langle f \rangle$ would be a field. Let $a \in \mathbb{Z}$. Then $a + \langle f \rangle$ is a nonzero element of this field, hence a unit. Let $g + \langle f \rangle$ be its inverse. Then $a g - 1 \in \langle f \rangle$, hence $ag(x)-1 = f(x)h(x)$ for some $h \in Z[x]$, hence $ag(0) + f(0)h(0) = 1$, thus $(a,f(0))=1$ for all $a \in \Bbb Z$, contradiction, hence the proof.  Is my argument correct? Is there any other method? How do I make my rim brakes stop squealing? My rear rim brakes are squeaking loudly. I don't know what the problem is, but I am sure it has nothing to do with rain because it happens all the time even if it is dry.  Anybody have an idea what could be problem and how to solve it? It makes the rear brakes kind of useless, because if I use them I will scare the people or drivers around me. I own a Panasonic DMC-G81 (same as G80/G85) with in-body Image Stabilization.  When turned on everything is just fine, but when turned off, the sensor is wobbling around in the body. When no lens attached, it's clearly visible moving about 1/2 cm in the body. I didn't find anything about it in the internet. Shouldn't the sensor be in a kind of parking position, should I worry about the sensor ?  I'm not sure if that is the usual behavior, maybe someone with the same or similar body can have a look. Google AdSense Policy Non Compliant "Site Behaviour: Navigation" I saw a code change at work, where the mode values were changed from 777 to 0777 to make nfs setattr work. What is the difference in the 2 values? Subfields of finite fields Any way to embed Pygame in webpages?