While reading about the motion of a car on a level road, I read that static friction provides centripetal acceleration? Please explain as simple as possible.
When an object is moving in a circle, won't the frictional force oppose it's motion? And if the velocity is always tangential to the path, there is no component of it towards the center, so there is no component of friction towards the center (since the frictional force is antiparallel). So how can friction be a centripetal force, like in the case of a car rounding a corner?
Is it possible to load a TikZ library locally? If $A = \tan6^{\circ} \tan42^{\circ},~~B = \cot 66^{\circ} \cot78^{\circ}$ find the relation between $A$ and $B$ My trigonometric problem is:     If $A = \tan6^{\circ} \tan42^{\circ}$ B = cot$66^{\circ} \cot78^{\circ}$ find the relation between $A$ and $B$.    Working :   $$B = \cot 66^{\circ} \cot78^{\circ} = 1- \frac{\tan24^{\circ}+\tan18^{\circ}}{\tan42^{\circ}}$$  $$A= \tan6^{\circ} \tan42^{\circ} = 1- \frac{\tan6^{\circ} +\tan42^{\circ}}{\tan48^{\circ}}$$  but it seems  this is the wrong way of doing this...please suggest. Thanks! Why don't cameras show an "accurate" histogram? Why don't cameras show a histogram based on the RAW data rather than on the JPG preview?  I know that a RAW file is not a viewable image and can't be displayed without applying curves and defining how the image should be interpreted. But why don't cameras show a histogram that accurately shows how much latitude I have in the image?  For example when shooting high contrast scenes (for example at sunrise) I know that I can overexpose the highlights to a certain extent to retain detail in the shadows and bring those areas that appear clipped in the JPG preview back in post.  But every camera I've worked with shows me the histogram based on the JPG preview and the picture style and tells me that those areas are clipped.   Is there no way of seeing the actual dynamic range captured by the sensor? Why does no camera manufacturer implement that? It shouldn't be too difficult. Which is correct?        She was told that it was against the law to steal.      Or        She was told that it is against the law to steal.        Background information: The original context is that I was relating an incident via email, where my colleague told a customer that some of our actions were part of the organisation's policy. The policy is still valid, but the statement I used to relate the incident in my email went like this:    "Mr Jay was informed that it was our policy to do this."   And I received feedback that it should go like this instead:    "Mr Jay was informed that it is our policy to do this." Regulatory bodies and authoritative dictionaries for English Some languages have a "regulatory body" issuing recommendations and guidelines regarding the use of that language.  For example in the case of Spanish it's the  whose status is recognised in all Spanish-speaking countries. The Academy, among other things, publishes a dictionary (""), in print and , which is usually given a lot of prestige (but is not without , of course).  Are there any such authorative—or at least influential—institution(s) or publication(s) for the English language? Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$ How do I scan for Wireless Access Points? I want to clear all previous commands from the history of my server. I used history -c and it seems all things are cleared but when I ssh to the server, all the commands are still there.  How can I clear them permanently? I've found some questions and those two badges "Epic" and "Legendary" regarding the "daily reputation cap". What is it and how can I hit it? How to get hardware specs of Android device? How can I find information on the hardware of my Android device like processor architecture, RAM, etc? Alt Tags Missing from code I've been looking at the python code loging of Blender. But in there things get loged as mouse clicks.  What i like to do is combine a few images into a larger one using compositor, but i need control over compositor by python script. The problem seams to me that it is a bit hard to "spawn" a few nodes, set their values and connect them.  I need an micture of:  image, scale, source image location, mix nodes, output nodes  I have no Code samples other then the log of blender python which in this case is of no big help. jQuery scrolltop firefox not working How can I stop using beta iOS on my iPhone? I'm currently on the beta program on my iPhone. How can I stop using the beta versions and go back to the newest version of iOS (non-beta)? When I have my external monitor hooked up, I access it by mousing off the left hand side of my Macbook display. Can I switch this so that I can access the external by mousing off to the right of My Macbook display?   The reason I ask, is my monitor is on the right side of my macbook, and it's unintuitive to mouse left to get to a screen on the right. $$\int_{-\infty}^{\infty} \frac{\cos(αx)}{(x^2+1)(x^2+4)} \mathrm dx. $$  I am not sure how to solve this question. Can anyone help me to approach this problem. Thanks. Comment submission broken for comments that end with @username How to relate combinatorial proof to bipartite graphs? The question is - Let $k \geq 1$ be an integer and consider a sequence $n_1,n_2,\cdots,n_k$ of positive integers. Use a combinatorial proof to show that  $\binom{n_1}{2} + \binom{n_2}{2} +\cdots+ \binom{n_k}{2} \leq \binom{n_1+n_2+\cdots+n_k}{2}$  How can i prove this without using induction?  Additionally, For each $i$ with $1 \leq i \leq k$,consider the complete graph on $n_i$ vertices. How many edges does this graph have?  I thought of making graphs and figuring out a relation but still wasnt able to. Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is:  Let's say I receive two envelopes. Both envelopes have this written on them:     Hello! Open this letter...   If the paper inside is red, then other envelope has blue paper.   If the paper inside is blue, then other envelope has red paper.   So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper.  Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope?  In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct?  Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue?  In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes?  In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? Would someone give a thorough explanation of 1.14 Minecraft's /data modify? Okay, so I've been searching all over the internet for an explanation of data modify ever since I heard Sethbling passively mention it in one of his videos. The only  thing I could find on it was the wiki and the update log for the 1.14 snapshot. So, I checked these, and they hardly explained it at all. I can get /data modify block 123 20 123... and that's as far as I get.  Minecraft wiki does not at all define clearly what  is (the thing meant to go after coords), nor does it specify what each operation does to what. Operations include (without explanation, and excluding set (which it does explain)): append, insert, merge, and prepend. Then, it has from|value as the next option, which aren't explained either. After this, it just has block/entity and coords/id. So, I know the format (mostly), but I haven't the slightest idea what any of it means. And nothing I've seen on the internet even mentions the command save for Minecraft wiki itself.  Please explain if you know what data modify is. Thanks!