Filling between three curves

I have been trying to fill the area between the three curves on the graph below (area between the points a, b, and c), but have had no successful result so far. I kept a simple filling command to ask how I can manipulate it in a way that I can fill the area between these points. Any help would be greatly appreciated. Here is my command:

Plot[{31.25/x, 11.1803 - x, Sqrt[100 - x^2]/2, Sqrt[100 - 4 x^2]}, {x, 0, 12}, PlotRange -> {0, 12}, Filling -> {2 -> {{3}, {None, Gray}}}, Epilog -> {Text[Style[TraditionalForm[a], Black, FontSize -> 12], {2.23607, 8.94}], Text[Style[TraditionalForm[b], Black, FontSize -> 12], {4.45, 4.45}],Text[Style[TraditionalForm[c], Black, FontSize -> 12], {8.94, 2.23607}]}] 

Capture User Email Address When Filling Out Form

We have a snippet of code that was provided by an optimization platform company we use that provides a real-time personalization to our website.

The user will fill out a form (Gravity Forms) and then be sent to one of our WordPress Thank You pages.

This code will be added to the Thank You page, but needs to be updated to capture the user’s email address once the Gravity Form has been completed:

<img src="//dasd65f4ds3e25u.cloudfront.net/pc/p5w6g1jy/?e=[customer's email address]" id="__tms_pc" height="1" width="1" /> 

Would you be able to help me replace the "customer’s email address" text with the appropriate code that will be able to capture each user’s email address when they fill out the form?

Is there a PHP string of code that could be used to replace the "customer’s email address" text? I have not been able to find a concrete answer while doing some research for this.

News terminals digital television installation in filling stations

https://www.google.com/search?q=news+terminals+on+digital+television+screens&oq=&aqs=chrome.1.35i39l4j46.-1j0j7&client=ms-android-lava&sourceid=chrome-mobile&ie=UTF-8

https://www.google.com/search?q=filling+station&oq=filling&aqs=chrome.0.69i59j69i57j0j69i61j69i60.2342j0j9&client=ms-android-lava&sourceid=chrome-mobile&ie=UTF-8

Do you recommend News terminals digital television installed in filling stations?

Using an example to comprehend why “safely” erasing a drive yields better results than filling it up with meaningless data

A hypothetical 1GB USB stick is full of sensitive documents/images/etc. and it is not encrypted.

The owner wishes to discard it and is aware of having to safely erase it first.

There are several tools and utilities to do this. Some can be configured to do it “faster yet less safely”, others do it “slower but more safely”.

As opposed to have it erased using all the different ways known to do this, the owner chooses to simply drag all the current items to the recycle bin and then paste one 1GB (~2-hour) black screen movie file to the USB stick.

Again, no fancy erase utilities are used. The USB stick is then discarded.

If it falls into the wrong hands, can any of the sensitive files (that filled the stick before the movie file was pasted) be retrieved?

(1) If no, why do complex hard drive erase utilities exist? Some of them feature “safe” erase procedures that take houuurs, when simply filling a soon to be discarded HD with meaningless files, can do the job?

(2) If yes, how can 2GB (movie file + sensitive files) co-exist in a 1GB stick? Seems to me like the only logical explanation is (a) the movie file was in fact less than 1GB, (b) the USB stick was secretly larger than 1GB as stated, or (c) the movie file was copy-pasted only partially and the owner did not notice.

Filling a hole in an image in O(nlogn)

I have a grayscale image (given by a float matrix with values between [0, 1]) with a hole in it (a cluster of pixels/cells with values of -1).

Definitions:

The boundary of the hole as all the cells that are 4-connected to a hole pixel (a pixel with -1 value) (you can read more about pixel connectivity here: https://en.wikipedia.org/wiki/Pixel_connectivity).

I(v) is the color of the pixel v.

I need the fill the hole using this formula:

Denote the boundary with B. So for each u – hole pixel:

\begin{equation} I(u) = \frac{\Sigma_v{_\in}_B w(u,v) * I(v))}{\Sigma_v{_\in}_B w(u,v)} \end{equation} Where w is some arbitrary weighting function (for example using euclidean distance)

\begin{equation} w(v,u) = \frac{1}{|| u – v||} \end{equation} Denote the number of hole pixels with n, the naive solution will be O(n^2), since for each hole pixel, we sum over all boundary pixels (and the upper bound for the amount of boundary pixels is 4n, of course).

I was told a solution could be achieved in O(nlogn), but I couldn’t think of anything even close to that.

I thought of doing some bitwise operations, but I reached a dead end. I also tried reusing computations, but I couldn’t find any.

Moreover, the way I see it, there’s no avoiding calculating w(u,v) for the n^2 pairs of hole/boundary pixels – which is already more than O(nlogn).

What am I missing? Could you point me at the right direction?

Thanks

Is filling up plan cache causes a decrease in space allocated for data cache?

SQL Server uses allocated server memory for different kind of purposes. Two of them are plan cache and data cache which are used to store execution plans and actual data correspondingly.

My question: Do these two caches have different allocated space section in Buffer pool, or in contrary, they have just one section in Buffer pool which they share between each other?

In other words, if plan cache is filling up, does space for data cache is reducing as well?

Minimization of DFA, Table Filling Method or Myhill-Nerode Theorem

I want to know, what if the DFA is merged states. So if my DFA starts with q0 and then have (q0,q1) state it goes to with an ‘a’ for example. How do I do the table filling method.

I tried to rename the merged state, for example turning (q0,q1) to q4 for example. But then the issue is when I try to do the table filling. With the input in the Automaton, I get only one state, sometimes the final state. So do I mark it.

For example, I renamed (q0,q1) to q4. Now in the table, if I want to find out the marking for q0 and q4. With an ‘a’ I get q4,q4 for both of the state and with ‘b’ I get nothing from q0 and q2(final state) from q4. I know since q4,q4 does not exist I do not mark. But I only get one state, which happens to be the final state. Do I mark q0,q4 part of the table or do I leave that blank aswell