anonymous asked:

Victor Nikiforov's recipe for happiness: 1. Touching the love of your life's shoulder. 2. A poodle in your lap. 3. Freed tiddies Like if u agree. Pls add stuff if u want.

shdiogfkhj ds freed tiddies

4. seeing world’s best figure skater yuuri katsuki win all the gold medals and world records he deserves

anonymous asked:

(1/3) in regards to 'delusional' Jonsa & antiD fans, I have to say we are the most rational. The meta out there is well constructed based on book & showverse reference, backed up with quotes, scene analysis & always exemplifies the best case scenario for individual character development for all parties. My issue with Aegony stans is they don't seem to be watching the same show. All their predictions are based on every other characters arc being crushed & a nonsensical plot that pushes Ds agenda

(2/4) According to them Sam will be so happy D burnt his family then bow at her feet, Jon will too especially after roasting those ‘evil’ unprepared Lannister soldiers-which he wanted her NOT to. Jon will tell all the northerners to fuck off because of his perfect queen & they will be completely ok with that & pledge their undying loyalty. Jaime will drop to his knees, proclaim her his queen even after he saw her roast all the men, burn all the resources & he tried to kill her (wish he had)

(¾) The food being burnt & everyone starving will be perfectly ok, I guess when it gets bad enough they’ll just eat eachother. The summer soldiers she bought to Westeros will be perfectly fine in the worst winter in 1k years that even the northerners & free folk will struggle to survive. The dothraki will be perfectly behaved & not rape and pillage. Arya the ‘despises all lords who take advantage of the common people & abuse power, loves her home & family’ stark will admire & love D

(4/4) for all she’s done and will gladly pledge herself/home to this violent foreign invader. Sansa will admire her strength and hand over her home and families well being (consensus is still out, some say she doesnt, gets roasted by D dragons and everyone cheers). D will have a magic targ baby and JD will get married and rule happily ever after, post defeating the NK. The delusional argument holds no ground, when they believe this ☝️


The feels man, lol. So ever since the cutscene in FNAF SL custom night, so I finally went to the conclusion that Michael turned into Springtrap and the girl and the boy from FNAF 4 are his little siblings and William being the father

Thats basically the change in DS of Michael Afton, and have a half Spring half Michael drawing in two filters lol XD

DS by me

Study With Me: Line Integrals

Hey guys! I’m currently studying for the Mathematics Subject Test of the GRE, which I plan on taking in the fall. One of the ways I like to study is by explaining the material to someone else. I currently have weekends off from research, and since Saturdays are for the boys, it leaves Sundays for GRE preparation. 

Because of this, every Sunday, I’ll explore a different undergraduate topic that could appear on the Mathematics Subject Test. This week: Line Integrals.

I’ll talk about the following:

  1. What is a line integral?
  2. How do you calculate a line integral?
  3. An Example

As a brief note, this post contains LaTeX code and will be much easier to read when viewed directly on my blog, where the code will compile!

What is a line integral?

Let’s first recall what we already know about integrals. We’re used to integrating functions of one variable over an interval [a,b]. We can think of this as integrating over the path on the x-axis from a to b, and the value of the integral as giving the area bounded by the curve y=f(x) over the path [a,b]. 

But! We can also integrate over paths that aren’t just straight lines along the x-axis. The resulting integral is called a curve, contour, or path integral. Most commonly, it is known as a line integral. 

In this post, I’ll be talking about line integrals with respect to arc length. 

Before we get into it, I’d like to start by defining what it means for a curve to be smooth. A curve, C, with parameterization r(t) = <x(t), y(t)> is smooth if the derivative r’(t) is continuous and nonzero. Additionally, we can say C is piecewise smooth if it is composed of a finite number of smooth curves joined at consecutive endpoints. Basically, this means I have a bunch of curves $C_1, C_2, …, C_n $ that are all individually smooth and Each $C_i$ has its endpoints connected to $C_{i-1}$ and $C_{i+1}$. 

Back to line integrals. Suppose we have a function f(x,y) and a smooth curve, C, in the x-y plane. We want to think about breaking C into n tiny pieces of arc length $\Delta s_i$. For each of the tiny pieces of C, choose any point $P_i = (x_i, y_i)$ and then multiply $f(P_i) = f(x_i, y_i)$ by the length $\Delta s_i$. This process is fairly similar to how we define integration for the case where the path is a line on the x-axis. We want to sum up these multiplied terms for all n terms. If the value of that sum approaches a finite, limiting value as $n \rightarrow \infty$, then the result is the line integral of f along C with respect to arc length. Below is a comparison of the single variable case integrating over a path [a,b] on the x-axis (left) and the line integral with respect to arc length over the curve C (right). 

Note the notation used for the line integral. If we’re integrating over a path C, we write C at the bottom of the integral. 

What does this mean geometrically?

The value of this integral is the area of the region whose base is C and whose height above each (x,y) point is given by f(x,y)

How do we actually calculate the line integral?

First, parameterize C. That is, for a parameter t, find the equations x=x(t) and y=y(t)  for $a \leq t \leq b$. We consider C to be directed, which means we’re saying that we trace C in a definite direction, which is called the positive direction. Basically, we’re saying that t runs from a to b, so A = (x(a), y(a)) is the initial point and B = (x(b), y(b)) is the final point. 

Since we have $(ds)^2 = (dx)^2 + (dy)^2$ (think Pythagorean theorem), we can write:

$\frac{ds}{dt} = \pm \sqrt{( \frac{dx}{dt})^2+(\frac{dy}{dt})^2}$

which can then be rewritten as:

$\pm \sqrt{(x’(t))^2+(y’(t))^2}$.

We use the + sign if the parameter t increases in the positive direction on C and the - sign if t decreases in the positive direction on C

So, we have:

$\int_C f \,ds = \int_{a}^{b} f(x(t), y(t))\frac{ds}{dt} \,dt$.

An Example

Determine the value of the line integral of the function f(x,y) = x + y^2 over the quarter-circle x^2 + y^2 = 4 in the first quadrant, from (2,0) to (0,2).

Solution below.

Keep reading


Have some headcanons for the Birthday boy!

1. Terrified of growing up!

2. Works part time at the nicest, little hole in the wall, cafe. 

3. Can demolish anyone at any DS game!

4. Have I mention he actively logs onto his old cringe Quotev account?

5. Was the kid who went through a hardcore creepypasta stage…

6. Cant keep fish alive but somehow owns a puffin and an owl (He kinda wants more birds)

7. The owl is a cute short eared owl but its name is Hedwig.

8. Constantly has a reoccurring dream where he has bird wings (AU mention)

9. American Licorice can die in a hole but Australian Licorice is okay. 

10. Likes to listen to music in languages he cant understand.

11. His Hogwarts house is Ravenclaw (He was almost sorted into Hufflepuff tho)

12. Unhealthy obsession with Game Of Thrones. 

Originally posted by redauroraskies

DS folk n more:_

I started my DS art 4-5 years ago on Deviantart, don’t go and follow me there just because of that, I’m moving boi, help me with that. I’m going to move them here mostly from now on (and patreon+more), aside from the more ‘serious’, fully rendered stuff. The rest I want to move here , the fanbase here is a lot more active. And that’s it, you can interact with me here actively in regard of anything really. 
For now_