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VIVIAN

Press release for this Canadian study [Metabolomic and immune alterations in long COVID patients with Chronic Fatigue Syndrome]:

“We do not actually believe that long COVID is a separate new disease,” explains rheumatologist and clinical immunologist Jan Willem Cohen Tervaert, professor of medicine, who is an expert in fatigue associated with rheumatic illnesses.

“Some symptoms — such as the loss of taste and chest pain — are very specific for COVID, but we see a common pathway with ME/CFS, which leads to the same fatigue, brain fog, post-exertional malaise, widespread pain and non-refreshing sleep,” he says.

I redownload this app for one day once every maybe two months and unfortunately I’m rewarded every time

I don't think this is possible????

Hello Ryan I am here to help. So the first step is pretty easy: Three cheeseburgers are worth 18, so each one is worth 6. If these are dollars, that's a steal!

From the second equation we get that cheeseburger plus fries-squared is five. Subtracting cheeseburger, which is six, from both sides, we get that fries-squared is negative-one. Math fans will know that there are two solutions to this; either fries are the "imaginary unit" 𝒾 or they are its negative, -𝒾. We'll do the rest of the problem with 𝒾, keeping in mind that at the end we should also take the complex conjugates as solutions.

Finally, we have that cup to the power of fries, minus cup, equals three. Replacing fries with 𝒾, and moving a cup to the other side, we get that cup-to-the-𝒾 is equal to cup-plus-three.

Now, the weird part about this is the cup-to-the-i. The problem with this is that complex exponentiation is technically not a thing. That is to say, there is no one function which is mathematically equal to "input-to-the-power-of-𝒾". In fact, there are infinitely many such functions.

Fortunately, due to reasons that take about six pages to explain (trust me I've done it), there is one particular function that many people have agreed is "the most reasonable one". This is not a mathematical notion, but a human preference. Seeing as this question was presumably written by a human, I am comfortable with using this function.

So, what function is this? Well, given a complex number r∠θ written in polar form (if you don't know what that means don't worry), where -π < θ ≤ π, then (r∠θ)^𝒾 = e^(-θ)∠ln(r).

Applying this to our problem a value r∠θ will be a possible solution for cup if e^(-θ)∠ln(r) = r∠θ + 3. Splitting this into real and imaginary parts, we get two equations: e^(-θ) cos(ln(r)) = r cos(θ) + 3 and e^(-θ) sin(ln(r)) = r sin(θ). We can graph these equations on Desmos:

The possible values of cup are the intersections between the red, green, and purple. There are infinitely many of these which have an angle of around -π/3, and there are two weirdos: One which is a complex number very close to -2.98, and one which is somewhere around -25. The possible values for cup are all of these infinitely many solutions, and also all of their complex conjugates.

A bit on the expensive side for cup tho innit?

-25 means they're paying you $25 to take it

donald trump is guilty on 34 counts due to a specific legal loophole! google donald trump rule 34 for more

I highly recommend that you do not do this.

Funny joke though.

google donald trump big thick ass dump truck plap plap plap oiled up tweeting jiggling booty twerk vids for more information on the verdict

national holiday

Here's my piece for the Paper Mario Zine! I thought it'd be cute to draw peach and tec dancing and it got away from me and became lesbians hell yeah

Check out other art from the zine at @paper-mario-zine

(source)

AUDIO ON IM NOT KIDDING

knights and wizards for hw