On public roads? The slip stream is too close for safe driving. It’s only effective at speeds where your following distance should be much higher so you have time to react in an emergency.

Nope, they're extracting oxygen gas that's dissolved in the water, not the O from H2O.

That's a much more difficult process.

> 1- The Chinese firewall doesn't control the internet, it only blocks access to some sites from within ISPs located there. Anyone can set a VPN, and it isn't illegal, even the government provides VPN.

This is extremely misleading, borderline false.

The only "legal" VPNs in China are the ones provided by the government which are backdoored by the government. They are not ways around censorship. Individuals running VPNs are absolutely illegal.

For actual info from not-a-tankie: https://nordvpn.com/blog/vpn-for-china/

> (that are basically color revolutions funded by imperialist countries)

wut lol

No monophyletic branch. But there's a paraphyletic branch, and a definition based on that won't be any less objective or consistent.

I have heard good things about the podcast, though

I was hoping people would search and find my favorite podcast. Obvs there is such a thing as a fish; for the sake of accuracy it's probably better to say for our taxonomy there is no branch that contains all the creatures we commonly call fish while also omitting every creatures we don't call a fish.

Also that birds aren't pressured as highly into camouflage because of their ability to fly. But given that they're not unique in their colors, I'm not sure how big of a contributor that actually is.

Well, be careful with that one, because I usually hear that one in the context of denigrating paraphyly, and paraphyly is a useful and valid method of taxonomic classification as long as there are also equivalent monophyletic words.

Same subject but slightly off-topic perhaps: so when fish extract oxygen from water they're freeing the hydrogen?!?

Or, if OP wants to stay on reddit and ask questions: /r/learnmath

There's also a bunch more learning resources posted there.

It's basically saying that you're differentiating (finding the rate of change) of Y compared to X. For example, if you're driving a car and you know how far you have traveled over time then you can call distance Y and time X then differentiate Distance over Time to get your speed at any point in time. You can differentiate this again to get your Acceleration. The important part is that this isn't just your average speed, it's the formula for calculating your speed at any time over your journey

The Y or X are just the standard names for the variables - you can call them anything you like. In the distance over time example I used, you can call distance D and time T and velocity V then you get V = dD/dT

You could then call acceleration A and get A = dV/dT

The whole idea of calculus is to look at rates of change which is useful for a wide range of applications

The "d" in dy/dx essentially means "difference". dy/dx is saying "the difference in y per difference in x", so when x changes a certain amount y changes, like how you might express "50 kilometers/hour" to mean how much change in kilometers per every 1 hour.

However, with that km/h example, you don't want to just be taking the average over a whole hour. Within that time period, you might be going faster or slower at different times. In calculus, we're more interested in the change in y at an exact moment. To do this, we essentially separate x (equivalent to time here) into infinitely small periods, until it's so small we can ignore the length of time. This is what the textbook means by "limit".

With the kilometers per hour example, you could split the hour into 2 sections of 30 minutes, maybe in the first you moved 30km (then went slower in the 2nd half of the hour). 30km/0.5h = 60km/h. You keep doing this, splitting up the time into smaller and smaller pieces until it's infinitely small. If you know an equation that describes the distance you've traveled at any particular time, you can find the exact speed at any individual moment using methods based on this idea.

Conceptually, implicit differentiation works because if one side of the equation equals the other side at all values of x, that means that the other side of the equation would have to be changing at the same rate no matter what the value of x is as well. This means that if you can find out the rate of change of the left side of the equation (d(left side)/dx), it will equal the rate of change of the right side of the equation (d(right side)/dx).

When you find both of these rates of change, you'll end up having the rate of change of y with respect to x in the equation for one or both sides (whichever have y in it to begin with), because the amount that the whole side of the equation changes with a change in x is dependent on how much y changes with that change in x.

SADs are much harder (perhaps impossible) to securely erase, you’re right

“A couple” is sometimes not enough, but a few more is considered secure enough for most contexts, though gov will often physically shred the disks to be sure.

I only know for sure with macOS, but I image isn’t this applies to all: the OS has a built in secure erase feature that will overwrite a whole disk enough times to be confident that the data is irrecoverable

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>They cannot target a specific part of the body.

Just to expand a bit, some medication can target specific parts of the body. Not in the way a layman thinks (like an arm) but in the sense it can target specific receptors only found on certain cells.

This is used in certain brain and cancer medication.

you know how slope for a line is (y2-y1)/(x2-x1)? this is usually written as Δy/Δx. But this only works for straight lines; the slope of a curve changes and so to find the slope at a given point, we can’t measure it across any sizeable Δx.

So what do we do? Well some mathematicians back in the day decided to use their imaginations. dy/dx just means, what if we imagine that x2 gets infinitely closer to x1 without actually being x1? This is dx. Then if y is dependent on an equation of x, let’s say y=x^2, what would be then the difference between y2=x2^2 and y1=x1^2? That would be dy.

You have two limits, and you divide 1 over the other (dy/dx) and if your plot has a smooth curve then the limits will solve out to something. Now extend it out to not just this x1 but for all the possible x in your original equation and you get dy/dx = 2x. This function gives you the slope function of your original function, or in other words, tells you the slope of any point on your original curve.

edit: mixed up an x and y, also some clarity

I think it's you being naive for thinking China is looking on Reddit for ways to prevent its population from sharing media. I think they know exactly how it is shared and do not look to Reddit for information.

It's also worth noting that colourful mating displays aren't useful to mammals because most mammals are colourblind. And since bright colours are expensive, and tan/brown/black/white does a perfectly good job of camouflage, there's no advantage for mammals to have the bright colours.

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Correct me if I'm wrong. I believe I read that there isn't any scientific studies that indicate vitamins work as described. The body tends to ignore the supplements as it is not recognized as food. Finished thinking that vitamins did more harm to the body than good.

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I think that is an anecdote with questionable validity. Crows have instincts to crack nuts on hard surfaces in general, not just roadways. If crows have been dropping nuts onto rocks for thousands of years then dropping them onto roads may not be considered tool use since there is no way to establish that they understand the role of the cars in cracking the nuts.

In calculus, it means "changes in y with respect to x". The 'd' is short for 'delta' (the symbol we use for "change" or "difference"), and the ratio of the dy and dx , is the "derivative" or the slope of a line at a points along the line.

Say you had a a line where y = x^(2). That means when x is -2, -1, 0, 1, and 2 that y is 4, 1, 0, 1, and 4 respectively -- it looks like a U-shaped cup. The derivative of that line, dy/dx is 2x. That means at x = -2, -1, 0, 1, and 2, the slope of the line (change in y with respect to x) is -4, -2, 0, 2, and 4 respectively. The line y = 2x + 1 has a derivative dy/dx = 2 -- meaning that the slope is constant all along the line, which is precisely what you expect for a straight line; moreover, it's pretty intuitive, y changes 2 for each 1 that x changes.

Calculus provides a way of figuring out the slopes of lines and the areas underneath them (and it can work with more variables too).

Imagine you have put two points on the line of a graph. You might want to calculate the average slope between these two points, that is how steep a straight line drawn between these two points is.

The way you do this is you take how far the two points are away from each other in the y-axis and divide that by how far the two points are from each other in the x-axis. This is commonly written as Δy/Δx.

Now imagine you start to move one of the points closer to the other one. As they get closer the value of the slope is going to start approaching whatever the slope is at exactly the first point.The problem is that we cannot get the points right on top of each other because then the difference in x-axis between the two points would be zero and we'd end up trying to divide by zero. Instead we see what happens as we get the points closer and closer to each other and observe what value the slope approaches as we do.

This value is what we call the limit of the slope as the distance between the points approaches zero. It's what we call the derivative of the function in that point. However unlike Δy/Δx it's not really a proper fraction.It's what that fraction approaches as we make x infinitely small. And to mark that it's not actually a proper fraction but rather the limit of a fraction we denote it as dy/dx.

Everyone else already gave the definition in terms of derivative and also slope.

Personally I like this definition from a nice 1914 book of Calculus:

http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf

Page 15 - dy/dx - a little bit of y over a little bit of x