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All comments forget the most important aspect: Any unspent dollar at the end of the year is profit, and profits are taxed

Don't you just feel it? I have always been aware of my head being crucial to my thinking and I should protect it more than anything else.

It's not the case that everyone everywhere everywhen has exposure to a corpus of knowledge about head injuries. Hence why some people went with "when I'm embarrassed/infatuated/etc I feel it in my 'heart', that must be where thinking happens".

Considering the average age of a sufferer of penile fracture is under 30, you might want to consider how 'senile' the victims are.

Nah, my head is not that interesting.

Also active noise canceling does not block sound and can still cause hearing damage

Ok, so I am actually a dog, but I was hoping to still fly under the radar because humans can technically fracture their dingledong. It’s just not a bony dingledong.

That question is one of the ones philosophy is all about.

I thought this was the other way to use a poop knife.

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It is quick but not instant which is why active noise cancellation works well on low frequencies and not too well for higher.

Low frequency sounds have a wider wavelength (and thus occur over a longer period of time). You can have a little latency between the live and generated sounds and they will still mostly overlap and cancel out. For high frequency sounds there could be several peaks and troughs in the offset gap and they're less likely to line up with the generated sound.

Because, if one department isn't spending all of their allocated budget, they means they don't need the amount allocated to them. And if they don't need it, some other department surely can use it because they didn't have enough allocated to them.

So department's try to spend their entire allocation so that when they actually do need it, it'll be there.

You don't need the money, right up until you do. And when you do need it, if you don't have that allocation to your department, you're SOL, you'll have to try to get it for next year's/quarterly budget.

Spending it just tells the people who make the budget that you do in fact need the amount allocated to you and to not give some of it to someone else.

Sound is air pressure changes. The canceling means the pressure is flattened. It's substracting two sound waves.

Add a third item for comparison - a 1 kg bottle of water. That weighs more than either the Snickers bar or cabbage, but it's clear why you won't gain any weight from drinking the water (assuming you weren't dehydrated and you've had a chance to piss it out) - there's nothing in the water your body can use for energy now or convert to something it can store and use for energy later. The water just passes through you.

The bulk of the cabbage passes through you too because it's over 90% water. Most of the rest is insoluble fiber that just passes through our digestive system unused. Take away the water and the insoluble fiber, and you're left with a tiny bit of actual usable nutrients, and only some of that is potentially storable by the body.

A Snickers bar is about 6% water, and the bulk of the remaining 94% is calorie dense fat and carbohydrates (with a bit of protein). The body uses some of that for immediate energy and stores almost all of the rest, resulting in weight gain.

This is the general reason why vegetables seldom lead to weight gain - they're mostly water and whatever is left isn't terribly calorie dense(ignoring starchy veggies like potatoes and fatty veggies like avocado for the moment). Doesn't mean you can't gain weight eating only veggies, but it's much harder to do compared to eating more calorically-dense foods.

'senile fracture'

Immagine a still lake. You throw a pebble in the water. Ripple spread out. Then quickly throw another pebble near by. It too makes ripple. Where the first p bibles ripples encountered the second ripples they kinda cancel each other out.

There's a lot that goes into noise cancelling, they are not always doing everything in real time. There are specially designed and fully dedicated chips on the sound devices that do just one thing, noise cancelling. They recognize certain sounds and apply the noise cancelling beforehand, thus eliminating that time window. They've been trained on millions of hours of noise and have gotten really good at what they do. Power of data, indeed.

It would only be a realized loss if they bought it for more than they sold it.

Because town names are usually a local consideration, whereas a large geographical chunk of an entire nation is a national consideration.

I mean, you would agree that we wouldn't ever give two states the same name, right?

Superposition is a fancy way of saying the whole is equal to the sum of its parts.

If you add two waves, the amplitude of the resulting wave at any point is the sum of both the original waves at the point.

So if wave 1 is sin(x)

And wave 2 is -sin(x)

The two combined give us sin(x) - sin(x) = 0

That's how noise cancelling works.

Note that superposition only works in linear systems. Sound is linear, electromagnetic waves are linear, electric circuits using only linear components (Resistors, Inductors, Capacitors) are linear, etc.

Linearity is definitely beyond an ELI5 discussion though, I think.

In my opinion, bad noise cancelling is worse than no noise cancelling at all. Yes, when the noise cancelling isn't that good and responsive, there are moments of noticeable white noise. But with time, brands have gotten really good at noise cancelling and the manufacturers claiming to have noise cancelling in them do their job well.

Maybe you can't see it, but I can.

I started with a triangle in a semi-circle as requested by OP and did not assume it was a right-angled triangle. However when completing the construction as I described, it is clear (to me at least) that it can only have been a right angle to start with. I filled out a couple of extra steps to help you complete the visualisation, but it seems you need the formal algebra. Maybe OP still needs the proof, but to me it is so obvious as not to need formal proof.

Makes me wish we could have that sense of urgency about things more often. Usually we get so wound up with red tape that we drag things out for years before they ever even see the light of day.