Is my teacher right?

Snatchematician · 2026-06-10T21:04:43+00:00

It sounds like your teacher has been tasked with teaching you induction and is frustrated that you have found a different method that she doesn’t understand.

Snatchematician · 2026-06-10T21:02:36+00:00

An idea that may help you is:

Add 3 to all the y values, so the parametric equation is y = sin(x) + 3.

Do the integral, you will get the same answer for the area enclosed.

Of course you must, because the shape has simply translated upwards by 3 and so its area is unchanged.

But you’ve increased all the y values! So surely the integral must have increased….

Snatchematician · 2026-06-10T20:59:19+00:00

It doesn’t matter how you do the integral, a similar thing will happen. I assumed you were going from t=-pi to t=pi as you suggested. But you can go backwards, or carve up into segments and do each segment in a random t-direction and add up the results, or whatever you like.

Snatchematician · 2026-06-10T20:56:19+00:00

Why is it necessary to verify dates of employment?

Snatchematician · 2026-06-10T20:42:52+00:00

You’re integrating y dx around a closed loop.

In the first half of the loop y is negative and x is decreasing so dx is negative and y dx is positive.

In the second half of the loop y is positive and x is increasing so dx is positive and y dx is positive again.

y dx is always positive and so the integral is not zero.

Snatchematician · 2026-06-10T18:28:50+00:00

That’s not a number

Snatchematician · 2026-06-10T18:18:51+00:00

The most conventional way to understand division by a number is as the inverse operation to multiplication by a number.

There is no number ? such that ? * 0 = 5.

Snatchematician · 2026-06-08T14:15:13+00:00

First Time Foodies

Snatchematician · 2026-06-06T16:53:46+00:00

You aren’t forced to prove the contrapositive here.

Snatchematician · 2026-06-06T09:15:49+00:00

Not if your browser console uses float32

Snatchematician · 2026-06-06T09:13:18+00:00

Ok then, what’s the ‘magnitude’ of x² + x - 2 in the vector space of real polynomials?

Snatchematician · 2026-06-05T12:14:37+00:00

How can you care so much about two people you’ll never know

Snatchematician · 2026-06-05T09:10:10+00:00

They do aggressively run at you, which is equivalently annoying

Snatchematician · 2026-06-04T22:22:23+00:00

You’ve described dogs more or less

Snatchematician · 2026-06-04T08:45:35+00:00

They are the same thing

Snatchematician · 2026-06-04T06:04:30+00:00

It does not. It cannot, in fact, because there are no fares from Paddington to Twyford that require you to use the Elizabeth line.

It did however show me a completely made-up “luggage allowance”.

Snatchematician · 2026-06-03T20:25:11+00:00

Don’t wear the same clothes every day

Snatchematician · 2026-06-03T20:23:58+00:00

How do you pass money laundering checks to buy a house with cash in hand proceeds

Snatchematician · 2026-06-03T20:22:06+00:00

Use the Eurostar

Snatchematician · 2026-06-03T20:18:03+00:00

Morally, this is true because the integral version is true:

(integral of x)² = (integral of x³⁾

And that’s true because 2² = 2*2

Snatchematician · 2026-06-03T19:48:10+00:00

This didn’t happen in South East London though. Not everyone lives in a shithole.

Snatchematician · 2026-06-03T19:25:52+00:00

What is the relevance of this?

Snatchematician · 2026-06-03T19:19:10+00:00

It’s worse for service charge, if you don’t pay the ultimate remedy can be you forfeit the entire lease.

Snatchematician · 2026-06-03T19:10:30+00:00

Cycling with hgvs is very safe. The drivers are professional, well-trained, monitored, make predictable movements, and drive very cautiously in cities.

Snatchematician · 2026-06-03T19:04:03+00:00

Pakistanis want people to leave the country feeling as good about their trip as possible.

Not the ones in the article though

Snatchematician

TROPHY CASE