Then go away and live your life. Let the people who are angry and energized yell at companies to try and get better conditions for consumers.
Then go away and live your life. Let the people who are angry and energized yell at companies to try and get better conditions for consumers.
Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ
You’re using the derivative of a polar equation as the basis for what a tangent line is. But as the textbook explains, that doesn’t give you a tangent line or describe the slope at that point. I never bothered defining what “tangent” means, but since this seems so important to you why don’t you try coming up with a reasonable definition?
I think we fundamentally don’t agree on what “tangent” means. You can use
x=f(θ)cosθ, y=f(θ)sinθ to compute dydx
as taken from the textbook, giving you a tangent line in the terms used in polar coordinates. I think your line of reasoning would lead to r=1 in polar coordinates being a line, even though it’s a circle with radius 1.
Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ
I think this part from the textbook describes what you’re talking about
Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.
And this would give you the actual tangent line, or at least the slope of that line.
Polar Functions and dydx
We are interested in the lines tangent a given graph, regardless of whether that graph is produced by rectangular, parametric, or polar equations. In each of these contexts, the slope of the tangent line is dydx. Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ. Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.
From the link above. I really don’t understand why you seem to think a tangent line in polar coordinates would be a circle.
A straight line in polar coordinates with the same tangent would be a circle.
I’m not sure that’s true. In non-euclidean geometry it might be, but aren’t polar coordinates just an alternative way of expressing cartesian?
Looking at a libre textbook, it seems to be showing that a tangent line in polar coordinates is still a straight line, not a circle.
The tangent of all points along the line equal that line
Looks like the back of someone’s head to me, but the picture is kind of blurry
https://www.tacobell.com/food/burritos/beefy-5-layer-burrito
Looks like the actual price is $3.79
No, I don’t think you’re going to do anything either way. When there was only the Raytheon protest, I doubt you called your state representatives about Palestine. Now that they’re also blocking traffic, I’m sure you’ll continue to do nothing.
I think the most effective protest would be one that directly acts against what they’re protesting against, like putting traffic cones on self driving cars or the Tyre Extinguishers deflating tires.
But that kind of protest doesn’t really apply to sending billions of dollars worth of weapons overseas unless you want to do something very illegal or violent. So whatever the people protesting think will help seems good enough to me.
Is getting a news story all that matters for an “effective” protest? If so, you must think blocking traffic is an incredibly effective protest strategy.
Protesters accuse Raytheon of abuses, block plant entrances
It’s amazing how protesters already tried that and nothing happened.
18 people facing charges for allegedly defacing Raytheon sign during protest in Tewksbury
Somehow, the “effective” protests you recommend don’t seem to be doing anything. Do you have any other bright ideas? Maybe something that the average person will actually learn about?
https://www.dndbeyond.com/spells/1995-animal-shapes
Another problem might be that animal shapes only has a range of 30 ft
Organic Maps (the app) lets you download maps of various areas ahead of time
https://wiki.openstreetmap.org/wiki/Street-level_imagery_services#With_photosphere_support
I was also looking into this recently, and I think one of the limiting factors would be the storage and processing power you’d need to blur faces and license plates and then let everyone have access to millions of photos on demand.
I’m no expert, but that looks like windows 10 on a steam deck.
The raccoons seem to agree with you
Looks like this one https://en.wikipedia.org/wiki/Superpermutation based on the content of the wikipedia article