Conic sections – Tangents are drawn to the circle $ x ^ 2 + y ^ 2 = 4 $ from points on the line $ 3x-4y + 12 = 0 $.

Then the contact chord passes through a fixed point. Find the chord slope of the circle with this fixed point as the center.

Let the tangents be drawn from the point (h, k)

$$ 3h-4k + 12 = 0 $$

The chord of the contact is
$$ hx + ky-4 = 0 $$

Now$$ h = frac {4k-12} {3} $$

Then $$ frac {4k-12} {3} x + ky-4 = 0 $$
$$ 4kx-12x + 3ky-12 = 0 $$
$$ k (4x + 3k) -12x-12 = 0 $$
Solve the given line family
$$ x = -1 $$ and $$ y = frac 43 $$

The fixed point is $ (- 1, frac 43) $

Slope of the line connection This point is to the center of the circle $ – frac $ 43

Then the chord slope will be $ frac $ 34

But the answer is $ frac $ 43 , What's going wrong

How are two equal fields (one filtered, one not) drawn in Google Data Studio?

I am trying to create a line chart with time series data for website users from Google Analytics in datastudio, which shows two diagrams, one of which users and one of the users only filter the organic data from the standard channel group. In Google Data Studio, you can't apply a filter to a single metric on the chart, and I can't figure out how to create a custom field that shows only the organic visitors and then draw both custom organic visitors, field and that GA Out-of-the-Box User field.

This kind of action is simple in Google Analytics, it's built right in, but it's not clear to me why they made it so damn difficult in Data Studio.

Surely I can't be the first person to want to show two fields (one a subset of the other) on a single chart?

Everyone is talking about Google searches.

Any help would be appreciated.

Certain Integrals – Calculate the area of ​​the figure drawn by the inequality system

I have the following system:

begin {cases}
1 le x le 3 \
-1 le y le 4 \
x ^ 3 + y ^ 3 le 29 \
y ^ ^ -2
end {cases} $$

How would I proceed to calculate the area of ​​the figure drawn by the system? This assumes that the bounding box is defined by the first two inequalities. I've been thinking about using integrals, but it's a bit tricky, as this is not a function.

Any hints?

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Draw – Can a ListPlot be drawn with a line around the "point cloud" with Mathematica?

Can Mathematica be used to create a ListPlot with the function shown below? a line around the point cloud?

I am not quite sure which rule would produce the desired effect (ie which points actually make up the red border), but I think the line should be drawn so that no point is "out of line". On the other hand, that leaves a lot of room.

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dnd 5e – Is the map of Kolat towers drawn correctly?

In Waterdeep: Dragon Heist, players can access a zone known as Kolat Towers. The map, however, is strangely drawn.

Enter image description here

It seems that the 2nd floor is not aligned with the 1st floor. I'm building the map in 3D for my Halloween session later this week and I'm not sure if I should build something like that

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Or if I should redraw the map so that the walls and stairs are aligned.

Is this map drawn correctly and the walls are not aligned (so I just have to reconfigure some stairs slightly), or did the designers only screw halfway through the floors, and it would be better to recreate the map?

legal – Where is the line drawn with domain names that contain a trademark?

I am not a lawyer and that is NOT LEGAL ADVICE!

To update

I read an article about Blogger Law and came across this direct problem. Here's an example case they quoted:

A leading case in the area of ​​trademark litigation is Continental Airlines, Inc. against In this case, the dotcom simply redirected visitors to a travel site where they could buy Continental Airline tickets and pay an additional $ 15 to use the service. The court awarded the airline's domain due to a trademark infringement.

I strongly recommend reading # 5 on this page as this is an excellent answer to this question.

Original answer

I would say no. You will not get permission from Google and the likelihood of confusion is high.

Here is an example:

In 1988, Quality Inns was planning to open a new chain of economy hotels 
under the name "McSleep." After McDonald's demanded that Quality Inns not 
use the name because it infringed, the hotel company filed a suit in federal 
court seeking a declaratory judgment that "McSleep" did not infringe. 
McDonald's counterclaimed, alleging trademark infringement and unfair 
competition. Eventually, McDonald's prevailed. The court's opinion noted that
the prefix "Mc" added to a generic word has acquired secondary meaning, 
so that in the eyes of the public it means McDonalds, and therefore the name
"McSleep" would infringe on McDonald's trademarks.


You can accept the same for YouTube as people would think it would be for a YouTube-sponsored or YouTube-sponsored branch.

It's not always about money that matters when a user confuses your domain with the Youtube domain and the answer is most likely yes.

A good book on copyright is intellectual property: patents, trademarks and copyrights by Richard Stim. Published by West Legal Studies. This book provides you with a good foundation and is used in law schools and you can understand it.

The best bet would be to name something generic against a mark.

Where is the line between good and bad ethics drawn?


So I have a question about the prices quoted and how to keep those prices.

I sign in to my Amazon Store account. I find the product I want to buy. It's called $ 10. I'll go to the cashier and if I have to pay, there's now $ 6, so I'll pay anyway, because the hell it's cheaper. Now the supplier has shipped the product and it's on its way, but now the extra $ 4 will be deducted from my credit card because it has been determined that the system is faulty.

If I register as a customer with a digital service provider and the price quoted on the website is $ 10 per month, and you checkout, you see that the recurring fee is now only $ 6 per month and you expect "Oh, that's cool, you must have lowered your price and not updated your website." So sign up and pay. Everything is set up and activated and you are on the way to use the service.

The next day you will receive an email with the message "We have lowered your recurring fee to $ 10, as it will be charged at the price quoted."

My questions are simple:

1. Is this ethical? Sure, I was willing to accept the $ 10 when I clicked on "sign up," but for me, this is a violation of ethics if they just change the price without notifying me, and their system It enabled me to purchase a recurring service for $ 6.
2. Is this legal at all, if the system allows a certain price and the customer continues with the price that goes into the agreement?
3. How should a person react to it and deal with it?

I'm just curious what everyone else thinks.

Thank you very much