I came across this during reading about multinominal theorem but I don't understand why the summation to n is required.

https://preview.redd.it/dqoue45dte4e1.png?width=1739&format=png&auto=webp&s=6dc92503cc0f19056ae3d4aae4249df1bfc1ee74

Why, in maths, do we always talk about distributions in terms of random variables ie. discrete or continuous random variables while in practice when using things like CDFs and PDFs our data are not really random. In fact we usually have measurements or observations of some kind so it wouldn't be correct to describe the data as random. If this is the case, why do we learn maths and statistical methods in the context of randomness when in reality thats not what we actually use them for?

UK A-level maths. year 12 mechanics and statistics. where is the best place like website to revise?

Overall view of all known dimensions

Specific angles required

Evening all! I'm not a student or mathematician, and it's been a while since my GCSEs so I'm reaching out for some help.

I'm trying to make a 2D template of a 3D model - specifically a hexagonal based cone with the top cut off. This is to use as a setting for hexagonal gemstones when making jewellery.

My thinking is I can make a 2D model of 6x trapeziums, cut them all out of a flat sheet of material, and fold it up to the shape required. In order to do this accurately I need to calculate the angles shown in the screenshots and just create a 2D template of them.

I'm unsure if I'm missing a better approach or if there are problems with my plan that I haven't anticipated. Any response is appreciated, and I can provide any additional details if needed. Thanks!

I have been thinking about this for a while, and wanted some perspective. In this equation, what is the difference between 1 and 1? Arithmetically, the difference is zero, so how can there be two of them if they are the same? It seems the only difference is that 1 is on the left and the other 1 is on the right. This reminds me of the issue of having to explain the Right Hand Rule without a common reference to say which is left and which is right.

I am curious if anyone knows of other "dark sided" mathematicians who have questioned this, like those that don't accept the Nontriviality Assumption that 0 =/= 1

I also see a relationship between this and negative numbers, long ignored for being physically impossible, and only really acceptable in the abstract. Numbers that exist to the left and right of zero on the number line. They are not true opposites, merely additive inverses. This fundamental difference is what propels us into higher dimensions with imaginary numbers.

Similarly, in 1+1=2, 1 and 1 are not truly identical, otherwise there would still be just 1 of them.

Thoughts? CONCERNS?

The distance between the Sun and Earth is 𝑟𝐸=1.5×10^11 m. The distance between the Sun and Jupiter is 𝑟𝐽=5.2𝑟𝐸. Jupiter completes one orbit around the Sun in 𝑇𝐽=11.86 Earth years. At a certain moment, the angle between the Sun and Jupiter, as observed from Earth, is 20∘ . Determine the instantaneous angular velocity of Jupiter as observed from Earth at that moment.

question no 3

I am kinda weak in math and needed help

https://preview.redd.it/m0uxtpdhca4e1.jpg?width=1599&format=pjpg&auto=webp&s=e974a2638092a6689ccf9aa63177aab8c1641351

(929 mod 9) ^ 929

As above, im working on a project where i have a unit that is measuring its dip and dip direction (relative to compass north after projecting the magnetic field on the accelerometer vector), and there will be another unit measuring the dip and dip direction of another plane. The result is an output that tells me how the second plane dips with respect to the first plane (ie if plane 1 was perfectly flat, what would the dip of the second plane be?)

I have the accelerometer unit vector, the magnetometer (calibrated) unit vector, and the magnetometer unit vector projected to the accelerometer plane. I also have the heading (compass) and accelerometer dip, (z/xy) and the correction to the accelerometer xy vector to give dip direction in compass north; what can i do now?

Is it a matter of applying a rotation matrix to correct the accelerometer vectors?

Is there a way to calculate how randomized a Trading Card Game deck is?

{y is a real number 0≤y< < 0.7} is this uncountable set or countably infinite?