I'm trying to find the sum of what I believe should be a geometric recurring series. The initial term a1 is 1. Each term is 10% higher than the last. That means the formula is:

an+1 = 1.1an

I want to find the sum of the first 100 terms. I should be able to figure this out myself but it's been a while since I last did any of these and I never fully understood them to begin with.

Thank you in advance for any help.

I know that if U and W are subspaces with this property, then they are called complementary. But if we assume they are just sets with this property, are they necessarily subspaces?

If someone was to match each number that isn’t a pure power of any prime number(1, 6, 10, 12, 14, 18, 20, 21, 22, 24, etc.) with an integer, what would a resulting mathematical formula be?

Say I throw a ball up and take a real world measurement once every second of its height. This measurement isn't perfect. I only want to know the balls height at x seconds. Do I use the one measurement at x seconds or do I fit all my data to a parabola and interpolate the balls height at x seconds? Is there a number of points where it switches? I need 3 points around the apex to get some fit, but more points to starts to reduce noise. How do I measure how good my curve fit is, and how do I compare that to how accurate a single data point is?

Can a matrix have more eigenvalues than eigenvectors? Ive been stuck on this true or false questio on my homework for a while and im not sure how to go about it. I need to provide an example or counter example which either proves or disproves it. Thanks!

I was playing around with Perlin Noise. I know that simplex noise exist. Classic Perlin Noise requires creating N-dimensional grid, with random, N-dimensional gradient vectors. In later studies, it was shown that using pseudo-random vector is not the greatest idea and etc.. But what if, instead of approach shown here, we would use hash-function R^(N) -> R^(N). Subsequently mapping coordinates of our N-dimensional grid to pseudo-random gradient vectors. Such a function will probably lie in N^2-dimensional space, so maybe it is better to think about it as a transformation. So is there a function which maps values from R^(N) to R^(N), if someone worked with noise-functions, will it theoretically produce good results?

Couldnt we solve the sofa problem way easier if we pushed a moldable mass through it, like sand or play-doh, instead of using complex math? Like would it deform and squeeze through the corner to find the optimal shape, or would it just get stuck or something.

Hello. This is probably a dumb question, but I am many years away from the last time I studied any kind of trig or geometry, so forgive my ignorance. I am using some software that requires inputing coordinate points point by point in a text file, and then it connects them to create a geometry. I want to create a fillet such that it is perfectly round and is tangent to the diagonal and bottom lines. The software only lets me create arcs with a define radius and angle, and it doesn't tell me what those have to be to find a perfect arc between the beginning and end points. As a result, my geometry looks like this:

https://preview.redd.it/qpq6i1yyuo6e1.png?width=161&format=png&auto=webp&s=dd5776ca9fafaf7cb07b7c10b6ead22b53f9f543

When in reality, I want it to look like this (in red):

https://preview.redd.it/sjo1fecqvo6e1.png?width=310&format=png&auto=webp&s=61e065f95b60e2f1d7b5d6025cbef9a7e60a2e15

TLDR. Find radius of circular arc that is tangent to two lines given a starting and end point in x,y coordinates

https://preview.redd.it/awcuwtdlro6e1.png?width=1312&format=png&auto=webp&s=0285af2db2d1e1031c5fc7bfa7fd59ccfcf5131d

I saw this pic and can't get my head around how he can be down $30.53 yet have withdrawn all but $17.49 of all the money he has ever deposited. What am I missing here?

Normally addition and multiplication are commutative.

That said, there are plenty of commonly used systems where multiplication isn't commutative. Quaternions, matrices, and vectors come to mind.

But in all of those, and any other system I can think of, addition is still commutative.

Now, I know you could just invent a system for my amusement in which addition isn't commutative. But is there one that mathematicians already use that fits the bill?

I've used the quotient rule and then multiplied the fraction by x to the 1/2 which allowed me to do some factorizing to cancel out the denominator however I am left with simply a square root x at the bottom and I'm not quite sure where that 2 comes from, starting to suspect the question might be wrong in of itself

https://preview.redd.it/66tw22mtlo6e1.png?width=552&format=png&auto=webp&s=fcd7b98a4bbd8b98db94656b7d3833492c3bd64b

25.1. F(x, y,z) = 2ze1+xe2+3ye3; γ is the ellipse that is the intersection of the plane z = x and the cylinder x 2+y 2 = 4, oriented clockwise

https://preview.redd.it/jy08ue5gio6e1.jpg?width=3024&format=pjpg&auto=webp&s=9d4a6a8348fe2a2af6ade52203ff3fff19b2a1b9

Does anyone see what I have done wrong here? I have a feeling I parametrized the surface wrong but i cant seem to figure it out. I think the answer is supposed to be 8pi.

Can it be proven or disproven that (x^y)/y can be an integer. Provided that x and y are not multiples of each other. E.g. 2^4 is divisible by 4, but 2 and 4 are multiples of each other and thus don't satisfy the question.

three groups of children 1)3g,1b 2)2g,3band 1g,3b one child is selected at random from a group show that the probability the selected children are 1g and 2 b is 13/22

I have been stuck on this problem for while now and I have tried to use the quadratic and I have also tried to use the rational root theorem but it just hasn't been the best time. Any help or suggestions would be appreciated!

Hello all, hoping to get some help finding a closed form solution to the maximum magnitude of an equation of the following form in terms of r:

f(r) = A r(1-r)^(2) + B r(r^(2)-r) + C r(3r^(2)-2)

Where A, B and C are 3D vectors that do not vary with r and 0 <= r <= 1

I tried formulating as the magnitude of the vector summation || A r(1-r)^(2) + B r(r^(2)-r) + C r(3r^(2)-2) || which produces a nice scalar valued equation in terms of the dot products of the vectors. Setting d/dr(|| A r(1-r)^(2) + B r(r^(2)-r) + C r(3r^(2)-2) ||) = 0 would find minimas and maximas, however when you carry this out, you get a quintic polynomial in terms of r which has no closed form general solution. I know that I could solve for the roots of the quintic with root finding methods in code, however, I would like a closed form solution.

I also got as far as formulating this as a matrix equation which I could then use to find eigenvalues/vectors but I'm unsure of what that would mean in terms of the equation. A vector that is invariant to the transformation of A, B, and C? Is that guaranteed to the vector on which the maximum will be found?

Let A = the set of integers that are > 5 and < 3.

Let B = the set of Netflix program titles that George Washington the first U.S president watched.

Is A = B a true statement,

Hello, i was in a discussion about social security and i had an idea of taxing 20% of your effective tax rate for it instead of the current way. So 2% of money earned in the 10% bracket, 2.4% of money earned in the 12% bracket and so on with no caps on income.

Can anyone calculate how much money you would need to make to make to where the break even point is for the current 6.2% tax on up to $168600 of income if you do it in the way i suggested?

I thought about posting this on askscience, but this is more a math question I think.

I have one equation: a(r)=0.4/r² m/s²

r is the distance from the sun in Astronomical Units.

This function gives us the acceleration from radiation pressure on some spacecraft (with specific parameters that don't matter here).

The acceleration then stays somewhat constant for a long time, because an AU is so much bigger than a meter.

But obviously, eventually the spacecraft will have accelerated enough to increase the distance from the sun enough that the craft's acceleration will have changed significantly.

How can I derive a function a(t) from the original a(r) ?

I have tried doing it with limits, but I keep getting stuck. a(r) gives us an acceleration a, which gives us v(t) which gives us r(t) , which then we would continually have to plug into a(r) .

I have a fairly good grasp of highschool calculus, but I suspect that there's something about limits I need to understand to get to the bottom of this.

Essentially, I need a function that gives me r(t)

So my credit card company and their infinite wisdom, has made it so you cannot repin your card with any consecutive numbers, for example 1233 would not be accepted . Even though their factory provided pin had two consecutive numbers. I'm certain that this reduces the security of the cards and eliminates a massive number of pin options. Anyone do the math on how many less 4 digit codes are available with this restriction than the 10000 you could get?

I can solve for one consecutive number, but not for many.

Thanks in advance!

https://preview.redd.it/t2fcuwhunm6e1.png?width=1473&format=png&auto=webp&s=3cdf6fbb97cf387abafe22b74b7cc2590f5fe544

I used the substitution, u = ln (x) and changed the limits and integrated. However, I can't seem to understand the last step where I have to get the value of p. It would have been easier if one of the limits was infinity but please explain to me how I would deal with this question.

Thanks in advance.

https://preview.redd.it/5cqurvfchm6e1.png?width=400&format=png&auto=webp&s=c8a35b2a18d9c927584f0d46f5c84721a749f4cf

I was recently playing around with numbers where you partition them somewhere to get two numbers, take the sum the integers between those two new numbers, and that sum is the original number. The pattern of them seemed to be pretty irregular except for the case of 1 followed by some number of 3s, a 5 and then another number of 3s. (i.e. 1353, 133533, 13335333).

I had a play around with this and made a proof which does check out, but it feels quite handwavey to me because I don't have a good way to represent the recurring 3s numerically. I can obviously represent the 5 and 1 by 5 * 10^n and 1 * 10^2n respectively (where n is the size of each partition / number of 3s + 1), but I had to make up some random notation for 3s which leaves the proof feeling a bit incomplete.

What I'm looking for is any way to represent these numbers in a more rigorous sense, or a proof that doesn't require playing with the numbers numerically so that you never need to operate with the recurring 3s.

Thanks in advance :)

I want to quickly calculate simple problems. For example, if someone asks me what 57 + 8 is, I would like to be able to answer without taking much time. I need strategies and want to develop my math skills, including the unitary method and algebra. Later on, I also want to learn calculus.

My professor from the analysis course mentioned that notable limits cannot be applied in cases where there are sums or differences between terms. They are specifically valid only in scenarios involving multiplication or division. However, I was told that in certain cases, they can still be used even when sums or differences are present.

For example

where you should use unilater limits for understand if the funciton is continue or not

but not in this case where you should use Hopital for example

https://preview.redd.it/j8wnm2xw3m6e1.png?width=494&format=png&auto=webp&s=c1a5b5355d8727401f816cbf3adc990cefe30de3

Could someone explain in detail when notable limits are applicable and when not and provide clear examples of cases where they cannot be used?

I am 14 years old i am exeptional for math at my age and in a question in math ( x - 1 )² = 3 We had to guess in a graph wat it was close to (2.7) and then calculate 2.6 and 2.8 to but never got the actual anser but i figuerd out if you √3 then plus 1 you get the exact anser when i asked her why we dont learn that she said it was ( to hard ) WHY DONT WE LEARN THAT ITS SO SIMPLE