# Questions tagged [applications]

The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)

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### How does and has researching mathematical juggling influenced broader branches? [closed]

I've read somewhere that juggling mathematics has influenced maths as a whole at least once with regards to some theorem in, Number Theory, I think. I'd be curious to know about the connections as ...
32 views

### x^{2} =εcos(x). Find a two-term asymptotic expansion, for small ε, of the solution. [closed]

a. Sketch the functions in this equation and then use this to explain why there are two solutions and describe where they are located for small values of ε. b. Find a two-term asymptotic expansion, ...
13 views

### Help needed Applications Fourier transform on sound wave propagatiom

[This image show an example in a textbook that am having difficulty in understand how they get 2.12.81 and 2.12.82] Kindly help with the value of B : https://i.stack.imgur.com/k4HaF.jpg
1 vote
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### The absurdity of $\Gamma(x)$'s minimum, and can it be applied to the factorial?

I know that the Gamma function can be used as a representation of the factorial, but, at the same time, it is an extrapolation of $x!$. The Gamma function is cool and all, but what are its ...
21 views

### Number of pulsations given an specfic keyboard

I am given a piano that has 88 keys and I am asked to find how many different melodies with 123 pulsations (each pulsation has obviously one key) are there. However, there is a restriction: there has ...
1 vote
53 views

### What is the equation and area under curve for Covid load dynamics?

Covid virions on infection, replicate exponentially and once the body's defense system starts attacking it then it also seems to decrease exponentially. Source The time period when the PCR test is ...
634 views

### Negative Numbers in Math & Physics

We say that $-4 < -2$ and that $-3 < 0$ and that $-192 < 24$. I'm aware that there are simple, easily understandable definitions for less than / greater than / equal to e.g. $a < b$ iff ...
19 views

### Calculating Rate of Change and using differentials to project 3 years from now

Currently, BC is helping $R=5,000$ refugees. The number of refugees that BC must help is rising at a rate of $\frac{dR}{dt}=1,000$ refugees per year. Currently, the number of staff members is $N=100$ ...
95 views

### Heat from a geothermal well: your take?

Imagine digging a cylinder-shaped (vertical) bore-well of depth $L$ and diameter $r$ ($L\gg r$). The (infinitely thin) cylinder-wall is made watertight and we split the well in half using a kind of ...
88 views

### How taut must a stretchable, horizontally-oriented string be in order for a straight line to approximate the string to within a given margin of error? [closed]

My question deals with a string that can stretch due to its own weight. If the string is allowed to stretch then I'd assume there would always be a bit of a bulge due to gravity. The only progress I'...
51 views

### Simulating Particle motion on a surface

I am working on a personal project to model the motion of a particle on a surface. Using calculus, I parametrized a surface and then found the normal vector to that surface. Using that normal vector, ...
119 views

### Why is the transpose so useful?

I am learning linear algebra using the textbook Linear Algebra Done Right, trying to understand the subject through a logical, pure math perspective. I'm, simultaneously, learning applied linear ...
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### Are there any applied mathematics problems which require a set with cardinality greater than the Reals?

I am just asking in general if problems arise in physics, astronomy, or biology which require large cardinalities, i.e. beyond the Reals?
195 views

### Best way to cut a pineapple ring?

I like to prepare pineapples by first cutting it into rounds and then slicing off the skin with a roast beef slicer. This leaves me with a hexagon "ring" around a circular core: I then don'...
44 views

### Where to apply binomial expansion?

I would like to know where I could apply the expression as part of other equation $$\bigg( 1 + \frac{x}{r} \bigg)^r$$ considering $r \in Z$. It means, in what kind of problem I can use this expression....
1 vote
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### Help in understanding this exercise (Linear Algebra)

I need some help in understanding the precise request of this exercise. Let the vectors of the plane be identified with oriented segments exiting from a fixed point, and let's identify $\mathcal{V}^2$...
77 views

### Useful length of Pi?

Not sure where this really fits, so am trying Mathematics first. Feel free to migrate to another StackExchange forum if more appropriate elsewhere. So I was listening to a podcast yesterday that was ...
22 views

### Interpolating functions into continous functions on topological spaces

In practical modelling, I'd argue that one of the most powerful concepts we have is the ability to interpolate functions between given data points. I want to ask, if any similar idea exists between ...
36 views

### What else can the principle of induction be used for? [duplicate]

This might be a random question, but I've always wondered, can the principle of induction be used not only for proving sum formulas, but something else? Is there anything else we can use it for?
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### Real world example of an equation with no solution? [closed]

I have just started reading basic algebra and I have this curiosity that came up when solving basic linear equations. Some equations have no solutions. Are there any real world example of equations ...
79 views

### Is there any practical use for octonions? [closed]

Quaternions are useful for describing orientation/ rotations in 3- dimensions, however is there much practical use for an 8-dimensional base hyper complex number id est Octonions?
13 views

### Hypothesis testing on the existence of a hypothesis (satisfying certain criteria)?

My understanding of probability and statistics is as yet not very good, so please correct me if I get anything wrong, terminologically or conceptually. Suppose I have a set $X$, and a property (binary ...
252 views

### How does the Pareto distribution represent the 80-20 rule?

According to the current Wikipedia article: The Pareto principle or "80-20 rule" stating that 80% of outcomes are due to 20% of causes was named in honour of Pareto, but the concepts are ...