All Questions
Tagged with applications functions
29
questions
0
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1
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66
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Maximum and Minimum of a cubic function
Maximum value of function
$y = x^3-5x^2+2$
a) 5
b) $\infty$
c) 2
d) -5
We know to find maximum value of a function we take first derivative of the function and make it zero and get some point. And ...
- 185
4
votes
6
answers
693
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Is $x^3$ really an increasing function for all intervals?
I had an argument with my maths teacher today...
He says, along with another classmate of mine that $x^3$ is increasing for all intervals. I argue that it isn't.
If we look at conditions for ...
- 45
3
votes
1
answer
134
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A "perfect" (chess) rating system
Assume we want to have a player rating system with the following conditions:
For simplicity, no draws.
If A wins against B with ratings $a,b$, their new ratings are $a'=f(a,b),b'=g(a,b)$.
Most ...
- 745
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0
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60
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Representing Submodular Functions As Maxima of Additive Functions
According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I am having trouble internalizing ...
- 1,922
1
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0
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72
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How units didn't change while differentiation?
In this example, rate of change has units cm², while the original quantity, area, also has same units. I learnt that units change just like normal ratio, that is dA/dr will have same units as A/r, so ...
- 61
3
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2
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127
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How are the functions determined for real-world applications (business, population models, etc.) of calculus?
The following problem has been taken from Paul's Online Notes:
"We need to enclose a rectangular field with a fence. We have 500 feet of fencing material and a building is on one side of the ...
- 33
3
votes
1
answer
67
views
Seemingly conflicting notions of a function
Throughout my mathematical education, I have seen a few, seemingly, different and conflicting notions of what a function is:
A function is a a type of mathematical object that maps every element of a ...
user997478
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48
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Find a function
It's a cuttout from Rempe article "A mathematical model of the sleep/wake cycle" about a function which I don't understand how to describe: $h(t)$ decays exponentially while the system is asleep
and ...
- 480
1
vote
1
answer
48
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Purpose of rotation of a Function or Graph
You are able to rotate any function by an arbitrary angle around the origin using the formula,
$$y\cos\theta-x\sin\theta=f(x\cos\theta+y\sin\theta)$$You can also do similar rotations for polar graphs, ...
- 388
0
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1
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81
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Closed-form solution for $f(x)/x=y$ using $f^{-1}$
I'm programming a piece of math that requires solving an equation of a form $f(x)/x=y$. Now I already have $f^{-1}(z)$ coded (efficiently, and not by me) so I'd prefer using this implementation ...
- 3,212
0
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2
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314
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Determine if function is injective, surjective, bijective [closed]
For
$$f : \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}$$
$$f(m,n) = 3m + 2n -1$$
I think it's injective, but don't know how to prove it. I've been trying numbers for m and n.
user481368
9
votes
4
answers
460
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"Class" of functions whose inverse, where defined, is the same "class"
Please excuse the amateurish use of the term "class", I don't know what the exact term is for what I'm looking for.
Anyway, details.
I'm asking specifically about real-valued functions on the real ...
- 101
1
vote
1
answer
52
views
Unit decomposition by three continuous functions
My current research project involves adaptive weights for three different loss functions so that I hope each the objective can focus on the different size of objects when given a different size of the ...
- 255
0
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1
answer
32
views
The shortest route of an amphibian vehicle
Let be the x axis the coast.
The speed of an amphibian vehicle in the upper half-plane (land) is $v_{1}$ and in the under half-plane (sea) is $v_{2}$ and $v_{2}<v_{1}$.
From the starting point (1,...
- 2,022
-1
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2
answers
145
views
Marginal revenue of a monopolist [closed]
A monopolist faces a demand function $Q=4000(p+7)^{-2}$. If she charges a price of p, her
marginal revenue will be:
(a) $p/2+ 7$
(b) $2p+ 3.50$
(c) $p/2-7/2$
(d) $-2(p+7)^{-3}$
Correct answer is ...
- 1,141
1
vote
1
answer
103
views
Production functions total cost
Production function is: $f(L,M)=L^{1/2}M^{1/2}$. L is the number of units of labour, M of machines used. Cost of labour is 9 per unit, whereas the cost of machine is 81 per unit. Total cost of ...
- 1,141
1
vote
2
answers
56
views
How to use the properties of the logarithmic function
I'm coding the game asteroids. I want to make a levels manager who can create a infinity number of level increasing in difficulty.
My levels have as parameters :
The number of asteroids on the board;...
- 1,620
1
vote
2
answers
61
views
Is there any way to find out how many intervals greater than x exist in a list of values?
I'm not a professional mathematics, but I have a problem of applied mathematics. Beforehand, I apologize for not using more technical terms. I hope I can be as clear as possible:
Given the following ...
- 179
1
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0
answers
14
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Indexing interactions between and withing entities
I'm trying to create/find an index to compare/order systems with multiple entities based on the diversity of the interaction between the entities.
Assume you have few systems of entities that can ...
- 11
0
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2
answers
778
views
Can any function represent something in the real world?
We know that the volume of a cube can be represented by the function: $V(x)=x^3$, where $x$ is side length. $x^2$ can represent the volume of some material that has a constant side ($1$). The function ...
- 159
0
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2
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1k
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Finding maximum of convex function (appliance of derivatives)
The task goes as following:
Divide the length of $14$ into parts $a$ and $b$, in a way that the sum of surfaces of two squares (which sizes are $a$ and $b$), is minimal.
$14=a+b => b=14-a$ $....(...
- 657
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1
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266
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An $\Bbb{R}\to\Bbb{R}$ function with two plateaus of different heights and a valley
I am looking for a $\Bbb{R}\to\Bbb{R}$ function $f$ with two plateaus of different heights and a valley.
The function has a minimum for $x=a$ and $f(a)=b$.
The first (the one for smaller $x$) ...
- 1,058
2
votes
2
answers
212
views
Function application (word problem)
The problem:
My work so far:
$3=log(\frac{A}{A_0})$--->$10^3=\frac{A}{A_0}$
$\frac{A}{A_0}=1000$
(Am I done there?)
Plugging it in:
$M=log(\frac{1900000}{1000})$
$10^M = \frac{1900000}{1000}$
$M=3....
- 309
1
vote
1
answer
46
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How to write this function?
I do not want the answer given to me, I just want assistance.
Problem: Marcus invests $750 in an account that pays 9.8% interest compounded annually. Write a function that describes the account ...
- 309
0
votes
1
answer
29
views
Evaluate a Variable Defined in Terms of its Function
I have a variable x which is defined as follows:
x = 150 / (7 + f(x)) where f(x) = 0.005 * x if x > 200, or 100 otherwise.
This is actually a simplified version of a real world problem.
How do I ...
- 201
1
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2
answers
1k
views
What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley?
What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley?
I have a set of points in $\Bbb{R^2}$ and I would like to fit a curve to the points, the points approximately lie on a ...
- 1,058
0
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3
answers
3k
views
I need a differentiable function whose plot is a plateau and the steepness and width can be varied arbitrarily and easily
I need to model the solar radiation incident on a solar panel. I tried using $$\tanh(b*(x-a))-\tanh(b*x)$$ but it does not give me a lot of flexibility with the characteristics of the curve, namely ...
- 11
2
votes
2
answers
390
views
An injective map where each value is mapped to many others?
I want "something" ("something" because maybe it is not really a mathematical function, called F in the above image) that can describe what is shown on the image. A given value from a domain Xi can be ...
- 1,072
6
votes
2
answers
15k
views
What are functions used for?
When I say functions, I don't mean the trigonometric functions like $\sin$, $\cos$, and $\tan$, I mean defined functions like $f(x) = 2x + 4$. Why is $f(x)$ used and why isn't a single variable ...
- 4,287