All Questions
Tagged with applications algebra-precalculus
44
questions
28
votes
4
answers
6k
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Consider a man who travelled exactly 2 km in two hours. Is there a one-hour interval when he traveled exactly 1 km?
Question :
Consider a man who travelled exactly 2 km in two hours.
Is there a one-hour interval when he traveled exactly 1 km?
Can we make a mathematical argument?
I have written my attempt in an ...
- 3,227
2
votes
1
answer
86
views
Extending baker's percentages to preferment recipes
I'm trying to solve a simple problem I created for myself. I'm no mathematician, so any help is greatly appreciated.
Background
In baking and "baker's math", the amount of each ingredient is ...
- 21
0
votes
0
answers
45
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....
- 459
3
votes
2
answers
1k
views
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 ...
3
votes
2
answers
92
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Can we find an inverse of a model for deadtime?
This is kind of a real-world question, in that it comes from the work I do, but I'm just pursuing it for my own edification.
When a radiation detector detects an event, it is insensitive to further ...
- 211
11
votes
3
answers
471
views
Roots of a set of nonlinear equations $ax + yz = b_1; ay + xz = b_2; az + xy = b_3$
Let $a$ be a non-negative real number, $b_1, b_2, b_3$ be real numbers, and $x, y, z$ be variables. Is it possible to analytically find the root closest to origin $(0, 0, 0)$ of the set of nonlinear ...
- 283
1
vote
1
answer
46
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What method should I use to solve rational equations like this for a different quantity?
With electronics, various characteristics of a device can often be described by solving one equation for different quantities. The problem that I run into a lot with my textbooks is that I can't ...
- 13
0
votes
0
answers
70
views
Arc length vs Surface of revolution.
I don't understand why these two problems are solved differently here the first one $fig(1)$ and 2nd one $fig(2)$. Why did we take the limit $\displaystyle \lim_{r\to0^+}\int_r^\pi \sqrt{2-2cost}\...
user1062191
0
votes
1
answer
63
views
Why can we apply the surface area of revolution theorem to a spiral?
To find the surface area generated by revolving function f which is smooth on the interval [a,b] and $f(y) \ge0$ around the y-axis we can use the formula $$S=\int_a^b 2\pi rdl =\int_a^b 2\pi f(y)\...
- 318
1
vote
1
answer
61
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Why can we say here that $\Delta x_i=dx$ as $i$ approaches infinity?
In the proof of the arc length formula we assume that an element of the arc length is $$\Delta L_i=\sqrt{(\Delta x_i)^2+(\Delta y_i)^2}=\sqrt{1+\left(\frac{\Delta y_i}{\Delta x_i}\right)^2}\space \...
user1062191
1
vote
1
answer
50
views
Calculus application question
My attempt:
Step 1: Find $x$ in terms of $t$.
$\frac{dt}{dx} = \frac{1}{-0.15x}$
$t = \frac{1}{-0.15}\ln(x) = x^{-1}(t)$
$x(t) = e^{-0.15t}+c$
However, here is where I am stuck. Without any extra ...
- 1,190
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
0
votes
1
answer
320
views
Calculus - Calculate Work done to lift water out of tank
I need help setting up the integral so that I can calculate the work done. I've tried it many times and have referred to Youtube, slader, the textbook, and also this site, but I still don't get how to ...
- 133
0
votes
0
answers
380
views
What are the real life application of absolute function?
The well-known absolute function $|x|$ has many uses in mathematics, physics, etc. I know one of the majority applications of abs function in the alternative current making with diodes. But it is ...
- 25.2k
0
votes
1
answer
60
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Interpretation and use of the logarithmic scale for high school students
Often when we discuss on the logarithms in high school we also talk about a scale called logarithmic.
In the he logarithmic scale: the distance from $1$ to $2$ is the same as the distance from $2$ to ...
- 7,792
1
vote
1
answer
90
views
Why $\int_0^h 2 \pi \frac{rx}{h} \, dx \neq \pi rl$
I'm new to calculus.
I saw a proof for volume of cone using integral. They taken the cone's vertex at $(0,0,0)$, it's base centre at $(h,0,0)$ and it's radius is $r$
$$V=\int_0^h \pi \left(\frac{rx}{h}...
- 15
0
votes
2
answers
195
views
One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town.
One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town. At time $t=0$, the first train is $70$ miles south and the ...
- 485
2
votes
1
answer
58
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Optimizing Video Game Crafting with Two Variables
In a certain video game, it is desirable to maximize the occurrence of crafting an item $B$, which depends on possessing the proper quantities of material. To construct 1 $B$ one needs 1 of ingredient ...
- 123
-1
votes
3
answers
2k
views
How to find effective rate of interest?
A man charges at the rate of $10$ paise per rupee per month, payable in advance. What effective rate of interest does he charges per annum?
Here rate is $10\%$ per month. So to change it in per annum,...
- 41
2
votes
0
answers
184
views
f(x+s)=f(x)f(s) imply that f is an exponential function when f(0) = 1.
I was reading a proof for a theorem in Erhan Cinlars intro to stochastic processes textbook that any equation with the following $f(x+s) = f(x)f(s)$, with $f(0)=1$. Then $f(x)=e^{(-ax)}$ for some $a$. ...
- 21
0
votes
1
answer
97
views
Related Rates (Shadows)
Let me first apologize for what must be the $\frac{1}{\epsilon}$ th related rates question on this site, but I really have no idea how to tackle this. From Keisler's "Elementary Calculus":
Problem 3....
- 123
0
votes
1
answer
206
views
Is there any reason to "anti-simplify" this expression?
I was tutoring a precalculus student, and the question at hand was asking to find the angle between two vectors, given the formula
$$\cos \theta = \dfrac {\mathbb{u} \cdot \mathbb{v}}{\|\mathbb{u}\|\...
- 23.8k
2
votes
0
answers
64
views
In search of a College Leve Pre Algebra Applications Textbook
I am looking for a textbook at the college level that mainly focuses on applying algebra to situations. I want students to know how to set up the equations, not just solve them.
- 21
2
votes
1
answer
775
views
Verify a scanned barcode with math
I have an id number that needs to be read off a sheet of paper with a barcode by a scanner. Most of the time this will work flawlessly but sometimes there are mistakes (like if paper is partly torn).
...
- 123
8
votes
2
answers
192
views
Imaginary $\cos^{-1}$ value significance?
When I was bored in AP Psych last year, I jokingly asked myself if there was a cosine inverse of $2$. Curious about it, I tried calculating it as follows:
$$
\begin{align*}
\cos (x) &= 2 \\
\sin (...
- 1,871
2
votes
1
answer
117
views
Creating a weighted score
I have an audit where there are six criteria, each can be scored Excellent (E), Satisfactory (S), Needs improvement (N) or Unsatisfactory (U).
I know that if someone scores Excellent in all six areas ...
- 123
2
votes
1
answer
105
views
Application of Dimensional Analysis Problem
It is given that the radius $R$, in meters, of the expansion of a liquid in the soil is given by $t$ (time elapsed since the liquid was released), the mass $M$ of the liquid released and of the ...
- 79
43
votes
18
answers
65k
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What is an example of real application of cubic equations?
I didn't yet encounter to a case that need to be solved by cubic equations (degree three) !
May you give me some information about the branches of science or criterion deal with such nature ?
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
4
votes
3
answers
12k
views
Real world situation with System of Equation with 3 variables?
Where do you run into a real world situation involving 3 variables and 3 equations? Can someone think of a specific example from business, etc? I recall taking an operations research course that ...
- 4,771