All Questions
Tagged with applications algebra-precalculus
44
questions
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
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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
views
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
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3
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2k
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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
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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
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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
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206
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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
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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
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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
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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
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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