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Question about a g-force simulator in question 6, part b, regarding the moments in a balanced system at rest.

The following is regarding question $6$, part $b$, in the following link: https://thol.sunway.edu.my/examdbase/alv/math/p3/math_p3_j96.pdf Using the principle of moments and considering the case ...
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0answers
22 views

Notation for points in 2d or 3d coordinate systems P(a|b|c)? Origin and reasons?

In every german high school book about vector geometry, points in 2d or 3d cartesian coordinate systems are denoted like $P(2|-1|5)$. Very rarely one also reads something like $P = P(2|-1|5)$. But I ...
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1answer
54 views

How do I find a percentage with only the mean and standard deviation?

'If we have a set of scores that are normally distributed and have a mean of 20 and a standard deviation of 5, what percentage of scores are greater than 20?' Now I know the answer is 50%, because ...
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2answers
30 views

Query on previous post regarding the distance formula for perpendicular lines and negative slopes made 2 years ago.

In the post made 2 yrs ago 'Explain why perpendicular lines have negative slopes', Explain why perpendicular lines have negative reciprocal slopes How does the distance formula get applied to obtain ...
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3answers
46 views

Suggestions on Progressing in (Meta)Mathematical Development [closed]

[Straight to the Point] I would really appreciate any suggestions on self-study materials that relate to math, logic, and/or the philosophy of both. Also, any thoughts or suggestions that you may ...
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4answers
428 views

Map closed under addition but not multiplication

I have been helping undergrads in an introduction to linear algebra course. When solving some exercise consisting in showing that a map is linear some get lazy after proving that it is closed under ...
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0answers
36 views

Can I get some help to make my answer more rigorous for this problem in the book Concrete Mathematics [duplicate]

I'm a freshman in college this semester without any previous experience in rigorous proofs or such, however I am interested in the learning more about mathematics and for that reason I picked up the ...
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2answers
90 views

What topics should be included in a course matching these specifications?

Say you have a calculus classroom full of liberal-arts majors who are not particularly mathematically inclined. Your goal is NOT to teach them everything on a list of topics that will be needed in ...
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0answers
17 views

Can sombody give me an ntuitive explanation about regression estimates as weighted averages?

I am trying to study weighted least square and found one article that sounds like it is explaining what I am trying to study. But I want to get some intuitive explanation about each calculation and ...
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0answers
15 views

Percentage Calculation - Cells per micro litre

I came across this simple percentage calculation and I couldn't solve it (I couldn't prove otherwise). Here's the problem. Find percentage for 11/0.1 ul (11 cells per 0.1 micro litre). Any pointers ...
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2answers
36 views

Prove that $|x − y| < \epsilon$ , $|y − z| < \epsilon$ implies $|x-z|<2\epsilon$

I need the math.triangle inequality formula, but I still didn't get it fully. be die|x|+|y| <= |x+y| |x|+|y| <= |x+y| I put in the values |x-y| < ε <= |x|-|y| < ε |y-z| < ε ...
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0answers
33 views

How can I explain a Zero Knowledge Proof with minimal mathematics

I asked this earlier on how to explain a Zero Knowledge Proof to a layman. but I'm looking for a mathematical analogy that might "enhance" the superpower explanation. In that linked superpower, that ...
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0answers
147 views

I have a free summer before university. What should I learn? [closed]

Note: This is a soft question. It may be a bit early to be thinking about this, but I figured I'd ask now and see what responses I get. I'm currently a high school senior, and I quite like pure ...
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0answers
90 views

Calculus as a structure in the sense of Model theory

I am not a specialist in Logic (my field is Functional Analysis), so excuse me my ignorance. I suppose there must be texts where Calculus is presented as a structure in the sense of Model theory. I ...
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0answers
52 views

What to do when finding “complex” result by accident?

This happened a couple of times today. While working on some problems, you find unexpected relationship between objects, which are not obvious to find directly. For example today I found out that $$\...
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7answers
1k views

Can someone provide the formal definition of the tangent line to a curve?

I was recently explaining differentiation from first principles to a colleague and how differentiation can be used to obtain the tangent line to a curve at any point. While doing this, my colleague ...
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3answers
147 views

Is it possible for extremely ingenious but elementary proofs for famous problems to exist?

As Erdős put it, "Mathematics is not ready for such problems." when faced with the great conjecture of Collatz. So is it impossible altogether for simple but ingenious proofs for famous problems ...
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3answers
1k views

Non-Euclidean Geometry for Children

I should've asked this question two years ago when my son (at that time, 9 years old) came to me and said: "Dad, today in school our teacher drew a line on a paper and said this is a straight line, it ...
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1answer
55 views

Subtlety in integration by parts

We all know the rule of integration by parts: $$\int a(x)b'(x)dx=a(x)b(x)-\int a'(x)b(x)dx$$ But most calculus textbooks lay it down without proper discussion, since what happens if the product $a(x)...
2
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1answer
95 views

Johann Carl Friedrich Gauss [closed]

I've been asked to give a brief over view of the mathematician Carl Gauss' life, so i should include his birth, family, education, occupation, death, who influenced him, his major contributions and ...
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5answers
464 views

Show $\lim\limits_{h\to 0} \frac{(a^h-1)}{h}$ exists without l'Hôpital or even referencing $e$ or natural log

Taking as our definition of exponentiation repeated multiplication (extended to real exponents by continuity), can we show that the limit $$\lim_{h\to 0}\dfrac{a^h-1}{h}$$ exists, without l'Hôpital,...
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1answer
28 views

A “Simple Chain of Regions” and Compactness in the Continuum

Let me just start by saying that I'm basically trying to prove this: How to prove every closed interval in R is compact? Except that I need to do it in a very strange way... I'm teaching an Inquiry-...
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1answer
84 views

Visual questions for 6th graders

I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed ...
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1answer
20 views

Annuities-calculating interest

Janet receives a $ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 1613.36. If a 2n-year annuity due is purchased, the annual ...
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1answer
20 views

Prove some divisibility with deductive way

I have some proves But I want to prove them with deductive not inductive. Here are my proves: 1) $2^{3n} - 1 $ is divisible by 7. 2) $2^n + (-1)^{n+1}$ is divisible by 3. 3) $n^2 + 2$ is not ...
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3answers
31 views

derive binomial distribution for a classroom

I am supposed to give a 20-min presentation to a group of kids aged around 14-15, so they have very limited knowledge about the topic in advance -- at the same time I want the talk to be something ...
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0answers
17 views

In-depth resources

How to learn mathematical topics in-depth? For instance, if you want to learn about Symmetry, you would use Google, you'll get results. Unfortunately, what you'll find is tutorials for beginners. But ...
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1answer
25 views

Linear problem using the simplex algorithm

Maximise $8x_1+4x_2+5x_3$ subject to $x_1+2x_2+x_3\le10\\2x_1-3x_2\le8\\x_1,x_2\ge0;x_3\text{free}$
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0answers
23 views

Find basic solutions using matrices? (and determine which ones are bfs)

I'm trying to find all basic solutions using matrices. Then I'll try to determine which ones are bfs. Minimize $3x_1-x_2$ subject to $x_1-3x_2\ge-3\\2x_1+x_2\ge-2\\2x_1+x_2\le8\\4x_1-x_2\le16\\...
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2answers
34 views

How to convert linear programming model to standard form?

This might be a stupid question. For that, I'm truly sorry. But I appreciate any help!
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1answer
53 views

find the derivative of (cosx)^(sinx)^x

Solve to find the derivative of the following function: (cosx)(sinx)x Do not simplify the answer.
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2answers
36 views

How to convert mathematical program into an LP?

This might be a stupid question. For that, I'm truly sorry. But I appreciate any help! minimize (max {2x-4, |x|}) subject to -3 <= x <= 6
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2answers
98 views

Showing that $\cos (\sqrt x)=e^x-2$ has solution in $(0,1)$

I rephrased this problem as finding a solution of $f(x)=e^x-2-\cos(\sqrt x)$ in $(0,1)$. I apply the intermediate value theorem: $f(0)=e^0-2-\cos0=-2$. The goal is to show $f(1)>0$ (which is true) ...
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0answers
30 views

Function satisfing : $h(x)=f(2x-1)$ with $f'(-1)=0 $ and $f'(2)=-2$ then what is $h'(x) $?

I find in some book this function defined as follow $h(x)=f(2x-1)$ . with $f'(2)=-2 $ and $f'(-1)=0$ , we would like to know $h'(3/2)$ ? In the book take $h'(x)=f'(2x-1)=(f'(2))x+f'(-1)=-2x $ but ...
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0answers
31 views

Powerful pictures or plain proceedings?

After tutoring someone about polynomial manipulation, my mind went back to this equivalence: $(a+b)\times (c+d)=ac+ad+bc+bd$ I realized that, while it can be memorized as it is, it has a very simple ...
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2answers
230 views

What is the right way to define a function?

Most authors define functions this way: Given the sets $A$ and $B$. A relation is a subset of $A\times B$. Then given a relation $R$, we define $Dom_R=\{x|(x,y)\in R\}$ and $Img_R=\{x|(y,x)\in R\}$. ...
2
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3answers
133 views

mathematical rigore for an engineer! [closed]

I recently bought a used copy of "Mathematical Analysis" by Apostol for \$1.0 and "Probability and Measure Theory" by Robert Ash for \$3.0 (well another \$3.99 for shipping)! When I read the first few ...
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1answer
19 views

Slope in algebra I

What is a good project for teaching y=mx + b and having students discover slopes of lines in classroom or on the classroom buildings?
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2answers
210 views

False notion of Limit in Stewart's “Calculus”

In calculus, when we take limits of functions, say $\lim_{x\to a}f(x),$ do we require that $x$ tends to $a$ from within the domain? For example, I would say $\lim_{x\to 0} \sqrt{x}=0$ since I am ...
3
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1answer
95 views

Publish pedagogical results as an undergraduate

As an undergraduate, I became fond of real analysis and complete metric spaces. Regarding completeness (mostly in R), I proved the same theorem in perhaps 10 different ways, using different approaches ...
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63 views

Undergrad looking for study material/advice for applied mathematics.

I am an undergraduate math student (junior) who is looking to get a masters degree in Applied Math. I like pure math, but I want to use my education to get a great-paying job. Here are a few questions ...
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1answer
51 views

Can we find $ a + b $? [closed]

How can we find the value of $ a + b $ in the following question? a & b are integers. Question: If $ a^{2} \times b^{3} = 216 $, find $ a + b $.
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2answers
115 views

What (previously and currently unsolved) problems motivate the study/development of analysis?

As I had ever know there are at least two (previously unsolved) problems motivate the study/development of abstract algebra: (1) the ancient Greeks' three problems in compass-and-straightedge ...
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0answers
40 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
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0answers
29 views

in nested brackets which would be outermost bracket

i wanna know that in an algebric equation of 2 level nested brackets which format of nested bracket is correct {4[3+5(3+2)]} [4{3+5(3+2)}] is curly would be outermost or square
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0answers
61 views

What to do with java-based math demos? [closed]

A large volume of mathematical demos were written in Java. Then came security warnings of all sorts. Currently it does not seem viable to direct students to such demos. Do you think an organization ...
0
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2answers
36 views

problem proof of induction $2\cdot3^0+2\cdot3^1+2\cdot3^2+…+2\cdot3^{n-1}=3^n-1$

I need to prove that $2\cdot3^0+2\cdot3^1+2\cdot3^2+...+2\cdot3^{n-1}=3^n-1,\, n=1,2,3,4...$ I know when n = 1 the left side $=2\cdot3^{1-1}=2$. The right side is $2^n - 1=2^1 - 1 = 1$. Thus the ...
3
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1answer
53 views

Could someone make the proof into a hinted exercise?

Let $(c_n)$ be a sequence of positive numbers. Could someone make the proof of the inequality $\displaystyle\limsup_{n\to\infty}\sqrt[n]{c_n}\leq\limsup_{n\to\infty}\frac{c_{n+1}}{c_n}$ into a ...
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1answer
56 views

For an introductory analysis class, why is it that many people avoid teaching it using sequences?

I am currently taking an honors introduction to analysis course, and it seems to me that to me defining all of the concepts in terms of sequences allows for much cleaner proofs, and the concepts are ...
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1answer
64 views

Variation on the “Number of non-bald people in NYC” problem

I have two questions about the following problem, taken from Challenging Problems in Algebra by Posamentier and Salkind: (1) Why is the answer not 1 person? (2) The answer given, without solution, is ...