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Questions tagged [education]

For questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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2answers
26 views

Solving PAT equation with 2 logs

Taken from the PAT (Physics Aptitude Test): $\log_x 25 = \log_5 x$ I've tried making them the same base but I ended up with: $\log_5 x (\log_5 x)= 2$ or $\log_x 25(\log_x 5) = 1$ which I then ...
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0answers
25 views

What are strategies to teach math to dyslexic? [on hold]

What are some resources and /or strategies to teaching math to a dyslexic grader schooler?
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0answers
28 views

Where can I study polynomials online?

I have one good book on polynomials. It is called (Level of Knowledge of Polynomials) by its author S. L. Tabachnikov. In principle, I could study it, but I am still mastering the Agebra I. Not long ...
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2answers
38 views

If $a, b, c,$ and $d$ are integers and $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}+\frac{1}{d}$ where both sides of the equation be the same

If we have integers $a$, $b$, $c$, $d$ and $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}+\frac{1}{d}$,when will both sides of the equation be the equal. So what that means is that for integers $a, b, c,$...
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0answers
54 views

Help with inequality with one unknown

Please could you help how to solve the inequality $(\sqrt{x-9})(2^{x-8}+3^{x-9}-9)\geq 0$
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2answers
25 views

What is measurement of angle D? [closed]

Angle 1= Angle 2, Angle 3 = Angle 4, Angle A = 90º What is the measurement of Angle D?
2
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1answer
46 views

I'm halfway stuck solving an Integral derivation.

I apologize beforehand for my handwriting. I hope it is legible. I worked the problem on a piece of paper. Took a picture and attached it to this query. I wrote the problem starting with Page 1 and ...
-1
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1answer
47 views

What is the meaning of sentence E | x?

How to read this math notation? Let closest(j) be the set of all points that are closest to centroid cj. The algorithm proceeds during several passes, during each of which it updates each centroid ...
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0answers
29 views

Calculating the asymptotes of an hyperbola from the general equation [duplicate]

Suppose that the conditions which ensure that the following equation is an hyperbola are verified: $$ax^2+2bxy+cy^2+2dx+2ey+f=0$$ What are the general expressions of the two asymptotes of the ...
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0answers
7 views

Q: How much overlap is there between pure and applied graduate courses, in the UK?

I am a final year BSc Mathematics student and I am seriously considering taking a Master's sometime soon. Some institutions have two separate courses for pure and applied maths. My question is, if I ...
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1answer
24 views

Rotation of a non rectangular hyperbola: equation of hyperbola referred to its asymptotes

I'm looking for a way in which I can rotate a non rectangular hyperbola; in particular I'd like to get the equation of a non rectangular hyperbola referred to its asymptotes. To do it I need to ...
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0answers
25 views

Partial derivatives and composite function

Given a function of two variables from $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$, we write/denote this function as $$f:(x,y)\mapsto (u(x,y), v(x,y)).$$ Consider another function, the polar coordinate ...
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1answer
23 views

Scalar relationships between the coordinates of two rotated coordinate systems

I'm wondering how come between the coordinate system $\xi \eta$, rotated -45° with respect to $x y$ coordinate system, and the $xy$ coordinate system there are the following relationships: $$x = \...
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2answers
23 views

Semi axes of a shifted rectangular hyperbola

I would like to know which are the semi axes of a shifted rectangular hyperbola: $$(x-c_0)(y-d_0)=A$$ In the classic case it is easy to find them: $$(x/a)^2-(y/b)^2=1$$ $a$ and $b$ are the semi ...
0
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1answer
35 views

is there a difference between the function y=x/x and the function y=1. [duplicate]

I have been asking people and have been getting mixed answers. some people think it is the same because when you simplify the first one you get y=1, but some people think that they are different ...
0
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1answer
72 views

If $x^y = xy$, what is $y$ in terms of $x$?

I know that $x=y^{\frac{1}{y-1}}$ but I cannot solve for $x$. Can somebody please help me? It should be possible because it is a very simple equation, can somebody please solve it.
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0answers
16 views

Meaning when a set has an accumulation point and its negation

Let $D'(a,r):=D(a,r)\setminus \{a\}$ be the punctured disc with centre $a\in \mathbb{C}$ and radius $r>0$. Let $A\subseteq \mathbb{C}$ be given. A point $a\in\mathbb{C}$ is called an ...
2
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0answers
49 views

Solving $x^x=y^y$ [closed]

In the equation $x^x=y^y$, how do you solve for $y$ in terms of $x$ when $y$ is not $x$? There is a small curve in the first quadrant which is not $y=x$. graph: https://www.desmos.com/calculator/...
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1answer
34 views

Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 6…5/1…5 [closed]

Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 6...5/1...5 Answer ASAP please
1
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2answers
24 views

Derivation of a well-known property of the standard normal distribution

I have found the following property of the standard normal distribution: $ \int_r^\infty xf(x) dx = f(r) $ where $f(.)$ is the pmf of the standard normal distribution. $f(r)$ and $F(r)$ are ...
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4answers
70 views

How to you use the trigonometric functions without a calculator?

Every single time I do anything with circles/triangles I always run into the primary trig ratios. With radians, I found some hope, but it was short-lived, because yet again we needed trig functions to ...
5
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1answer
73 views

Request for info about Real Analysis to a beginner [closed]

So I'm a junior HS student very interested in mathematics and I think I have pretty good chances to get admitted into Stanford online HS and take a university level real analysis course that's worth 5 ...
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0answers
37 views

When do you learn calculus 1, calculus 2 and calculus 3?

As an English student who is using an American resource for learning material, could someone explain at what age you would learn calculus 1, calculus 2 and calculus 3?
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0answers
11 views

How to decide weights for calculating weighted mean to penalize extreme values

I want to find a weighted mean of some positive numbers. Weights should be calculated to 'penalize' extreme values. What an extreme value is depends on the other values in the set. For simplicity, ...
23
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6answers
3k views

Why do early math courses focus on the cross sections of a cone and not on other 3D objects?

Conic sections seem to get special attention in early math classes. My question is why do these cross sections of cones deserve more attention than those of, say, a rectangular prism, a cube, or some ...
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0answers
44 views

Japanese mathematics textbooks past grade 9

I cam across a list of mathematics textbooks used in japanese schools http://mathforum.org/kb/servlet/JiveServlet/download/206-2579263-9150698-840231/MathInternational0313_s%20GER.pdf Are there ...
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1answer
21 views

is the correlation between two things separated by a comma a compact way of writing two statements?

I want to know if corr({a,b},c) = 0 is the same as saying that corr(a,c) = 0 corr(b,c) = 0 But that the first is just a short-hand way of writing it.
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1answer
40 views

Infinite sums and squares

So, I'm sure this has been thought of and said before but I'm curious. So $\sum \frac{1}{2^n}$ can be thought of by filling up a square. First we color in a whole square and then we draw a second ...
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2answers
52 views

sigmoid function: an algebraic solution

if we have a sigmoid function $1/(1+e^a)$, where $a$ is in the form of $(x-b)/c$ and the sigmoid equals function a value, called $k$. This $k$ is in the form of $1/x^2$. So something like: $1/x^2= 1/(...
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0answers
33 views

Benefit of doing real analysis to understanding earlier topics.

I am not in the senior year of high school yet, and I am self-learning real analysis using Terrence Tao's book (with knowledge in calculus), and have only skimmed through the year 12 (=senior year) ...
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0answers
26 views

Degree of $(y^{\prime\prime})^2(y^\prime)^2=x\sin(y^\prime)$

Degree of $(y^{\prime\prime})^2(y^\prime)^2=x\sin(y^\prime)$ My try: since the highest order derivative is $y^{\prime\prime}$ and it's raised to power $2$, therefore I think that degree should be $2$...
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0answers
17 views

Time difference of arrival - obtaining a hyperbola from equations, I have the starting values but I'm super confused with the equations.

I need help figuring out some calculations relating to Time Difference Of Arrival, I have two reference points (mics in the real wold), mic 1 and mic 2 are 1.01706 (feet) away from each other, this ...
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0answers
21 views

Taylor Polynomial for Log(1-t) derivation {confused}

I need some help understanding something from my textbook. In the book they are deriving a taylor polynomial approximation for log(1-t), the first thing they do is integrate log(1-t) from 0 to t. ...
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2answers
61 views

How to prove that $\sum\limits_{j = 1}^{n} j(j + 1) = \frac{1}{3}n(n + 1)(n + 2)\ \text{where }\ n \geq 1.$

I would like to know how it is to prove this problem: $$\sum_{j = 1}^{n} j(j + 1) = \frac{1}{3}n(n + 1)(n + 2) \text{where } n \geq 1 \\ $$
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1answer
19 views

how to workout the “finding route” problems, so I won't missing or duplicated in counting.

how to work out this kind of routes counting problem? I always missing or duplicated when counting, is there any good method to do counting or even best, there is a method to calculate for the result?...
2
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3answers
72 views

Understanding Mathematical Induction problems

I have problem to understand this 3 formulas, I am new in this type of problems. I have to solve this problems by induction. \begin{align} \sum_{j = 1}^{j = n} j^3 &= \left(\frac{n(n + 1)}{2}\...
3
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0answers
54 views

Geogebra for Blind People [closed]

I work in the University with students in a situation of disability, specifically, teaching them math and related things. I have a few students that are blind, they work with JAWS or NVDA usually. ...
2
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0answers
37 views

Educational gif-animations on mathematical analysis [closed]

I drew some simplified gif-animations by math. Do you think, they will help in the study of mathematics to people, who have difficulties with this?
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0answers
38 views

how to improve Normalized cross correlation

I used the Normal cross correlation (NCC) calculation to find an equation between two signals or images. now I'm trying to improve the calculations but have no idea. I just need a little improvement. ...
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0answers
22 views

Learning order: improper integrals or integrals applications first?

I am first year's non-math student and during our calculus lectures we were first introduced to definite integrals and their applications, and then to improper integrals. After that we went straight ...
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0answers
18 views

What should be the order of things on an introduction to pure mathematics module?

I want to produce a resource that has a narrative and includes the following topics: Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, ...
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0answers
50 views

How to motivate students to do proofs? [closed]

I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this. How can ...
0
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1answer
72 views

A lamina occupies the part of the disk $x^2+y^2\leq 25$ in the first quadrant.

Here is the question: A lamina occupies the part of the disk $x^2+y^2\leq 25$ in the first quadrant. Its density is $\rho=4$. What is the total mass? What is the moment about the x-axis? What is ...
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1answer
77 views

How to pump water out of a trough to ground level?

Here is the question: A trough shaped tank is located 3 meters underground (The top of the tank is 3 meters away from ground level.) The dimensions of the tank are: height h = 5 meters, length c = ...
1
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3answers
58 views

Looking for a conceptual proof of the pythagorean theorem from first principles

I was considering asking this question on math stack exchange but decided not to because "first principles" seems like more of a physics thing. I'm looking for a conceptual proof of the pythagorean ...
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1answer
83 views

chessboard 7x 7

A 7 × 7 chessboard that is painted black and white, with the corners painted black;and we have the operator "inverse", which can be applied to a single row or single column in a table that it change ...
2
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1answer
41 views

Is there a symbol to mean “$x$ fits completely $v$ times in $y$”?

Is there a simpler way to write "$x$ fits completely $v$ times in $y$," i.e. is there a mathematical symbol or way to write for example: "32 fits 0 times completely in 4" or for example "32 fits 1 ...
2
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2answers
44 views

Soft question: solution strategies, how to attack the problem when using pen and paper?

Whenever I solve a problem (textbook or exams), I always copy key parts of the question to my paper where I'm doing my calculations, even though I have the problem in text-format right next to me on ...
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0answers
17 views

Modeling the relationship between dilations and area?

On a rather basic high school level I want my students to understand the relationship between the scale factor of a dilation and the area of the pre-image and image. For instance if a rectangle has a ...
5
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4answers
77 views

Methodology for Verifying Trigonometric Identities

Lets say I have an equation like: $$\frac{\sin^2x+\cos^2x}{\cos^2x\sec^2x}=1$$ Our teacher said you have to verify the equality by simplifying the left hand side or the right hand side without moving(...