# Tagged Questions

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### Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?

My idea is that the two functions are not the same since for the first function, the domain of the function is only non negative reals for the numerator and positive reals for the denominator. ...
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### The steps to becoming a Pure Mathematician

I'm a college freshmen intending to major in Mathematics. I started college with not so great grades in my calculus courses. However, I realized that to get the grades I just have to practice. I ...
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### Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
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### “Full”-Simplification of arbitrary mathematical expressions

I've come across many (classroom) problems, like Roy did, whereby the solution to a problem, $$−3(7−2x)^2−5(1+x)^2$$ is the result of simplifying that expression as much as is possible, i.e. ...
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### What is $(k+1)^2[(k+1)+1]^2$ in factored form?

What is $(k+1)^2[(k+1)+1]^2$ in factored form? I'm a bit confused as to what the term "factored form" means in this context. Thank you.
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### Arithmetic and Algebra exercises on latex source code.

I´m currently writing a little book for two student that I teach. The book covers school arithmetics and algebra, and it include theory and examples. Since I don´t have time to prepare a good sets of ...
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### $2 \cos^2 x − 2 \cos x− 1 = 0$ Find the solutions if $0^\circ \le x < 360^\circ$

Find the solutions of $$2 \cos^2 x − 2 \cos x− 1 = 0$$ for all $0^\circ ≤ x < 360^\circ$. For $0^\circ \le x < 360^\circ$, I'm getting $x=111.5^\circ$ and $x=248.5^\circ$. Is this ...
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### How to teach newbie multiply of complex number

I want to teach a newbie the arithmetic law of complex numbers. the law of add is acceptable psychological. but multiply is not. for example, assume $$z = a+bi, w = c+di$$ He (She) may ask me: why ...
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### Parabola problem. How far from the vertex is the focus?

A spotlight has a parabolic cross section that is 8 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? I'm getting 8/5 ft. Is this correct? Appreciated!
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### best books for learning algebra

My name is Aniket and I have started 11th class recently. I have studied only my school textbooks(NCERT Books) and I am not happy with them. I want to learn Algebra,i.e, all the topics covered in ...
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### Find Vector and Parametric Equation

I'm having some trouble finding answers to these problems. When i try to find help online, all i find are (x,y,z) problems and I'm simply looking for a PreCalculus (x,y) problem solving technique: ...
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### function inversion and the horizontal shift

I am currently doing inverse functions and graphing radical equations of the form $y=a\sqrt{x-h}+k$ with my algebra class and one of my students asked me the following question. "Why is it that we ...
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### How would you prove that the graph of a linear equation is a straight line, and vice versa, at a “high school” level? [duplicate]

This is something I've been wondering about. Namely, I've always accepted "on intuition" that the equation $$ax + by = c$$ is, when graphed, a line. You can plot the points $(x, y)$ satisfying the ...
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### Should i continue trying or am i just not good enough [closed]

You've probably seen many of these, and i'm sorry to create another one but i'm at loss. I want to be a programmer at some point in my life (just finishing highschool) I want to go to university ...
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### Explaining how to simplify a quotient with negative exponents?

I work as an after school tutor at my high school. I've had kids come up to me asking how to do these types of problems: $\left(\displaystyle \frac{5xy^{-2}}{3z^{-1}} \right)^{-2}$ My approach is ...
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### How to combat memorization

As a student in high school, I never bothered to memorize equations or methods of solving, rather I would try to identify the logic behind the operations and apply them. However, now that I've begun ...
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### What we're never taught explicitly

I would like to make a complaint really. School math(s) can be the most boring way to learn: sitting down and rote learning binomial expansion or the volume of a cylinder is just not interesting. It ...
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### How can I convince my math teacher?

Ok, so I got an answer wrong on my exam because my teacher says that the function $f(x)=\frac{(x+2)x}{x+2}=x$ but I insist that it isn't defined for x=-2. If it was then $\frac{x}{x}=1$ for all reals ...
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### Elementary Algebra question

Ok guys so I've been out of school for eight years, never used algebra again, also I was forcibly removed from school in 9th grade. I need to ask a few questions on Elementary Algebra, what are the () ...
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### why 0=0 is not possible??

Hi one of my friend showed me one proof i.e. $1)$ $2^2 - 2^2 = 10 - 10$ $2)$ $(2+2) (2-2) = 5 (2-2)$ $3)$ dividing both sides by (2-2) $4)$ $(2 + 2) = 5$ I know this is wrong in first line as ...
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### How to get better at algebraic manipulations?

I've always been able to manipulate equations found in school homework easily. But when tackling more challenging questions from puzzle books - where I might need three quarters of a page to ...
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### Should the domain of a function be inferred?

It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collection ...
Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to ...