# Tagged Questions

Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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### Expand $\ln\left[\frac{(4x^5-x-1)\sqrt{x-7}}{(x^2+1)^3}\right]$.

Expand this expression to the greatest possible terms with the lowest possible exponents. $\ln\left[\dfrac{(4x^5-x-1)\sqrt{x-7}}{(x^2+1)^3}\right]$ There are two ways at which I approached this ...
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### How do I transform the equation based on this condition?

If a and b are the roots of the equation $$2x^2-px+7=0$$ Then a-b is a root of ?
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### Finding the remainder from equations.

I am having problems solving this question : When n is divide by 4 the remainder is 2 what will the remainder be when 6n is divided by 4 ? Ans=$0$ Here is what I have got so far ...
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### Express each of the following expressions in the form $2^m3^na^rb^s$, where $m$, $n$,$r$ and $s$ are positive integers.

I just recently started relearning math as an adult, this should be easy but I have trouble understanding what the actual question is. I am not just looking for the answer to this, I merely wish to ...
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### Prove that $\sum_{k=0}^n k^2{n \choose k} = {(n+n^2)2^{n-2}}$

Prove that: $$\sum_{k=0}^n k^2{n \choose k} = {(n+n^2)2^{n-2}}$$ i know that: $$\sum_{k=0}^n {n \choose k} = {2^n}$$ how to get the (n + n^2)?
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### Composition of a piecewise and non-piecewise function

Say you have 2 functions, one of which being a piecewise function: $f(x)= x^2+2, x<1$ or $2x^2+2, x>=1$ And the other: $g(x)=x^4+1$ How would you find the $f[g(x))]$? I understand regular ...
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### Solving $x^3 + x^2 - 4 = 0$

Does anyone know how to solve $$x^3 + x^2 - 4 = 0$$ analytically? That is, without using numerical methods to attain an approximate solution.
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### Intersection of a plane with an infinite right circular cylinder by means of coordinates

So, I started studying analytic geometry and I must say I'm finding it much harder than "classic" geometry, because of the equations without help from diagrams... Still, I wanted to see how to use it ...
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### integer ordered pair,s $(x,y)$ in $1!+2!+3!+…+x! =y^3$

(1) Total no. of integer ordered pair,s $(x,y)$ in $1!+2!+3!+............+x! =y^2$ (2) Total no. of integer ordered pair,s $(x,y)$ in $1!+2!+3!+............+x! =y^3$ (3) Total no. of integer ordered ...