# 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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### ratio of derivatives

({deriv(y, x)}^7derivN(x, y, 3)+{deriv(y, x)}^3derivN(y, x, 3))/({deriv(y, x)}^2{derivN(y, x, 2)}^2) When I looked at this problem I thought the problem is incorrect as we have not been given y as a ...
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### What is the greatest remainder if you divide a 2-digit number by its digit sum

I just found this problem and tried to solve it. I wrote x=90a+b and tried to maximize the function f(a,b)=(9a+b)/(a+b) but did not come to any solution. Then I considered 10a+b = x (mod a+b) which ...
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### Algorithm for multiplying infinite decimals?

What is the (best) algorithm for multiplying two real numbers based on their decimal expansions? Obviously the algorithm can't be completed but I mean an algorithm that will successively approximate ...
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### What is the value of xyz?

If $a,b$ and $c$ are not equal to $0$ and $1$ and if $a^x=b,b^y=c,c^z=a$,then $xyz=?$ We have tried to solve by equation,but it can't produce the desired result.
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### Hoses in the Road [on hold]

Perhaps you have seen the hoses in the road measuring traffic flow and vehicle speed. A car traveling over them will first hit the back hose and then the front hose. A computer measures the time ...
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### Finding the domain and range of a difficult piecewise composite function

I recently inquired about finding a formula for a composition of two piecewise functions, but I have been thoroughly confused by a slightly different example. In this case, I have a question about ...
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### Convert ranges to other ranges

It may be pretty basic but I am looking for an efficient way to convert a number with a range of 15-40 to another number in the range of 255-0. so at ...
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### Maximum and minimum of $f(x)=\cos(\sin(x))-\sin(\cos(x))$

Given the function: $$f(x)=\cos(\sin(x))-\sin(\cos(x))$$ it has absolute maxima at $x=(2k+1)\pi$ with $k=0,1,..N$ and relative maxima at $x=2k\pi$. It is not clear where are the minima. Putting the ...
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### if $x \neq 0$ and $x = \sqrt{4xy - 4y^2}$, then how does expressing $x$ in terms of $y$ mean $x = 2y$?

I have the equation $x=\sqrt{4xy - 4y^2}$, and I know that $x=2y$ when expressed in terms of $y$, but I'm not sure of the process to get there. I know that \begin{align}\sqrt{4xy - 4y^2} &= \...
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### Correct Order of Applying Graphical Transformation with Absolute Value

I was going through this website, reading about transformations of graph when $| |$ is applied to various parts of a given function, $y=f(x)$. Going through the fourth example of the page, I came ...
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### Calculating length of vertical line bisecting parallel arcs

I have 2 arcs, offset from one another (never intersecting) and a vertical line through them both (NOT at the center of the arcs). Is there a way to calculate the vertical distance between the 2 arcs? ...
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### Solving Quadratic system of equations

Solve this system of equations: $$(1) \quad 0=-10x^2-9xy+50x-25y-7y^2+5$$ $$(2) \quad 0=-5x^2-17xy+25x+50y-14y^2+7$$ Shame on me but I'm failing to solve this system. I can't see a short (...
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### Find equation for $f(x)=a^{-x}$ graph from points given?

An example of the graph I want to find the equation for this graph with the known point of (120,5)and approximate points of (300,2) (225,2.5) and (150,4). Can I do this or do i need more information?...
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### Proving that $x^{16} > 5$ when given a polynomial of degree $15$. [on hold]

I am unable to prove the following If $x^{15}-x^{13}+x^{11}-x^9+x^7-x^5+x^3-x = 7$ prove that $x^{16} > 15$.
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### Simplify this equation.

Can I simplify or approximate this equation without sigma and combination? \begin{align} \sum_{i = 0}^n (-1)^i {n \choose i} \frac{{d+1}}{d(di + 1)} \end{align}
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### Intersection of Circles and Triangulation [on hold]

Tracking a Cellphone CT1 to CT2 = 700m CT2 to CT3 = 1200m CT1 to CT3 = 1350m Cell Phone is 600m from CT1, 650m from CT2, and 800m from CT3 Draw a circle in each Cell Tower, indicating the distance ...
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### On linear equations and equations with fractions

I'm learning how to solve equations. When solving linear equations I've learnt we have 2 elemental and allowed operations, one of them is the following: If $P=Q$ is an equation then $aP=aQ$ is an ...
Six congruent isosceles triangles with equal sides $x$ cm are removed from the six corners of a paper in the shape of a regular hexagon of sides 20cm . The remaining portion is in the shoe of a 12 ...