# 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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### Even numbers in Pascal's triangle.

Basically i've been looking at Pascal's triangle and been wondering how it represents Sierpinski's triangle once the even numbers are shaded. Once I rewrote the triangle in terms of C I observed that ...
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### Discrete and combinatoric mathematics (Functions)

$f = ax^2 - b$ and $g = cx + d$ Where $a,b,c,d$ are all coefficients. Find $a,b,c,d$ when $f◦g = g◦f$. Here is what I have: \begin{align*} f◦g &= a(cx + d)^2 -b = a(c^2)(x^2) + ...
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### Growth factor and percent change problems? [closed]

The exercise is Thank you for your help.
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### Show that a complex equation represents a circle

I'm having troubling understanding the answer to a question. The question is: If $\ v=1+i$ and $\ z=x+iy$, for any real numbers x and y: Show that the equation $\left|z-v\right|= \left|vz\right|$ ...
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### Integer coefficients polynomial. Find largest number of roots.

The polynomial $p(x)$ has integer coefficients, and $p(100)=100$. Let $r_1, r_2, …, r_k$ be distinct integers that satisfy the equation $p(x)=x^3$. What is the largest possible value of $k$?
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### Optimizing number of production runs?

I am having trouble with the following problem: A manufacturer of hospital supplies has a uniform annual demand for $180, 000$ boxes of bandages. It costs $20$ dollars to store one box of bandages ...
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### finding the matrix $P$ and $Q$ such that $A=P^{-1}D_rQ^{-1}$ for given matrices $D_r$, and $A$

Let $$D_r=\left[\begin{matrix} I_r &0\\0&0\end{matrix}\right]$$ And $$A=\left[\begin{matrix} 1&4&0&2\\1&1&15&5\\1&3&5&3\end{matrix}\right]$$ By using ...
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### Finding a quadratic's preimage of an open interval

Let $f:\mathbb{R}\rightarrow \mathbb{R}$ $x\rightarrow x^2+2$ Find $f^{-1}((0,2))$ $f(x)=2+x^2$ So then $x\in \mathbb{R}: f(x) \in (0,2)$ So then I did $0<2+x^2<2$ and I got ...
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