# Tagged Questions

Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...

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### Proving a Subset Identity

Working on part A of this problem: I worked out the first part like this: 1) If $A$ is a subset of $B$ then $\forall~x~[x\in A \implies x\in B]$ 2) Same goes for $C$ being a subset of $D$ (If ...
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### Given that $i$ is a root of: $P(x)=x^4 + 2x^3+ 3x^2 + 2x+2$ find all the other roots

I have a simple question here but I don't know how to solve it. Given that $i$ is a root of: $P(x)=x^4 + 2x^3+ 3x^2 + 2x+2$ find all the other roots. Help is much appreciated. Thanks.
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### Modeling salt and water with differential equations

From Differential Equations (Blanchard, Devaney, and Hall, page 35). My question is about the model. I let $x$ be the amount of salt and $t$ the minutes passed. Then ...
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### How to properly generalize a definite integral?

I know, I know. On the can, this problem seems simple. Just take $\int_a^bf(x)\mathrm{d}x$ and write is as $\int f(x)\mathrm{d}x$. However, when I tried to do that on an Engineering Dynamics ...
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### graph theory: show that for k=4 hesse diagram is not a planar graph

In this picture you can see the hesse diagrem of $\subseteq$ over $P(\{x,y,z\})$ For the set $A$ with $k$ elements, $k>0$ look at the diagram as a graph, it's vertices are the members of $P(A)$ ...
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### Subsets and Cardinality

I'm confused on if I should count a subset as one element or if I should count all the elements of that subset when computing cardinality. Example: Given the set $A = \{1,2,3,\{4,5,6\}\}$ does $A$ ...
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### Maximal Ideals and Maximal Subspaces in normed algebras

This is a kind of "prove or give a counter-example" question, and I'm having some difficults with it: By a maximal ideal $I$ of an algebra $A$, we mean an ideal $I\neq A$ which is not properly ...
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### inequality method of solution

Im looking for an efficent method of solving the following inequality: $$\left(\frac{x-3}{x+1}\right)^2-7 \left|\frac{x-3}{x+1}\right|+ 10 <0$$ I've tried first determining when the absolute value ...
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### vector question assistance

let there be 2 lines: $(2,-3,1) + s(3,-2,1)$ and $(2,-1,-3) +t(3,-2,1)$ which are parallel to each other. find the formula of the plane determined by them. my try: a vector perpendicular to ...
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### Exponential Distribution question

I'm having some trouble understanding the mechanics of how to solve with this distribution. The question: The number of years that a washing machine functions is a random variable whose hazard rate ...
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### A question on Abstract measure spaces

Let $(X,M)$ be a measurable space then 1) if $\mu$ and $\lambda$ are measures in $M$ st $\mu \ge$ $\lambda$ then show that $m$ defined as $\mu= \lambda + m$ is a measure 2) Prove that if ...
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### A simple limit problem

How do you solve this limit? I know this is probably really easy. $$\lim_{x \to ∞} \left(f(x) = (1 / x) * e ^ x\right)$$
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### Selecting 6 people from a group of 10 people with special conditions

Sorry for a misleading or such title, but i didn't know how to make it short enough. Anyways, if we have 10 people in a group such that 8 people eat apples, 1 eats pears and one eats watermelons, ...
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### Permutation and Combinations (Separation) [on hold]

Eight students are to be arranged in a row. Find the number of ways to arrange them if three particular students must be separated.
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### How do you know if you properly simplified the rational expressions to it's lowest terms?

Good day, my name is Tony and I'm from Philippines. This morning, our professor discussed about Simplifying Rational Expressions to the Lowest Terms, and later on he gave us a homework. There are some ...
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### graph theory: the degree of vertices in an hesse diagrem graph

In this picture you can see the hesse diagrem of $\subseteq$ over $P(\{x,y,z\})$ For the set $A$ with $k$ elements, $k>0$ look at the diagram as a graph, it's vertices are the members of $P(A)$ ...
$$\mbox{How do I find the sum of this series}\quad \sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}\ {\large ?}$$ Hints in the right direction would be appreciated.