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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4
votes
1answer
36 views

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 ...
0
votes
6answers
93 views

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.
1
vote
2answers
49 views

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 ...
0
votes
0answers
33 views

show by using leibniz formula

There are given $ r, s,n \in\mathbb N$ and $r+s=n$. It also given $A \in M_{r,K} $, $B \in M_{r\times s,K} $ and $C \in M_{s,K} $. Let $M$ be the matrix $\begin{bmatrix}A & B\\0 & ...
4
votes
1answer
79 views

Differential equation $\frac{dy}{dt}=y(1-y)$

I'm starting with $$\frac{dy}{dt}=y(1-y)$$ Then I take the obvious steps. ...
1
vote
2answers
75 views

Algebra clock problem

An absent-minded watch repairman connected the hour hand to the minute hand pinion and the minute hand to the hour hand pinion and set the clock at 6AM which was the correct time then. How soon after ...
0
votes
1answer
36 views

How many even numbers greater than 50 000 can be formed from specified digits without repeat?

The digits are 3,4,5,6,7,0 My working is as follows: I realize that you would need to start with either 5,6 or 7. From there you have 5 digits to re-arrange, but the permutation would have to end in ...
2
votes
0answers
14 views

Set with relative complement forms partition

Prove that if $S$ is a set and $ \emptyset \subsetneq A \subsetneq S $ then $\Pi = \{A , S-A \}$ is a partition of $S$. Proposed Solution: Since $ A \subsetneq S$ , we have $S - A \neq ...
1
vote
1answer
44 views

Need help considering series like these: $\sum_{n=1}^\infty\langle x,e_n\rangle e_n$

I'm working in a Hilbert space $H$ with ONB $(e_n)$ and I have $\alpha=(\alpha_n)\in\ell^\infty$. I have an operator that looks like this: $$T_\alpha x=\sum_{n=1}^{\infty}\alpha_n\langle ...
2
votes
0answers
33 views

perturbation theory solution of forced Duffing's equation

Question: Find the leading order of the asymptotic expansion for large t: $\frac{d^2x}{dt}+\varepsilon\beta\frac{dx}{dt}+x+\varepsilon x^3=Fcos(\frac{1}{3}\big(1+\varepsilon\omega)t\big)$ I have ...
0
votes
0answers
16 views

Finding $V(X)$ when you don't have a density/distribution function.

I just did the first part of this problem: You have a lot of $50$ items and are taking a sample size of $15$. In the lot $3$ items are defective. The lot is accepted if the number of defective items, ...
1
vote
1answer
16 views

constant deceleration problem

A train bracking with constant deceleration covers $1km$ in $20s$, and a second kilometre in $30s$ find the deceleration. Here is what I did: Since the deceleration is constant it would reach the ...
0
votes
1answer
20 views

Finding the $75$th percentile of a distribution.

So, I came across a couple of homework problems on finding percentiles. The first was: pdf of $X$ is $f(x)=\frac{10}{x^2}$ for $x\gt 10$, and $0$ otherwise. Finding the $75$th percentile here was ...
-1
votes
0answers
27 views

Continuous maps [on hold]

Let $\tau$ be the smallest topology on $\mathbb R$ containing all open subsets of $[0,1]$ as well as all subsets of $\mathbb R-[0,1].$ Let $\sigma$ be the usual topology on $\mathbb R$ and consider a ...
2
votes
0answers
64 views

Given the function $f(x)=(1+x)^n$ Show that $L(x)=1$+nx is the linearization of $f$ at $0$ …

So this is how the question goes. 1. Given the function $f(x)=(1+x)^n$.$$$$ a. Show that $L(x)=1$+nx is the linearization of $f$ at $0$.$$$$ b. A friend claims that the cube root of 1.1 is ...
1
vote
0answers
20 views

For a discrete abelian group $G$, is the Gelfand Representation of $\ell^1(G)$ injective?

Given a discrete group $G$, we can consider the Banach $*$-algebra $\ell^1(G)$, with convolution product $(\xi*\eta)(g)=\sum_{h\in G}\xi(h)\eta(h^{-1}g)$ and involution ...
0
votes
1answer
22 views

Cramer's rule and linear dependence/independence test

When you have the system of equations: $$ax + by = e\\cx + dy = f$$ And you do some row operations to eliminate $y$, we get: $$x = \frac{ed-bf}{ad-bc}\tag{1}$$ If we eliminate $x$ we get: $$y = ...
1
vote
1answer
41 views

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 ...
1
vote
2answers
35 views

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 $P(A)$ ...
0
votes
2answers
29 views

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 $A$ ...
4
votes
1answer
38 views

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 ...
3
votes
4answers
231 views

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 ...
0
votes
2answers
29 views

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 ...
1
vote
1answer
61 views

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 ...
1
vote
0answers
24 views

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 ...
4
votes
5answers
391 views

A simple limit problem

How do you solve this limit? I know this is probably really easy. $$ \lim_{x \to ∞} \left(f(x) = (1 / x) * e ^ x\right) $$
0
votes
1answer
30 views

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, ...
0
votes
1answer
24 views

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.
0
votes
0answers
16 views

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 ...
0
votes
1answer
18 views

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 $P(A)$ ...
6
votes
2answers
500 views

Sum of this series

$$ \mbox{How do I find the sum of this series}\quad \sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}\ {\large ?} $$ Hints in the right direction would be appreciated.
0
votes
0answers
39 views

solving the logaritham [duplicate]

I was trying to solve: $\log_2 x \cdot \log_{0.25} x \cdot \log_{0.125} x \cdot \log_{16} x > \frac {2}3$ heres my attempt at it; using logaritham laws and a little algebra we get from $\log_2 x ...
1
vote
1answer
36 views

Arc Length in two dimensions by integration

I'm really at the end of my wits on this problem. Basically I'm trying to find arc length. The vector-valued function is: $R=\langle t,\sqrt{t}\rangle$ and $t\ge0$. We're looking for the length of ...
4
votes
6answers
826 views

Calculate $\sum_{k=1}^n \frac 1 {(k+1)(k+2)}$

I have homework questions to calculate infinity sum, and when I write it into wolfram, it knows to calculate partial sum... So... How can I calculate this: $$\sum_{k=1}^n \frac 1 {(k+1)(k+2)}$$
0
votes
2answers
29 views

Determine whether or not a set is linearly independent

Prove or give a counter example: if $v_1, ..., v_n$ is linearly independent, is $5v_1-4v_2, v_2,...v_m$ also linearly independent. I'm not sure how to go about this. I tried a couple ways to prove ...
2
votes
2answers
44 views

Finding a basis for a set of polynomials

Let $U = \{p \in P_4(\mathbb{R}): p''(6) = 0\}$. Find a basis for $U$, then expand that basis to be a basis of $P_4(\mathbb{R})$. So I've been trying to find examples on how to approach this. I am ...
1
vote
3answers
71 views

If $f(3) = 12$ and $f(2.8) = 12.6$. Then approximate $f'(3)$

I am new to this site and old to my problem in calculus. I hope, some one will guide. If $f(3) = 12$ and $f(2.8) = 12.6$. Then approximate $f'(3)$ ? Please let me know
2
votes
1answer
53 views

Filling of a tank - recurrence relation

Suppose a tank has a maximum limit of 100 units. Each day 2,1 and 0 units are added to the water level with probability p,r and q. Any excess water would overflow and if it reaches the minimum level ...
0
votes
3answers
59 views

Let $T : M_{\text{2x2}} (\mathbb{R}) \rightarrow \mathbb{P}_2$ be a linear transformation give by …

Hey guys could someone who is good at this take a look and tell me if I did it right =) I did all the work so it shouldn't take long to verify my results ... Thank you in advance Problem: Let ...
-1
votes
0answers
72 views

Solution verification: In $\mathbb{P}_2$ [on hold]

Can someone please help me out here =) and confirm that i did my work right, i rechecked it as many times as i could but i am afraid i might be missing something =) anyone can please put my mind at ...
1
vote
2answers
34 views

Is there anything more I can say about a vector function that is parallel to its derivative?

The problem is to find the set of curves in $\mathbb{R}^3$ given by a vector equation $\mathbf{r}(t)$ with the property that the vector $\mathbf{r}'(t)$ is parallel to $\mathbf{r}(t)$ for all $t$ in ...
0
votes
3answers
23 views

In each part, find a basis for the given subspace ofR 3 , and state its dimension

guys I gotta be honest, I've taken notes on everything in the last two sections for this but I'm not sure how to find a basis for a subspace that is a lone plane/line etc.. a full explanation would ...
0
votes
1answer
49 views

Seeking Help on Linear Algebra Problem, Thank you all (YES or NO ANSWER)

Did i do the 1st one correct? Having difficulty understanding 2...1 step at a time just want to know if i did 1 correct
1
vote
2answers
65 views

Prove that if $n \geq 2$, then $\sqrt[n]{n}$ is irrational. Hint, show that if $n \geq 2$, then $2^{n} > n$.

Prove that if $n \geq 2$, then $\sqrt[n]{n}$ is irrational. Hint, show that if $n \geq 2$, then $2^{n} > n$. So, my thought process was that I could show that $2^{n} > n$ using induction, but ...
1
vote
1answer
54 views

I need help proving a statement about rational roots

I have no idea where to start...this is the statement: If a polynomial of degree not greater than 5 with rational coefficients has multiple roots, it has also a rational root, except in the case ...
0
votes
2answers
40 views

Finding the equation of a plane, provided a line and a point?

Question: Given the line $$\begin{pmatrix} x \\ y \\ z \\ \end{pmatrix} = \begin{pmatrix} 1 \\ -3 \\ 2 \\ \end{pmatrix} + t \begin{pmatrix} -2 \\ 4 \\ 7 \\ \end{pmatrix},$$ find a plane which is ...
5
votes
2answers
53 views

How to compute $\int_C {e^{3z}-z\over (z+1)^2z^2}$?

I am asked to compute the integral $$ \int_C {e^{3z}-z\over (z+1)^2z^2} $$ where $C$ is a circle with the center at the origin and radius ${1 \over 2}$. My approach was to separate the integral as a ...
3
votes
1answer
69 views

Solving $|z-3| \leq|z-1-i|$

I was trying to solve graphicly: $$|z-3| \leq |z-1-i|$$ I plugged x and y in proper places as real componenets of the comlex number yielding in the end $-4x+2y+7 \leq0$ this might be tackled if ...
1
vote
2answers
55 views

Minimizing Question

A closed box constructed from a tin sheet has a square base and a volume of $343 \text{in}^3$. Find the dimensions of the box, assuming the minimum amount of material was used in its construction. ...
1
vote
0answers
31 views

Strongly regular tournament

A digraph on $n$ vertices is called a tournament if there is a exactly one directed edge between any two distinct vertices. A vertex $v$ dominates a vertex $w$ if there is an edge from $v$ to $w$. ...