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 ...
-10
votes
1answer
58 views
Nate's older brother! [closed]
Nate's older brother Mickey has been looking for an old used car just to drive to work. An advertisement in the paper is offering a car listed at $899.95 for sale at 25 percent off. The best estimate ...
0
votes
0answers
16 views
Survival Analysis Partial Likelihood
Part of a medical statistics course is on Survival Analysis. We are introduced to the Cox Proportional Hazard model and then move on to look at partial likelihood $L(\beta)$. There is little on what ...
1
vote
1answer
30 views
How to construct an LP problem that makes a (partial) theorem fail?
I am following a course on linear programming, and one of the exercises calls for an example, that may show that a theorem fails, if a assumption is omitted from the theorem.
The theorem is Theorem ...
-1
votes
3answers
42 views
question about percentages
At the start of the new year, the price for a gallon of milk at a local grocery store increased by 2.4% as a result of inflation. If a gallon of milk cost $2.92 last year, about how much does it cost ...
0
votes
2answers
40 views
General solution of differential equation of order 3
Please ,how to find that the general solution of $u'''(t)=e(t) , t\in [0,1]$ is given by
$u(t)=c_0+c_1t+c_2 t^2 +\frac12 \int_0^1 (t-s)^2 e(s) ds$
$e:(0,1)\rightarrow \mathbb{R}$, and $e\in ...
3
votes
2answers
54 views
Unable to get to all permutations after $n-1$ transpositions
Problem: Give an example of a permutation of the first $n$ natural numbers from which it is impossible to get to the standard permutation $1,2,\ldots,n$ after less than $n-1$ transposition operations ...
1
vote
0answers
28 views
Basis of kernel and image of a linear transformation - verification
The transformation matrix I found is: $$\begin{pmatrix} 1 & -1 \\ 1 & 1 \\ 0 & 0\end{pmatrix}$$
Is this how a basis for $\ker$ and $\mathrm{im}$ is calculated?
$$\begin{pmatrix} 1 & ...
1
vote
3answers
94 views
Improper Integral Question $ \int^{\infty}_0 \frac{\mathrm dx}{1+e^{2x}}$
I want to check if it's improper integral or not
$$ \int^{\infty}_0 \frac{\mathrm dx}{1+e^{2x}}.$$
What I did so far is :
set $t=e^{x} \rightarrow \mathrm dt=e^x\mathrm dx \rightarrow \frac{\mathrm ...
2
votes
3answers
91 views
Improper Integral Question $\int_0^1 \ln\sqrt{x}dx $
I'm trying to compute this integral and check if it's an improper integral.
What I did so far is to write the limit.
$$\begin{align*}
\int_0^1\ln\sqrt x\, dx &= x\ln\sqrt x - \int \frac12\, dx = ...
3
votes
2answers
71 views
Improper Integral $\int_{1/e}^1 \frac{dx}{x\sqrt{\ln{(x)}}} $
I need some advice on how to evaluate it.
$$\int\limits_\frac{1}{e}^1 \frac{dx}{x\sqrt{\ln{(x)}}} $$
Thanks!
0
votes
2answers
70 views
How to calculate $\lim_{n \to \infty}\frac{r^n}{n}$
I'm a bit rusty on calculus and I'm not able to solve this rather simple limit:
$$\lim_{n \to \infty}\frac{r^n}{n}$$
In my case $r = -1$, and "just by looking at it" I'd guess that for $\left|r\right| ...
0
votes
1answer
16 views
Problem on hyperbolic hyperboloid generated by a rotation
This is the problem:
In $\mathbb{E}^3$ we consider the conic $\gamma$ of equations $x=yz-2=0$ , the line $a$ of equations $x=y+z=0$ and the surface $Q$, that is generated by the rotation of $\gamma$ ...
6
votes
2answers
93 views
A simple 2 grade equations system
If we have:
$$x^2 + xy + y^2 = 25 $$
$$x^2 + xz + z^2 = 49 $$
$$y^2 + yz + z^2 = 64 $$
How do we calculate $$x + y + z$$
0
votes
2answers
41 views
Find the relation between the dimension of the nullspace of $A$ and $A^t$
Let $A$ be a $n \times n$ matrix, what is the relation between the dimension of the nullspace of the homogeneous system of $A$ and the one of $A^t$?
0
votes
0answers
38 views
property of an increasing or decreasing function
For $x \in \mathbb{R}$, and $f(x)$ an increasing function, can we prove whether
$$ af(x)\lesseqgtr f(ax) $$
for $a >0$? If we have additional information that $f$ is homogeneous of some degree, ...
5
votes
2answers
49 views
number of all inconstant maps f from A to A [duplicate]
Let $ A=\{1, 2, 3,..., n\}$. Find the number of all nonconstant maps $f: A \rightarrow A$ for which $f(k) \le f(k + 1)$ and $f(k) = f(f(k + 1))$ for $k = 1, \dots, n-1$..
1
vote
3answers
35 views
Please help with this probalility problem.
Vince buys a box of candy that consists of six chocolate pieces, four fruit pieces and two mint pieces. He selects three pieces of candy at random without replacement.
Calculate the ...
0
votes
1answer
29 views
$U\subseteq V$ is $T$ invartiant $\Rightarrow$ $\left(T\,|_{U}\right)^{*}=\left(P \circ T^{*}\right)\bigl|_{U}$
I want to proove that given $T\in\mathcal{L}\left(V,V\right)$ ($V$ is a finite dimensional inner product space) and a subspace $U\subseteq V$ which is $T$ invariant that
...
2
votes
4answers
54 views
initial value problem: y'' + 4y = f(t) , y(0)= y'(0)=0. f(t) = { 0 if t <3; t if t >3}
Solve the initial value problem:
$$y'' + 4y = f(t) , y(0)= y'(0)=0. $$
where
$$ f(t) = \begin{cases} 0 &t < 3 \\ t & t > 3\end{cases} $$
I've solved for the homogeneous equation, y'' ...
0
votes
0answers
19 views
Variation of 3SAT is in NP-Complete
Consider the problem of "K-3SAT", a variation of 3SAT: Given a 3CNF formula O and an integer k, the machine determines whether the formula O has a satisfying assignment in which at most k variables ...
1
vote
1answer
33 views
question about Morse theory in Hilbert space
This is sade to be the Morse theory in Hilbert space ,and i want to know the definition (or where i can find it ) of :
The qth singular relative homology groupe
The qth critical group
Please;
...
1
vote
1answer
16 views
Proving that the independent set problem is in NP-Complete
Consider the problem of "Independent set" in grahps. Given a graph G and an integer k, the machine determines whether the graph G contains an independent set of size k.
I need to prove that it's in ...
2
votes
1answer
32 views
Prove that equation has exactly 2 solutions
Question:
Given $\lambda_1<\lambda_2<\lambda_3 \in \Bbb R, a_1,a_2,a_3>0 $
Show that this equation has exactly 2 solutions:
$\frac {a_1}{x-\lambda_1}+\frac {a_2}{x-\lambda_2}+\frac ...
0
votes
1answer
33 views
calculus and exponential functions
$0\leq t\leq3$, $t$ (measured in hours)
$$G_1(t)=4e^{t/2}$$ Diabetic
$$G_2(t)=8-4e^{-t/2}$$ Non diabetic-
Relating to the question but the whole question isn't important, there are six parts and I ...
0
votes
1answer
40 views
Find the smallest m for which this is possible
Problem:
Eight singers participate in an art festival where m songs are performed. Each song is performed by 4 singers, and each pair of singers performs together in the same number of songs. Find the ...
0
votes
2answers
22 views
How to find density function?
$X \sim N(1,4)$ and $Y = 3 - 5X$. How to find the density function of $Y$?
I tried first to find the distribution function of Y, but got stuck.
$$F(y) = P(Y <= y) = P(3 - 5X <= y) = P(X >= ...
0
votes
1answer
37 views
Ordinary differential equations with double resonance
I want to know what is the definition of "resonance, double resonance" in
ordinary differential equations with double resonance
Please,
Thank you.
0
votes
1answer
17 views
Example on Correspondences
Giva an example of correspondence $F : \mathbb{R} \rightarrow \mathbb{R}$ such that the closure of $F$ is $ \overline{F}: \mathbb{R} \rightarrow \mathbb{R}$, upper semi continuous on $\mathbb{R}$, ...
0
votes
3answers
13 views
exponential functions and calculus
Assume the rate of change of a quantity T is proportional to the difference between the quantity T and some fixed constant A.
That is
dT/dt = K(T-A)
show that T=A+Ce^(kt) (where C is a constant) is ...
1
vote
1answer
22 views
expected value of random variables
Take two random variables $X=a+bX_0$ and $Y=c+dY_0$, and define $T=X-Y=\mu+\sigma Z$ where $\mu$ is the mean of $T$, $\sigma$ its standard deviation and $Z$ is a standardized random variable with mean ...
2
votes
1answer
38 views
If $V$ is a vector space over a division ring $K$, and $A=\mathrm{End}_K(V)$, then every quotient ring of $A$ is a prime ring
Let $K$ be a division ring, let $V=V_{K}$ a vector space over $K$, and let $A=\mathrm{End}_{K}(V)$. Could anyone give me an idea of ​​how to prove that every quotient ring of $A$ is a prime ring?
1
vote
2answers
35 views
Define Indefinite integrals Question
I was asked to define the next intergrals and I want to know if I did it right:
$$1) \int^\infty_a f(x)dx = \lim_{b \to \infty}\int^b_af(x)dx$$
$$2) \int^b_{-\infty} f(x)dx = \lim_{a \to ...
0
votes
1answer
24 views
For which p>0 does $S_t=W_t+t^p$ admit an equivalent martingale measure?
Let W be a brownian motion and p>0.
For which p does $S_t=W_t+t^p$ admit an equivalent martingale measure?
I recently saw at my lectures that
NFLVR cond:
There does not exist a sequence $\{H_n\}_{n ...
0
votes
0answers
14 views
CYK algorithm and CNF
Why do we need CNF to be able to apply CYK algorithm? Because it operates on two symbols on table or other reason?
1
vote
0answers
33 views
Model Linear-Programming Problem
A factory needs to complete $n$ jobs by using $m$ machines. To complete each job $j, j=1,\dots,n$, an amount of $r_j\geq 0$ processing units is required. Each machine $i$ has a processing speed ...
0
votes
2answers
67 views
Taylor series of $f(x)=\frac {e^x-1}{x}$
I am asked to expand $f(x)=\frac {e^x-1}{x}$ centered at 0 using the known Talyor series of functions.
How to simplify the function so that it can be expanded more easily?
0
votes
0answers
25 views
Hyperbolic PDE classification
Considering the following equation
$$u_t + A u_x = 0,\quad t> 0$$
where
$$ A = \begin{pmatrix} 1 & \sin t \\ \sin t & -1 \end{pmatrix} $$
Naturally, the system is hyperbolic if $A$ consist ...
0
votes
1answer
38 views
Question about eigenvalues
I have this :
i dont understand why they write $\lambda=m^2 , m\in \mathbb{N}\cup\lbrace0\rbrace$ ,
it's right that $\lambda=m^2$ is the eigenvalues of $(P_0)$ ,but $0$ is not an eigenvalue !.
...
-3
votes
2answers
32 views
general properties of equivalence relations
let ~1 and ~2 be distinct equivalence relations on A. Define ~3 by a ~3 b iff a ~1 b and a ~2 b. prove that ~3 is an equivalence relation on A. if [x]i denotes the equivalence class of x for ~i (i = 1 ...
0
votes
1answer
24 views
Minimal polynomials over the rationals and the reals
Find the minimal polynomial over $\mathbb Q$ and $\mathbb R$ for ...$\sqrt[3]{3}$, $1- i\sqrt{3}$, $2 + i$, $i\sqrt[3]{3}$
Sorry for my sqrt formulas .. I'm new here, hope to learn really fast to ...
2
votes
1answer
179 views
How can I prove this inequality?
I have a pretty nasty looking function
$$\sigma (t,y) = \sqrt{\frac{\sum_{i=1}^N \lambda_i \sigma_i \exp \left \{-\frac{1}{2 t \sigma_i^2}\left[\ln{\frac{y}{S_0}} - \left(r - \frac{\sigma_i^2}{2} ...
0
votes
0answers
24 views
Question on Polynomials
I have to determine the value of a $\in \mathbb{R}$, if any such that
$$\sum_{x=1/2}^{15/2} (a + 2x)^{[8]} =0$$
Ordering = ${1 \over 2}, {3 \over 2},{5 \over 2},... ,{15 \over 2}$
Note: To define ...
-1
votes
1answer
43 views
elementary consequences of Lagrange's theorem
Let G be a finite group. if G has an element of order p and an element of order q, where p and q are distinct primes, then the order of G is multiple of pq
0
votes
1answer
24 views
Question on integration
Let $(p,q)\in \mathbb{R}^2$ , and $H: \mathbb{R}\times \mathbb{R} \rightarrow \mathbb{R}$
if $q'=\frac{\partial H}{\partial p} (p,q) ~~\text{and}~~ p'=-\frac{\partial H}{\partial q} (p,q)$
How to ...
-1
votes
2answers
30 views
Counting Cosets
Describe the cosets of the subgroups described:
The subgroup $\langle\frac{1}{2}\rangle$ of $\mathbb{R}^*$, where $\mathbb{R}^*$ is the group of non-zero real numbers with multiplication.
The ...
-1
votes
0answers
24 views
equivalence relations on group
Let $G$ be a group. A relation on $G$ is defined: if $H$ is a group of $G$, let $a\sim b$ iff $a^{-1}b\in H$. Is this the same equivalence relation as if $H$ is a subgroup of $G$, let $a\sim b$ iff ...
3
votes
1answer
37 views
Calculation of ordered pair $(x,y,z)$ in $x^2 = yz\;\;,y^2=zx\;\;,z^2 = xy$
(1) Total no. of integer ordered pair $(x,y,z)$ in $x^2 = yz\;\;,y^2=zx\;\;,z^2 = xy$
(2) Total no. of integer ordered pair $(x,y,z)$ in $x+yz = 1\;\;,y+zx = 1\;\;,z+xy = 1$
My Try:: (1) Clearly $ x ...
2
votes
2answers
33 views
Find $u\in\mathbb{R}$ such that $\mathbb{Q}(u) = \mathbb{Q}(2^{1/2}, 5^{1/3})$.
I am having trouble finding such a $u$. My instincts at first told me to do the obvious thing and let $u = 2^{1/2}5^{1/3}$ but $u^{2} = \left(2^{1/2}5^{1/3}\right)^{2} = 2\cdot5^{2/3}$ but we want ...
1
vote
3answers
49 views
Mathematical Systems Question Help
Alright, this is another question for my math for teachers course. This question is not actually in the homework, but there are problems similar to it. I'd really like to learn how to do problems like ...
0
votes
1answer
149 views
Need help finding value (or contingency table) for Chi-squared critical value.
I need help finding value (or contingency table) for Chi-squared critical value at 95% significance level when degrees of freedom is 58.
I have calculated the chi-square calculated value, and I need ...
