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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1
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2answers
31 views

Inequality - Find what value of $t$ satisfies: $ (t/24) - (t+1) + (3t/8) < (5/12) (t+1)$

Inequality - Find what value of $t$ satisfies: $(t/24) - (t+1) + (3t/8) < (5/12) (t+1)$. Step 1: I multiplied both sides by $24$ and divided to get: $t-24(t+1)+9t < 10+24(t+1)$. Step 2: I ...
1
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2answers
62 views

Free action by cyclic group.

Let $G$ be a group acting on a set $X$. If $g\in G$ has no fixed points, prove or disprove the cyclic group $\left \langle g \right \rangle$ acts freely on $X$. edit: Can also assume $g$ has finite ...
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0answers
17 views

To derive the weak of this fem?

It was long ago I studied FEM, and now, I am stucked in this exercise. \begin{equation} -\Delta u + u = f \text{ in } \Omega \\ u = 0 \text{ on } \partial \Omega \end{equation} where the domain ...
0
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0answers
17 views

Finding cut-off point for utility function

OK, so apologies for the easy question, but I'm new to this! This is somewhere between elementary algebra, and beginner's game theory. The question comes from a paper I read here (see p. 193): ...
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0answers
22 views

Need a solution to find the locus of an equation. [on hold]

Find the equation of the locus of a point which moves so that its distance from $(a,0)$ is equal to its distance from the $y$-axis. The answer is $$y^2 - 2ax + a^2 =0$$ Please can someone find the ...
2
votes
3answers
2k views

Complicated Logic Proof involving Tautology and Law of Excluded Middle

I'm having great difficulty solving the following problem, and even figuring out where to start with the proof. $$ \neg A\lor\neg(\neg B\land(\neg A\lor B)) $$ Please see the following examples of ...
-4
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3answers
165 views

Why integers are not enough? [on hold]

My Maths teacher asks me this in my homework and i cant find it anywhere. Thanks for your help. P.S.: she asks another thing... ''why rational numbers are not enough?'' could you help me with that ...
1
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1answer
1k views

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. (weird equation)

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five ...
2
votes
3answers
749 views

What did I do wrong?

A question I was faced with asked "For which $x$ is $\log_{10}(x)^{\log_{10}(\log_{10}(x))}= 10,000$?" My instincts tell me I can say $$\log_{10}(x)=10$$ and $$\log_{10}(\log_{10}(x))=4$$ However, ...
1
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3answers
441 views

Linear Programming to find the loan plan to minimize the interest payment

Assume that it is the first of July and you are running a small shop. The sales revenue and the amount of bills you have to pay for the next six months are estimated as following: In short, you ...
2
votes
4answers
88 views

Proof that $1+4^n+7^n$ is divisible by 3 for all $n \in \mathbb{N}$

So, as the title said I have to proof that $1+4^n+7^n$ is divisible by 3 for all $n \in \mathbb{N}$. I have to do it with induction. So I got my start, for $n=0$: We have $1+4^0+7^0 = 1+1+1 = 3$ and ...
15
votes
3answers
285 views
+50

Continuity of a function in two variables

Function $f(x,y)$ is continuous in each variable separately. Prove that there exists a point where it is continuous in two variables. I do not quite understand how to act here. I know the ...
5
votes
5answers
177 views

An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$

How to evaluate the following improper integral:$$\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx,$$ where $a,b>0$. I tried to suppose $$f(a)=\int_0^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx,$$ based ...
0
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0answers
23 views

Please help me check this derivative work

I have $$ J_{\theta}(X) = - \frac 1 m \cdot \left[ y \cdot ln( h_{\theta} (X ) ) + ( 1 - y) \cdot ln ( 1 - h_{\theta}(X) ) \right] $$ I need $\frac d {d\theta} J_{\theta}(X)$. I tried many time, and ...
0
votes
1answer
27 views

How can i find $dz$ and $d^2(z)$ from implicit equation?

Given the function $F(x+z,y+z)=0$,i need to find $dz$ and $d^2z$....here's my attempt: $$dF=F'_1d(x+z)+F'_2d(y+z)=0$$ $$F'_1(x'dx+z'dz)+F'_2(y'dy+z'dz)=0$$ $$F'_1(dx+dz)+F'_2(dy+dz)=0$$ ...
0
votes
1answer
21 views

Points defined by relations (an exercise from “System of Coordinates”)?

An exercise from "System of Coordinates" (by Gelfand, Glagoleva and Kirilov) asks me to "[t]ry to decide by yourself which sets of points are defined by these relations" and relations given are: a. ...
0
votes
0answers
68 views

Related rates of change: distance between a plane and a car

A highway patrol plane flies $3 m$ above a level, straight road at a constant speed of $120 m/s$. The pilot sees an oncoming car and with radar determines that at the instant the line of sight ...
0
votes
1answer
77 views

Linear algebraic group

Let A be a finite dimensional algebra over C . This means that there is a multiplication map $f : A \times A \to A$ that is bilinear ( it is not assumed to be associative). Define the automorphism ...
0
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0answers
41 views

Copy of C in H , trace is independent of the choice

Let X€ Mn(H). For each of the choices of a copy of C in H , write out the corresponding matrix of X as an element of M(2n,C). Use this formula to show that the trace of X is independent of the choice. ...
0
votes
0answers
22 views

On modular group and quadratic forms

Let $\Gamma$ be the modular group, is the group of linear transformations of the upper half of the complex plane. Let $\mathbb Q_{N^2{d_K}}/\Gamma$ (the group of positive definite primitive quadratic ...
0
votes
0answers
31 views

An application of squeeze theorem to the limit of $(\sin x)/x$ [duplicate]

How can I solve the following problem using elementary trigonometry? Use the Squeeze Theorem to conclude that $$\lim_{x\to 0^+} \frac{\sin(x)}{x} =1.$$ Use symmetries of $y = \frac{\sin(x)}{x}$ to ...
1
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0answers
44 views

How to obtain Black-Scholes from displaced diffusion process?

The displaced diffusion process is $$ d(F_t+a)=\sigma(F_t+a)dW_t $$ I have solved it and found it to be $$ F_t={F_0\over\beta} \exp\left( -\frac 12\beta^2\sigma^2t + \beta\sigma W_t \right) ...
0
votes
0answers
15 views

How can I get a function to calculate non-cumulative increment?

If you pay $0,045 monthly, and you need to pay $0,16 monthly, how do you get a function to calculate, in terms of percentage ...
1
vote
1answer
34 views

Electromagnetic fields and Laplace equations along a square

I'd like to solve Laplace equation satisfying the following BCs: $$\phi(x,y=0)=0$$ $$\phi(x=0,y)=0$$ $$\phi(x,y=1)=9\sin(2\pi x)+3x$$ $$\phi(x=1,y)=10\sin(\pi y)+3x$$ where $0\leq x,y\leq 1$. I have ...
0
votes
0answers
25 views

About First Orthogonality theorem

Let $G$ be a finite group, $(U,\theta_1)$ and $(V,\theta_2)$ be irreducible $k$-representations, $m=\dim_k U$ and $n=\dim_kV$. By the way, $K$ is an algebraically closed field. Let ...
0
votes
1answer
219 views

Solving a nonlinear equation for one of variables with the help of a computer algebra system

Are there any solutions out there that can take a wide variety of equations with variables, like the one below, and transpose or isolate variables to other sides of the equation automatically? For ...
0
votes
1answer
39 views

Pointwise convergence and uniform convergence of a sequence of functions

Let $\{f_{n}\}_{n\geq 1}$ be a sequence of function given by $f_{n}(x)=\frac{1}{x}+\frac{1}{n}$. Does $f$ converge pointwise on $\mathbb{R}\setminus\{0\}$? Does $f$ converge uniformly ...
1
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2answers
635 views

How to find the coordinates of the intersection of median

Given the triangle $ABC$ with its vertices $A(0,1)$, $B(-2,1)$, $C(8,-8)$. Determine the intersection point of the median $AM$ and the line $l$, if $l\parallel AB$ and $C$ is element of $l$.
0
votes
2answers
30 views

Splitting a segment with a ratio

I came across the homework question that I attempted to do. After looking at the answers, and getting it wrong I didn't understand why. I'm specifically lost at why we would get a fraction of 2/5 ...
1
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0answers
21 views

Rapidly Decreasing Functions

Can someone explain the notion of a rapidly decreasing function? Namely, a function in the Schwartz space: $$\mathscr{S}(\mathbb{R}^n):= \{ f \in C^{\infty} (\mathbb{R}^n) : ||f||_{\alpha, \beta} ...
-4
votes
1answer
107 views

Real inner product from a complex one

Let $V$ be a complex vector space. We may view $V $ as a real vector space by simply ignoring non-real scalars. Now suppose that $\langle \cdot,\cdot,\rangle$ is a complex inner product on $V$, and ...
-4
votes
1answer
64 views

I know the perimeter of the rectangle but not the area. How do I find the length and width?

The perimeter of the rectangle is 986. I don't know the area and I need to find the length and width. The problem states that the length is 199 ft more than the width. That is all the information that ...
-4
votes
3answers
68 views

How to solve this: $|3-x|\ge2$

How to solve $|3-x|\ge2$ ? I know that if $|x| < y$, then $-y < x < y$. But in this case what to do? Thanks. Here, $|x|$ is the absolute value of $x$.
0
votes
0answers
29 views

Convergence of norms

I have this space $H_{0,p}^1=\lbrace u\in AC([0,+\infty),\mathbb{R}),u(0)=u(+\infty)=0, \sqrt{p} u'\in L^2(0,+\infty)\rbrace $ endowed with the norm $||u||^2=\int_0^{+\infty} p(t) u'^2(t) dt$ ...
1
vote
1answer
28 views

How to show the cyclotomic polynomial is irreducible over $\mathbb{R}(T,\sqrt[n]{T})$

I'm trying to solve the following problem. Let $T$ be a transcendental over $\mathbb{R}$. Put $K=\mathbb{R}(T), n\geq3$. Let $L$ be the least splitting field of $X^n-T$. Then, calculate $[L:K]$. I ...
0
votes
0answers
8 views

Determining Moving-Average Representation of AR(2) Process

Consider a stationary $AR(2)$ process given by $$X_{t} - X_{t-1} + 0.25X_{t-2} = 5 + a_{t}$$ where $a_{t} \sim WN(0,1)$ (white noise). I am interested in obtaining the causal representation of ...
1
vote
0answers
32 views

Ordinary differential equation­

$$\dfrac{dy}{dx}-\dfrac{\tan y}{1+x}=(1+x)e^x\sin y$$ I tried $\sin y=t$ but failed. It seems to immune to methods I know of or I am just unable to make the right substitution... Wolfram alpha ...
1
vote
1answer
38 views

Quadratics Word Problem

The path of a football flying through the air can be modelled by a quadratic equation. The football reaches the ground after 12 seconds in flight and is kicked from a height of 1 meter. The parabola ...
2
votes
1answer
92 views
+50

Deducing an optimal gambling strategy (using martingales).

Apologies in advance for the length, I tried being precise. Suppose a game where in each turn you can gamble a certain amount of money on the result of a fair coin toss. If the coin comes out tails ...
0
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1answer
33 views

exercise on $ L(0,1) $ and functional analysis

how could i prove that $ u_{k}(x)=sin(kx) \to 0 $ as $x\to \infty$ in $ L^{2}(0,1) $ how could i prove that for fixed a,b real numbers and $ 0 < \lambda <1 $ and for the function defined as ...
2
votes
1answer
41 views

The complex equation

In solving $|z|i +2z =1$, I seem to be constantly getting two solutions while both answer key and Wolfram claim to be only one. What am I doing wrong? Let's share the fun: $(\sqrt{x^2 +y^2}) i +2x ...
1
vote
3answers
33 views

Given the equation of the parabola, for what values of $t$ will the quadratics have $0$, $1$, or $2$ solutions?

Given the equation of the parabola, for what values of $t$ will the quadratics have $0$, $1$, or $2$ solutions? Equation: $$0 = 3x^2 + tx + 10$$ Can you please explain the answer in simple terms, ...
1
vote
1answer
35 views

Find value of $x$ for: $(1/3)(1-x) \geq 2(x-3)$

Find what value of $x$ satisfy: $(1/3)(1-x) \geq 2(x-3)$ First I multiplied both sides by $3$ so that $1/3$ became $3/3=1$. So I tried to find $x$ this way: $(1-x) \geq 6(x-3)$. I tried solving it ...
0
votes
1answer
47 views

Probability and coin tosses

Taking a Probability & Statistics class this term and trying to get my head wrapped around how I calculate coin tosses with specific out comes in mind. We're using the nCr and nPr functions on our ...
1
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0answers
17 views

finding the symmetric point

let there be $4$ points. $A(-1,1,1), B(2,0,-1), C(1,3,-2), D(-2,-1,0)$. the $4$ points are not on the same line. the plane which goes through the points $A$ and $B$, and which is also paralel to the ...
1
vote
2answers
55 views

Solve $f(x) = ax^2 + bx + c$ to find the value of $K$

$f(x)=ax^2+bx+c$, where $a=-9$, $b=12$ and $c=16$. If $$-1<f'(x)<1$$ then $h<x<k$. To $2$ decimal places, what is the value of $k$? Hi, this is working for solving $f(x) = ax^2 + bx + ...
0
votes
1answer
40 views

How to compute the length of line segments inside an isosceles trapezoid parallel to the base

here is the problem in a picture, sorry for the drawing. i have found how to compute the midline of the isosceles trapezoid, 1/2 (top+bottom) , but there seems to be no formula for other line segments ...
0
votes
1answer
33 views

Equation of horizontal/vertical line and changing to $y=mx+c$ format

I've been given the equation $2x-3y=5$. I was wondering whether this is a horizontal or vertical equation and how would I rearrange this to $y=mx+c$. I know that this is a fairly basic equation but ...
0
votes
0answers
50 views

What is a bi-rhombus? [on hold]

Can anyone tell me what a bi-rhombus is? I need it for my school project. If possible could you explain the relationship between a equilateral triangle, a rhombus and a bi-rhombus. This is how my ...
11
votes
3answers
217 views

Suggestion for Computing an Integral

Let $$A=\left\{(x,y,z)\in \mathbb R^3:\dfrac{x^2}{2}+\dfrac{y^4}{4}+\dfrac{z^6}{6}\leq1\right\}.$$ Then I want to compute the following integral: ...