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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2
votes
2answers
24 views

Topology and Arithmetic Progressions

I'm self-studying from "Elementary Topology Problem Textbook" by O.Ya.Viro et al. This is Exercise 2.Lx : Consider the following property of a subset $F$ of the set $\mathbb{N}$ of positive ...
0
votes
0answers
5 views

solving system of equations involving basic trigonometry

I am trying to solve the following system of equations: $$\frac{kq^2}{d}=mg(L-L\cos(α))+\frac{kq^2}{r}$$ $$\sin(α)=\frac{x}{L}$$ $$r^2=(L-L\cos(α))^2+(x+d)^2$$ $$\frac{kq^2}{r^2} cos (β) = Tsin(a)$$ ...
1
vote
2answers
13 views

Problems with Simplifying Using Factoring of Binomial Expressions

I am running into problems simplifying using factoring of binomial expressions. The problem at hand is this: $(x-1)^3*(2x-3)-(2x+12)*(x-1)^2$ I first expanded the left side of the minus sign, like ...
1
vote
1answer
217 views

How to get numbers with distinct digits within some range?

I have a little program I'm working on for my project (a simple practice in school), part of the program is that it should receive input composed of an array of 7 digit (or less) numbers which should ...
1
vote
1answer
22 views

solving system of equations(nonlinear)

I am trying to solve the following system of equations: $$\frac{kq^2}{d}=mg(L-L\cos(t))+\frac{kq^2}{r}$$ $$\sin(t)=\frac{x}{L}$$ $$r^2=(L-L\cos(t))^2+(x+d)^2$$ The parameters are: $k,L,d,q,m,g$ The ...
1
vote
2answers
16 views

Fourier Transform of Poisson Equation

While trying to solve the Poisson Equation by using Green's Function I have to Fourier transform the equation i.e $$-\nabla^{2}\phi(r)=\rho(r).$$ In the book after Fourier transform, the solution ...
0
votes
1answer
57 views

solving the equation

let there be a function $ f(x)= \ln x-kx^2, k>0$ determine for whihc values of $ k$ ,the equation $f(x)=0.5$ has a single solution; attemp to solve: $$0.5 = \ln x-kx^2$$ $$kx^2 +0.5 = \ln x $$ ...
3
votes
2answers
347 views

Show that $rank(A)+rank(B) \leq n$, when $A,B$ are $2$ matrices of size $n \times n$, and $AB=0$

Question from homework in Linear Algebra: Let $A,B$ be two matrices of size $n \times n$ such that $AB=0$. Show that: $rank(A) + rank(B) \le n$ . It probably has something to do with the dim of ...
0
votes
1answer
35 views

Time and work aptitude problem for CAT preparation [on hold]

$A$ can do a job in $10$ days, $B$ in $12$ days and $C$ in $15$ days. They all start working together but $A$ leaves after $2$ days and $B$ leaves $3$ days before the job is completed (i.e. $C$ works ...
2
votes
1answer
30 views

Parametrizing to Calculate Flux

Evaluate the flux of $\mathbf{f}$ across the oriented surface $\Sigma$ by computing the surface integral $\iint_{\Sigma} \mathbf{f} \cdot d\sigma$, where $\Sigma$ is the surface $z=xe^y$ for $0 \leq x ...
2
votes
2answers
120 views

Solve for $x$: $\frac1e = e^{2x}$

I tried making it to $e^{-1} = e^{2x}$ and had the exponents equal each other $-1=2x$ and the I solved for $x$, making it $x=-1/2$, but that answer is wrong. please help I don't know why that ...
1
vote
4answers
63 views

inverse trigonometric equation $\displaystyle \tan^{-1}{x}+\cot^{-1}{x}=\frac{\pi}{2}$

I have problem with showing that $\displaystyle \tan^{-1}{x}+\cot^{-1}{x}=\frac{\pi}{2}$ I think there have to be used formula: $\displaystyle ...
0
votes
1answer
12 views

Matrix Rank calculation

I have a matrix A . A can be written as A=B+D. I know rank of B. It is 3. Is it possible for A to have ranks $<3$ . If so please prove.
3
votes
1answer
554 views

Need help with statistics homework

The financial department at a large hospital would like to estimate the average outstanding balance owed by patients who have not paid their bills in full. In order for the interval to be useful in ...
2
votes
1answer
42 views

Radius of convergence

(a) Determine the radius of convergence to the power series $f(x)= \displaystyle\sum\limits_{n=0}^\infty \frac{(2n)!}{(n!)^2}x^n$. Should I use the ratio test? (b) Assume the validity of the ...
-1
votes
1answer
29 views

Can we deduce that $X$ is $\sigma-$compact? [on hold]

Assume that a quotient space of the space $X$ is compact. Can we deduce that $X$ is $\sigma-$compact?
1
vote
6answers
42 views

Using Chain Rule and Product Rule to find derivative

I have to find the derivative of the following function: $$f(x) = (x^3+ 4)(4x^5 + 2x − 5)^{1/2}$$ To start solving this, I've dissected the equation and realize that I must use the product and chain ...
0
votes
0answers
16 views

Solve the given differential equation by using Green's function method

I am really struggling with the concept and handling of the Green's function. I have to solve the given differential equation using Green's function method $$\frac{d^{2}y}{dx^{2}}+k^{2}y=\delta ...
-1
votes
0answers
18 views

The number of antisymmetric relations which does not contain $(a,b)$

I can not find the solution for that If $A=\{a,b,c,d\}$, determine the number of relations on $A$ that are antisymmetric and do not contain $(a,b)$. I guess the answer is $2^5\cdot3^5$ But I am not ...
0
votes
3answers
61 views

How do I find the sum of the series?

$$\sum_{k=1}^{7}40 \left( \frac{1}{2}\right)^{k-1} = \frac{635}{8}$$ The image of the orginial eqn is on the link above and so is the answer, but I need help in how to solve it. when I did solve it I ...
1
vote
1answer
28 views

A circle wheel 28 inches in diameter rotates (moves) the same number of inches per second

A circle wheel 28 inches in diameter rotates (moves) the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many ...
2
votes
3answers
93 views

How does $\frac{t^2}{t+1}$ equal $t-1+\frac{1}{t+1}$?

I do the long division: 1: t+1 goes into $t^2$ t times 2: Subtract $t^2$ + 1 from $t^2$ and get -1 3: Answer: t - $\frac{1}{t+1}$ Am I missing something here?
1
vote
1answer
35 views

How would I solve these types of equations

Going back to college and been a few years since I've had to do any algebra/trig. How would I go about solving these types of equations and do they have a name? a(y-b)=by+c then, except when the ...
3
votes
2answers
34 views

Binomial dependent on a Poisson

I have been working on a problem with a binomial rv dependent on a poisson rv and have worked through to this point: $P(X=x) = \sum_{n=x}^{\infty} \dfrac{n!}{x!(n-x)!} p^x(1−p)^{n−x} ...
7
votes
3answers
167 views

Calculate $\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$

I'm an eight-grader and I need help to answer this math problem. Problem: Calculate $$\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$$ This one is very hard for me. It ...
-1
votes
0answers
17 views

Accuracy of line intersecting algorithem decrase with large precisions

from the above pic I found the value of x from equation of line p1-p2 and perpendicular line from point a to the Line(p1,p2) .The intersecting point is X ,but the accuracy is less see the result ...
2
votes
3answers
555 views

Looking for examples of first countable, compact spaces which is not separable

Could someone give me some classical examples of first countable, compact spaces which is not separable? However, other examples are also welcome. Any help will be appreciated.
2
votes
1answer
44 views

Simplify: $\ln(x^2 − 4)− \ln(x − 2)− \ln 2$

Simplify: $$\ln(x^2 − 4)− \ln(x − 2)− \ln2$$ $$\ln\dfrac{x^2 − 4}{x − 2}− \ln2$$ $$\ln(x + 2)− \ln2$$ $$\ln(x + 2)/2$$ I got this far, is there any other way to simplify it, or do I stop here?
13
votes
2answers
497 views

Intuitive ways to get formula of cubic sum

Is there an intuitive way to get cubic sum? From this post: combination of quadratic and cubic series and Wikipedia: Faulhaber formula, I get $$1^3 + 2^3 + \dots + n^3 = \frac{n^2(n+1)^2}{4}$$ I think ...
3
votes
3answers
44 views

Trigonometry Question: find Value of…

Find value of $3 + \cos2x + \cos4x + \cos6x - 4\cos x\cos2x\cos3x$. I tried with $\cos A + \cos B$ identity but it was not simplifying.... Help..
1
vote
2answers
46 views

If $a_i>o$ then $(a_1a_2\cdots a_{2^n})^{1/2^n}\leq \frac{a_1+a_2+\cdots+a_{2^n}}{2^n}$

I need help to prove this inequality, I have no idea how to proceed with the inductive step: $$a_1,a_2,\ldots,a_{2^n}>0 \Longrightarrow(a_1a_2\cdots a_{2^n})^{1/2^n}\leq ...
1
vote
1answer
25 views

find a $B_{n,j}$ such that $|A_{n,j}-L_j| \leq B_{n,j}$ $\forall n,j$ and $\sum_{j=0}^{\infty}B_{n,j}$ converges

We have $A_{n,j}= 3(-1)^j2^{n-j+1}\frac{(2(n-j)-4)!}{(n-j)!(n-j-2)!}\binom{j+2}{2}\frac{n^\frac{5}{2}}{8^n}$ and $L_j=(-\frac{1}{8})^j\binom{j+2}{2}\frac{3}{8\sqrt{\pi}}$ So I know $\lim_{n \to ...
2
votes
4answers
26 views

Heaviside Unit Step Function

Convert to heaviside function: $$f(t) = \begin{cases}e^t ,& 0 \leq t \leq 1 \\0 ,& t > 1\end{cases}$$ My attempt: $f(t) = U(t) e^t - U(t-1) e^t $ I think my solution is not right because ...
5
votes
1answer
84 views

A number related to the roots of a quartic polynomial is a root of a cubic polynomial

So here is the problem, $a$ and $b$ are two distinct real roots of $f(x)=0$ where $f(x)=x^4-6x+3$, show that $(a+b)^2$ is a root of $g(x)=x^3-12x-36$. I have tried many methods, such as substitution, ...
6
votes
6answers
382 views

How to calculate this $\sqrt{3\sqrt{5\sqrt{3\sqrt{5\cdots}}}}$

I didn't know how to calculate this: $$\sqrt{3\sqrt{5\sqrt{3\sqrt{5\cdots}}}}$$ Please help me. Thanks.
6
votes
3answers
50 views

Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$

I have the following problem: Be the equation: $$u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw$$ Show that $u\rightarrow 0$ as $x\rightarrow \infty$, even when $e^{-iwx}$ does not falter ...
6
votes
4answers
449 views

For what values of m are the roots of $x^2 +2x+3 = m(2x+1)$ real and positive

I am only able to show that to be real, $m <-1$ or $m\geq2$ Don't know how to finish solution Answer is $2 \leq m < 3$ So far: After expanding and factorising, $x^2 + 2(1-m)x + (3-m) = 0 $ ...
0
votes
0answers
19 views

Solve the given differential equation by using Green's function method

I am really struggling with the concept and handling of the green's function. I have to solve the given differential equation using Green's function method $\frac{d^{2}y}{dx^{2}}+k^{2}y=\delta ...
0
votes
2answers
24 views

Doubts on locus and its equation

Find the equation to the locus of a point which is col-linear with points M(a,0) and N(0,b) Answer is:- x/a + y/b How i tried to find the solution:- P is a point whose assigned coordinates are (x,y) ...
5
votes
1answer
46 views

Is S a group under matrix addition

Another matrix question! Let $$S=\{A \in M_2(\mathbb{R}):f(A)=0\}\text{ and }f\left(\begin{bmatrix}a&b\\c&d \end{bmatrix}\right)=b$$ Is S a group under matrix addition. Either prove that ...
1
vote
1answer
23 views

How is the power rule applied to whole numbers

For the following function, how does the $+1$ become $0$ when finding its derivative via the power rule? Original function: $f(x) = 6x^2 − 4x^{-1} + 5x^{-2} − 2x + 1$ Derivative: $f '(x) = 12x + ...
0
votes
0answers
40 views

Complex Fourier Series and using the square norm

Find the complex Fourier series of $f(x)=e^{(-πx/2)}$ on $-π < x < π$ Discuss the significance of $|C_n|$ in the solution. I've tried so far Using the Complex Fourier Series: $$ %% ...
0
votes
0answers
53 views

$H_I^n(R)=0$ and $H_I^n(M)\neq 0$ [on hold]

Find R and M as an R-module such that $H_I^n(M)\neq 0$ and $H_I^n(R)=0$, where I an ideal of R and $n\in N$. I found it in Cohen Macaulay rings. there`s nothing to find.
1
vote
2answers
71 views

Polynomial Division - “Define the largest natural number…” [on hold]

Would someone mind helping me with this question? The more detailed possible so I can have 100% of understanding. Thanks. Question: Define the largest natural number m such that the polynomial ...
1
vote
4answers
53 views

Trigonometric functions of the acute angle

Find the other five trigonometric functions of the acute angle A, given that: \begin{align} &\text{a)}\ \ \sec A = 2 \\[15pt] &\text{b)}\ \ \cos A = \frac{m^2 - n^2}{m^2 + n^2} \end{align} ...
2
votes
1answer
150 views
+50

An arithmetic sequence whose members do not contain the digit ‘9’

There is a non-constant arithmetic progression made of natural numbers only; none of them contains the digit $9$. Prove that such an arithmetic progression has no more than $72$ terms.
2
votes
1answer
19 views

finding parallel sides from a irregular decagon?

Is it possible to find out that which of two sides are parallel in this irregular decagon.If,it is yes;then how can I proceed? I have tried with "Consecutive Interior Angles".but can't come to a ...
0
votes
1answer
44 views

Help with math steps, chain rule.

I'm trying to to understand the math steps to go from Eqn. (1) to Eqn. (2). $$\tag{1} q(x,t)=\frac{-V_t(1+\delta f(c,g))}{P(x,t)}\cdot \left(\frac{dP_o}{dt}\right)$$ $$\tag{2} \frac{-V_t ...
0
votes
1answer
30 views

Total derivative proof [on hold]

The wikipedia article does not prove it http://en.wikipedia.org/wiki/Total_derivative Neither the top articles in google search. Could somebody help me proving it? I've found this: ...
0
votes
1answer
35 views

Trigonometry Question - Tough one [on hold]

If in triangle ABC, sin A sin B sin C + cos A cos B = 1. Then find the value of sin C.