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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0
votes
1answer
38 views

Volume of the pyramid…

I have such a problem from geometry: Five edges of a regular triangular pyramid have the length of $6$ $dm$, but the sixth- $4$ $dm$. Determine the volume of the pyramid. For me the problem is quiet ...
2
votes
1answer
29 views

Geometry and Triangles

A triangle ABC is such that AB = 12 cm and AC = 8cm. X is the midpoint of the base BC. If the area of the triangle is 72 square centimetres what is the length of the perpendicular from X to AB and ...
2
votes
1answer
30 views

One step Gauss Seidel method

Apply one step of the Gauss Seidel method to $A\textbf{x} = b$ with A = $\begin{bmatrix} 4 & 2 & 1 \\ 1 & 4 & 1 \\ 1 & 2 & 4 \end{bmatrix}$, b = $\begin{bmatrix} 4\\ ...
1
vote
1answer
16 views

Intersection of graphs, and no solution for trig functions.

All I know is the c=asin(x-b) I don't know how to check the values of b for 'no solutions,' in the case of trig functions. Can someone people provide an algebraic method to solve this.
0
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0answers
53 views

Proof for A majorizes B

$\alpha = [\alpha_i] \in\mathbb R^n$ and $\beta = [\beta_i]$ where $\beta_1 = \beta_2 = ......=\beta_n = \frac{1}{n}\sum\alpha_i$ How can i show that $\alpha$ majorizes $\beta$ I tried to get a ...
0
votes
1answer
42 views

How to prove that $\max\{f,g\}$ is Riemann integrable? [duplicate]

If f(x) and g(x) are Riemann integrable in [a,b], why $h(x)=\max\{f(x),g(x)\}$ is still Riemann integrable in [a,b]? Or maybe it is wrong?
1
vote
1answer
48 views

Prove that this matrix is not diagonalizable WITHOUT determinants

I have this matrix: $ \left( \begin{array}{cccc} 22 & 23 & 10 & -98\\ 12 & 18 & 16 & -38\\ -15 & -19 & -13 & 58 \\ 6 & 7 & 4 & -25 \end{array} \right) ...
0
votes
1answer
31 views

a question about integral? I have no idea about that!

If f(x) and g(x) are integrable in [a,b], can we say that f(x)g(x) is still integrable in [a,b]? I am referring to Riemann integration!
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votes
2answers
38 views

Prove that the vectors $v_1,v_2,\ldots,v_k \operatorname{span}R^n$ if and only if $[v_1]_B,[v_2]_B,\ldots,[v_k]_B \operatorname{span}R^n$.

From section on Change of Basis $\longrightarrow$ Assume the vectors $v_1,v_2,\ldots,v_k\operatorname{span}R^n$, we must show that $[v_1]_B,[v_2]_B,\ldots,[v_k]_B\operatorname{span}R^n$. We can ...
0
votes
1answer
28 views

Determine which of the following subsets of $\Bbb{R}^n$ are subspaces of $\Bbb{R}^n (n>2)$.

I'm having a bit of trouble showing that the following subsets of $\Bbb{R}^n$ are subspaces of $\Bbb{R}^n (n>2)$. I know that I need to show that they are closed under addition and multiplication, ...
-1
votes
1answer
42 views

Heat Equation Steady state question

Say you have a slab of material occupying the region $0\leq x\leq a$. Heat is supplied at a constant unit rate so the temperature $T(x,t)$ satisfies $$\frac{\partial T}{\partial t}= k ...
0
votes
2answers
41 views

Why does this form a basis for $V$? (Intuitive explanations please)

Let $V$ be the space spanned by $\mathbf f_1=\sin(x)$ and $\mathbf f_2=\cos(x)$. Show that $\mathbf g_1=2\sin(x)+\cos(x$) and $\mathbf g_2=3\cos(x)$ form a basis for $V$. We can see that $$\mathbf ...
0
votes
1answer
23 views

Lie bracket of vector fields on $R^2$

Compute the Lie bracket$$\Big[-y\frac{\partial}{\partial x}+x\frac{\partial}{\partial y},\frac{\partial}{\partial x}\Big]$$ on $R^2$ Can you help me please?
1
vote
2answers
71 views

Solve second order differential equation with Heaviside function using Laplace transform

The equation is: $$y'' + 3y = u_4(t)\cos(5(t-4)), \quad y(0) = 0, \quad y'(0) = -2$$ Here $u_4$ is the Heaviside function with activation switch at $t=4$. I can get all the way to the partial ...
3
votes
0answers
23 views

Showing iterates of a complex function on the upper half plane converges uniformly on compact sets

The following is an irksome problem that my complex analysis class is having trouble solving: Let $*$ be an operator that takes a function $F:\mathcal{H}\to\mathcal{H}$ to a function ...
-1
votes
1answer
31 views

question about rational expressions

i can't understand how to do this 5 question please help me ! Thank you
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votes
0answers
13 views

Expected number of feed-forward/backward triangles in a random graph with internal nodes.

Suppose we have a graph with N* nodes (these are internal nodes. they all have at least one child). Every directed link in the network exists with probability p. What would be the expected number of: ...
-5
votes
0answers
37 views

need help to prove the following problem [on hold]

Show that $s_n$ is a Cauchy sequence.
2
votes
2answers
60 views

number of solutions to $x_1 + x_2 + x_3 + x_4 + x_5 = 31$ via generating function?

I will be very happy to understand how to solve this problem with generating function: How many solutions are there to the equation $$x_1 + x_2 + x_3 + x_4 + x_5 = 31$$ where $x_i$ is a nonnegative ...
1
vote
0answers
33 views

Quadratic reciprocity problem

How can I use quadratic reciprocity to prove that $-3$ is a quadratic residue $\pmod p$ if and only if $p=2$ or $p \equiv 1 \pmod 6$ and deduce that $\mathbb{Z}[\sqrt{-3}]/(p)\cong \mathbb{F}_p ...
1
vote
1answer
87 views

i need help to prove this problem(functional analysis)

show that the annihilator of a set M in an inner product space X is a closed subspace of X.
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votes
2answers
25 views

Show that the set $W$ of all polynomials in $P_2$ such that $p(1)=0$ is a subspace of $P_2$. Find a basis for $W$.

a.) Show that the set $W$ of all polynomials in $P_2$ such that $p(1)=0$ is a subspace of $P_2$. b.) Make a conjecture about the dimension of $W$. c.) Confirm your conjecture by finding a ...
0
votes
0answers
28 views

Solving $u_{yy} + (2-x)u_y - 2xu = 1$

I want to solve the pde $$ u_{yy} + (2-x)u_y - 2xu = 1 $$ so if I treat $x$ in the coefficients as arbitrary but fixed it is equivalent to solving the ode $$ y'' + (2-x) y' - 2x y = 1. $$ For the ...
1
vote
2answers
18 views

Why is x1 and y1 constants in linear equation

In the equation $ y = mx + (y_1 - mx_1)$ , why is $ y_1$ and $ x_1 $ constant?
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votes
0answers
21 views

Linear algebra.Proof proportinal between minors and cofactors

$B$ is square matrix. Order of matrix $B$ is $n$. First $m$ lines form the matrix $C$, $rank (C)=m$.Last $n-m$ lines form fundamental system solutions of homogeneous linear equation with matrix $C$ ...
0
votes
3answers
45 views

Sequence problem.

Help for this problem would be much appreciated, as I am expected to solve it without being properly taught how. Suppose a single cell of bacteria divides into three every 12 hours. Suppose that the ...
0
votes
0answers
3 views

some past paper questions in Discrete Time Systems i couldnt solve.

I am working on past papers of my exam which is in two days, there was one particular year , 2009, which I could not solve quite a lot of its questions... i only could solve 5 out of 10, can anyone ...
1
vote
2answers
33 views

Prove $f(x) = \frac{1}{x^2}$ is uniformly continuous on $[1, \infty]$

I am trying to prove this function is uniformily continuous on $[1, \infty]$, so far i have; $$|f(x) - f(x)| = |\frac{1}{x^2} - \frac{1}{y^2}| = |\frac{(x-y)(x+y)}{x^2y^2}|$$ and then, ...
0
votes
3answers
23 views

Euclidean algorithm in the ring of polynomials over a field

I need some help with the following division proofs. I suppose my biggest problem is not being able to visualize the algebra for one GCD equaling another GCD. I'm not sure of how to arrange the ...
0
votes
4answers
47 views

A seemingly basic PEMDAS problem… [duplicate]

There's one of those meme-type images posted on Facebook with the equation 6/2(1+2), challenging you to solve it. So, parenthesis first, ...
2
votes
1answer
24 views

Determine the values of real parameters …

If you have an idea, please, do not leave the page, just write it, I will be very thankful. We have the function $$f:R\setminus \{-1 \}\to{R}$$ ...
0
votes
1answer
32 views

Lambda Calculus using $\beta$-reductions

Use $\beta$ reductions to compute the final answer for the following $\lambda$ terms. Use a "fake" reduction step for "+" operator. Identify each redex for $\beta$-reduction steps. Does the order in ...
0
votes
0answers
14 views

Find the values of the parameters for which the function admits an oblique asymptote…

can you please help me solve this exercise: Find the values of real parameters $a$ and $b$ so that the function $$\color{maroon}{f(x)={(ax^3+bx^2)}^{1/ 3}}$$ admits an oblique asymptote: ...
0
votes
0answers
30 views

Find E[MSLOF]. Please help.

Find the expected mean squares error of lack of fit. Trial: $$SSLOF=\sum_{1}^mn_i(\bar y_i-\hat y_i)^2\\=\sum_{1}^mn_i(\bar y_i-\bar y)^2-\sum_{1}^mn_i \hat\beta_i^2(x_i-\bar x)^2$$ and ...
1
vote
0answers
25 views

Bounded on an union of squares

I would like to do this exercise : Let $\displaystyle h(z) = \pi \mathrm{cotan}(\pi z) = \pi \frac{\cos(\pi z)}{\sin(\pi z)}$. And for $q \in \mathbb{N}^{*}$, let $C_{q}$ be the square in the ...
1
vote
1answer
26 views

Compute infinite sum of a arithmetico-geometric series $\sum_{i=0}^{\infty} \frac{i}{2^i}$ [duplicate]

I am trying to compute the sum $\sum_{i=0}^{\infty} \frac{i}{2^i}$ which I know should be equal to $2$, but I cannot prove it. If I am not mistaken, it should be a arithmetico-geometric series ...
1
vote
1answer
55 views

Two touching circles inscribed in an angle

There are two touching circles inscribed in a $60^\circ$ angle. The distance between the vertex of angle and the center of smaller circle is $5j$. What is the ratio of the surfaces of two circles?
0
votes
1answer
19 views

2 dice are rolled: what is P(at least one lands on 6 | dice land on different numbers)?

$P$(at least one 6)$=1-(\frac{5}{6})(\frac{5}{6})=\frac{11}{36}$ $P$(different numbers)$=(\frac{6}{6})(\frac{5}{6})=\frac{30}{36}$ I know that $P$(at least one six | different numbers) = $\frac{P(at ...
0
votes
3answers
25 views

Find all points on the curve $y=2x+x^{-1}$ which have a tangent parallel to the x-axis

Find all the points on the curve $y=2x+x^{-1}$ which have a tangent parallel to the $x$-axis.
1
vote
1answer
38 views

Prove for all $ n \in N,gcd(2n+1,9n+4)=1$

Question: Prove for all $ n \in N,gcd(2n+1,9n+4)=1$ Attempt: I want to use Euclid's Algorithm because it seemed to be easier than what my book was doing which was manually finding the linear ...
1
vote
3answers
66 views

An infinite generating set of a finite dimensional vector space contains a basis

Let $S$ be an infinite generating set of a finite dimensional vector space , then how do we prove that there is a subset of $S$ which is a basis of the vector space ? Please help
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votes
2answers
38 views

Feedback on Euclidean Algorithm: $gcd(277, 301)$

Ans: $301 =277 \cdot 1 + 24$ $277 =24 \cdot 11 + 13$ $24 = 13 \cdot 1 + 11$ $13 = 11 \cdot 1 + 2$ $11 = 2 \cdot 5 + 1$ $2 = 1 \cdot 2 + 0$ Is this correct?
-1
votes
0answers
33 views

Euclidean alogrithm [on hold]

Use the Euclidean alogrithm to compute the greatest common diviser of 277 and 301. my solution Let a=277 and b=301 . Also, let's introduce the variable "r" for the remainder Let's evaluate ...
11
votes
7answers
993 views

What's wrong with these equations? [duplicate]

My friend Boris (Boryan) gave me a task, and completely refuses to give the answer what's wrong here. $$x^2=\overbrace{x+\cdots+x} ^{x\text{ times}}$$ $$(x^2)'=(x+\cdots+x)'$$ $$2x=1+\cdots+1$$ ...
0
votes
2answers
25 views

Probability Density Function with continuous random variables

Let $X$ have density $$ f_X(x) = \begin{cases} \sqrt{3(x+2)}/6 & -2 \leq x \leq 1 \\ 0 & \text{otherwise}. \end{cases} $$ Find the probability that $X$ is positive. Would this just ...
0
votes
2answers
19 views

Probability of weather on consecutive days.

Probability of a cloudy day is .55 Probability of a sunny day is .45 A)What is the probability of three consecutive cloudy days, followed by a sunny day? B)What is the probability that exactly 1 out ...
1
vote
1answer
28 views

Finite subcover of pairwise disjoint open intervals

I have the following exercise: Prove that if $X$ is a countable compact subset of $ \mathbb{R}$, then for any $\varepsilon>0$ there is a finite collection of pairwise disjoint open intervals ...
-1
votes
0answers
12 views

Using BCR experiment [on hold]

consider a random experiment of observing a mechanical or electrical unit consisting of five components and determining which components are working and which have failed. Use the BCR to find the ...
1
vote
1answer
51 views

Lambda calculus logical operators

Define the and operator in lambda calculus and prove your definition Define the exclusive or operator in lambda calculus, and prove your definition My answer for #1 is: AND $\equiv$ ...
-1
votes
2answers
40 views

In tossing 5 6-sided fair dice, what is the probability of at least one 2 if the dice are indistinguishable?

I know that the answer is .4 because it is given. I just do not know how to get there. The answer would be .598 if the dice were distinguishable (ordered).