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 ...
0
votes
0answers
23 views
Is Multiplication A System?
I don't understand how to identify the properties of a system.
What possible properties could a system have?
Are a certain number of properties required in order to be classified as a system?
The ...
2
votes
1answer
24 views
Find the smallest possible integer that satisfies both modular equations
Find the smallest positive integer that satisfies both. x ≡ 4 (mod 9) and x ≡ 7 (mod 8) Explain how you calculated this answer.
I am taking a math for teachers course in university, so I'm worried ...
-4
votes
1answer
19 views
Cost and Marginal cost
Nissan has determined the following for its Sunny model:
Price function: $p(x)= \frac{1}{5} (45-x)$
Cost function: $C(x)= \frac{1}{4}x^2+3x+67$
Find the following:
Revenue & Profit functions.
...
0
votes
1answer
21 views
Solving Modular Equations With Identities
$4+2x≡7 \pmod 8$
Find all possible solutions and note any identities.
Identify how you found the solutions.
Explain what identities are.
2
votes
1answer
25 views
how to dot product two vectors with different planes?
how to dot product two vectors with different planes?
I have vectors $A$,$B$ and $C$, vectors $A$ and $B$ is on $xy$ plane while vector $C$ is on $xz$ plane. I need to find the dot product of $A.C$ ...
0
votes
0answers
14 views
Finding rate of maximum temperature increase along surface
So I know that the rate of maximum increase of some function (say, $f(x,y)$) is given by the gradient ($\nabla f$), where the direction is the direction of maximum increase of the function, and the ...
2
votes
0answers
30 views
Linearization of an implicitly defined function.
Problem:
Given the equation: $xz^{2}+y^{2}z^{5}=19$
Also given: (3,4,1) is a solution to the equation. This point is not the only solution.
1) Find dz/dx and dz/dy (through implicit ...
4
votes
3answers
41 views
Prove equality in triangle inequality for complex numbers
We need to show that
$$ |z_{1}+z_{2}+\cdots+z_{n}|=|z_{1}|+|z_{2}|+\cdots+|z_{n}|$$
if and only if $z_{1},z_{2},\dots,z_{n}$ have the same argument (i.e. $z_{j}=r_{j}e^{i\theta}$ for $j=1,\dots,n$).
...
0
votes
0answers
34 views
How to solve for $z$ in $\dfrac{xy}{1-x}=(1-z)(x-x^{1/z})$
How to solve the following for $z$:
$$\frac{xy}{1-x}=(1-z)(x-x^{1/z})$$
where $0 < x < 1$, $\;0 < y < 1$, $\;0 < z \leq 1$.
-1
votes
2answers
46 views
General Linear Groups with Homomorphisms [closed]
Let $G=\mathrm{GL}_n(\mathbb R)$ and $H=\mathbb R^*$. Let $\phi : G=\mathrm{GL}_n(\mathbb R) \rightarrow \mathbb R^*$ be the map defined by $\phi(A)=\det(A)$. Show that $\phi$ is a group ...
1
vote
0answers
18 views
Hahn Banach to get linear functional bounded by sub/superlinear functionals
I am working in a real vector space $V$. I have seen it written that if I have a sublinear functional $p$ and a superlinear functional $q$ such that $q \le p$ then there exists some linear functional ...
0
votes
3answers
47 views
Pigeon holes principle
Let $P$ be a group that it's elements are 257 sentences in which only atomic sentences from $A,B,C$ exist (i.e. $A \iff B,\space\space A \wedge B \wedge C, \space\space...$) Show that there exists two ...
2
votes
4answers
43 views
How can I solve this Laws of Sines problem?
This is a homework question that was set by my teacher, but it's to see the topic our class should go over in revision, etc.
I have calculated $AB$ to be 5.26m for part (a). I simply used the law ...
3
votes
3answers
42 views
$ e^{At}$ for $A = B^{-1} \lvert \cdots \rvert B $
For a homework problem, I have to compute $ e^{At}$ for
$$ A = B^{-1} \begin{pmatrix}
-1 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 3 \end{pmatrix} B$$
I know how to compute the result ...
1
vote
0answers
54 views
How does this violate probability theory?
Given: $X = Y^2 + Z^2$ (hence $E[X] = E[Y^2] + E[Z^2]$)
$p(X = 1) = .52$, $p(X = 4) = .24$, $p(X = 16) = .24$
$p(Y = -1) = .5$, $p(Y = 3) = .5$
Question: Despite not being handed any information ...
0
votes
0answers
14 views
XS 3 - correction
When adding together two XS-3 (Excess-3) numbers, what are the rules for correction? For example, adding 0011 and 1101 correctly.
It's not my homework, but I don't know how to tag it.
0
votes
0answers
17 views
finding the optimal solution of the dual problem
This is homework.
I have the following dual problem, formed by using lagrangian relaxation.
$$
\begin{align}
min & \{&89y_1 +&3y_2 +&10y_3\}\\
s.t.& &3y_1+& &y_3 ...
0
votes
0answers
19 views
General solution of diff.eq of order 3
please , why the general solution of $u'''(t)=e(t) , t\in [0,1]$ is given by
$u(t)=c_0+c_1t+c_2 t^2 +\frac12 \int_0^1 (t-s)^2 e(s) ds$
$e:(0,1)\rightarrow \mathbb{R}$, and $e\in L(0,1)$.
Thank ...
1
vote
3answers
33 views
Series of $\int_0^z \zeta^{-1} \sin \zeta d \zeta$
This is a homeworkquestion so I would appreciate some good hints. I have $f(z) = \int_0^z \zeta^{-1} \sin \zeta d \zeta$. Can this be written as a power-series in $\mathbb C$ around $z = 0$?
1
vote
2answers
35 views
Solve the Lagrangian dual problem
Consider the (non-linear) optimization problem ($P$)
$$max \quad3x_1 + 4x_2$$
$$s.t. \quad x_1^2 + x_2^2 \leq 25$$
$$ \quad x_1,x_2 \geq 0$$
Solve the Lagrangian dual problem.
I ...
1
vote
1answer
22 views
Eigenvectors and differential equations
I was able to find part (a), and I got 4 and -1 for the eigenvalues and from these values I got eigenvectors of [1,1] and [-3,2], but I don't know what to do for part (b) and (c)
0
votes
1answer
80 views
Geometric question?
First of all, is it Geometric?
Image of the drafted:
I need help solving this question, and I am completely lost on how can I solve this.
Could anyone explain the way of solving this geometric ...
2
votes
3answers
141 views
The negative square root of $-1$ as the value of $i$
I have a small point to be clarified.We all know $ i^2 = -1 $ when we define complex numbers, and we usually take the positive square root of $-1$ as the value of "$i$" , i.e, $i = (-1)^{1/2} $.
I ...
0
votes
1answer
31 views
Show convergence for this sequence only by using the definition
I need to prove convergence for
$(b_n)_{n ∈ ℕ}=\left(\frac{(-1)^nn}{2n+1}\right)_{n∈ℕ}$ and also show the limit.
I may only use the following definition: $∀ɛ > 0∃n_0∈ℕ∀n≥n_0:|a_n-a|< ɛ$.
So far ...
0
votes
0answers
17 views
Prove that this linear programming problem has the following dual problem
Consider the following Linear Programming problem:
$$max \sum_{j=1}^nc_jx_j$$
\begin{align} s.t. \quad
\sum_{j=1}^na_{ij}x_j=b_i \quad 1\leq i\leq m\\
x_j\geq 0 \quad 1\leq j \leq n.\\
...
0
votes
1answer
12 views
Body Volume Rotation Of Shape Question
I want to know if I`m following the correct step to evaluate the body volume rotation of shape.
my function is : $$y=ln(x)$$ and I want to evaluate the body volume rotation of it between
$y=0$ and ...
0
votes
0answers
19 views
Question About Indefinite Integrals
I`m trying to understand how should I evaluate this indefinite integral with this data on the integral :
the question is : "Draw the shapes on the plain blocked - by the data lines and evaluate"
:
1) ...
1
vote
1answer
45 views
Prove that a cylinder have a infinite number of planes of symmetry.
My definition of cylinder is:
A cylinder is the surface formed by parallel lines, where each line contains a point of a curve called guideline. Each lines is called a generatrix of that cylinder.
...
2
votes
0answers
69 views
Prime numbers problem - discrete math
Show that natural numbers of the form $n^2+1$ are not divisible by primes of the form $p=4k-1$.
I can't really find a place to start.
Thank you very much in advance,
Yaron.
1
vote
2answers
41 views
Application of Urysohn's lemma
I am working on the following hw problem: If we have that $X$ is a compact Hausdorff space, with $\{U_\alpha\}_{\alpha\in A}$, then we can find a finite number of continous functions $f_1,...,f_k$, ...
12
votes
3answers
294 views
$\sum\limits_{\text{prime }p} 2^{-p}$ is an irrational number
I need help to prove the following result.
$\displaystyle\sum_{\text{prime }p} 2^{-p}$ is an irrational number.
1
vote
1answer
24 views
Approximating a Poisson distribution to a Normal distribution
I have the following problem I'm trying to solve:
I know that the quantity of complains in a call center is a Poisson variable with $\lambda=18 $ costumers/hour, and that the probability of being ...
0
votes
1answer
19 views
Finding perimeter using unknown variables
Rectangle region ABCD show in below partitioned into 14 identical small rectangles, each of which has width x.
What is perimeter of ABCD in terms of x?
I have used rectangle perimeter formula but ...
-4
votes
0answers
38 views
Find ebook A.V. Pogorelov, “Foundations of geometry”. [closed]
Can you help me find ebook : A.V. Pogorelov, "Foundations of geometry" , Noordhoff (1966).
Or book write about axoxiom systems Pogorelov in Euclidean geometry.
2
votes
2answers
42 views
mixture problem
From Stewart, Precalculus, $5$th ed, p.$71$, q.$55$
The radiator in a car is filled with a solution of $60\%$ antifreeze and $40\%$ water. The manufacturer of the antifreeze suggests that, for summer ...
0
votes
1answer
29 views
The sum of the integration of g and $g^{-1}$
Let $g$ be a strictly increasing continuous function mapping $[a,b]$ onto
$[A,B]$, and, as usual, let $g^{-1}: [A,B] \to [a,b]$ denote its inverse function.
Use geometric insight to visualize the ...
1
vote
0answers
27 views
To prove that an operator is bounded [duplicate]
I have this problem:
Let $(H, \langle\cdot,\cdot\rangle)$ a Hilbert space on $\mathbb{C}$
and $A:H\rightarrow H$ a linear operator such that $$\langle A(x),
y\rangle\ =\ \langle x, ...
0
votes
0answers
51 views
Automorphisms of fields
How can I prove that there is an element of order 23 in $\mathrm{Aut}\mathbb{Q}(K)$, where K is a subfield of complex numbers generated by all complex roots of $x^{23}-6x^{22}+3$?
0
votes
3answers
61 views
How to solve these?
Inverse Trigonometric Functions
They are incomplete and I don't know how to complete them.
Who can help me?
1st
$$
\int\frac 1{ x \sqrt{x^{6} - 4}}dx
$$
I tried with:
$$u = x^3 $$
$$du= 3x^2dx$$
...
6
votes
2answers
121 views
does a matrix like this exist?
Question:
Does a matrix $A \in M_{3 \times 3}(F)$ exist s.t. $A^4=
\begin{bmatrix} 0&0&1\\0&0&0\\0&0&0\end{bmatrix}$
What I thought:
I think it doesn't. How do you start a ...
4
votes
0answers
44 views
On an exercise from Hartshone's Algebraic Geometry, Ch I sect 4
My question is about the Ex. 4.9 page 31 in the book GTM52 by Robin Hartshone.
Let $X$ be a projective variety of dimension $r$ in $\mathbb{P}^n$, with $n\geq r+2$. Show that for suitable choice ...
1
vote
3answers
68 views
Using induction to verify a statement
I have to prove that this statement is true.
For $n = 1, 2, 3, ...,$ we have $ 1² + 2² + 3² + ... + n² = n(n + 1)(2n + 1)/6$
Basically I thought I'd use induction to prove this. Setting $n = p+1$, I ...
1
vote
1answer
29 views
Using Square area finding quadrilateral area
Area of square ABCD is 169 and that of square EFGD is 49. Find area of quadrilateral FBCG
I am stuck and just thinking which way can be helpful for me finding this area of quadrilateral FBCG. ...
1
vote
1answer
34 views
Understanding when convergence implies uniform convergence for sequences of non-continuous functions
I am working on the following problem:
Let $(f_n)$ be a sequence of functions $[a,b] \rightarrow \mathbb{R}$ such that: (i) $f_n(x)≤0$ if $n$ is even, $f_n(x)≥0$ if $n$ is odd; (ii) ...
1
vote
1answer
34 views
strict ordering a Set
Given:
$(A,<)$ is a strictly ordered set and $b \notin A$.
Define:
a relation $\prec$ in $ B = A \bigcup \{b\} $ as:
$x\prec y $ if and only if $(x,y \in A \text{ and } x<y)$ or $(x \in A ...
2
votes
2answers
21 views
Equivalence Relations and functions on partitions of Sets
let $f$ be a function on $A$ onto $B$. Define an equivalence relation $E$ in $A$ by: $aEb$ if and only if $f(a)=f(b)$.
Define a function $\phi$ on $A/E$ by $\phi([a]_{E})=f(a)$.
Hint: Verify that ...
5
votes
3answers
96 views
How can I prove that $\sin (10^\circ), \sin(1^\circ), \sin(2^\circ), \sin(3^\circ), \tan(10^\circ)$ are irrational
How can I prove that $\sin (10^\circ), \sin(1^\circ), \sin(2^\circ), \sin(3^\circ), \tan(10^\circ)$ are irrational?
My try:: Let $x = 10^\circ$, Then $3x = 30^\circ$
Now $\sin (3x) = \sin ...
-1
votes
0answers
28 views
Continuity of quotient map
$f:X\to X/\mathord{\sim}$ is continuous for any space $X$ and equivalence relation $\sim$, where $f$ is defined to be $f(x)=[x]$, and $[x]$ is the equivalence class of $x$.
How can I prove this?
1
vote
1answer
30 views
Solving Euler-equation alike 2nd order DE with disturbing RHS
For a homework problem, I have to solve
$$ t^2 \ddot{x} - 3 t \dot{x} + 3x = t^2 $$
which seems quite similar to the Euler Equation, which I would know how to solve, apart from the disturbing $ t^2 ...
3
votes
1answer
27 views
Evaluating order of convergence
I think this is quite a simple question, I just want to make sure I understood all correctly.
Here's the problem: I have a numerical method, which is in some way dependent on its spacing $h$ (like ...
