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 views

Finding the cubic near minimax approximation for sin(x) on (0,pi/2)

I am really stuck here. Here is the question that I have. Find the cubic near minimax approximation for f(x)=sin(x) on (0,pi/2). So I defined h(x)=ax^3 + bx^2 + cx + d - sin(x) The max of this ...
0
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0answers
10 views

Math A probabilty question

In Year 11 maths A there are three classes with 28,25 and 13 students in them respectively. A committee of three students is to be chosen. one from each class to represent a Maths Task Force. In how ...
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1answer
14 views

Rolling a balanced die 10 times

A balanced die is rolled 10 times by 5 different people. What is the probability that at least two people rolled exactly 4 twos, 3 fours and 3 sixes? So I know I'm looking for $P(X\ge 2)= ...
0
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1answer
24 views

How to solve this type of problems?

I'm struggling in solving this equation and tried to use the elimination method but did not work with me. Can anyone please show me how it can be solved? $$ -555=0.862X+0.138Y-0.345Z, \\ ...
0
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1answer
25 views

How to simplify the expression with sigma notation?

$$\sum\limits_{i=1}^n (n-i+1)(2i-1)^2= \frac{n(2n^3+4n^2+n-1)}{6}$$ how does this work? Could anybody show the details.
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3answers
30 views

Proving that function $f:[0,\infty)\rightarrow [0,\infty)$ defined by $f(x)=\frac{x^2}{1-x}$ is bijective.

I am having a bit of trouble with the algebra for proving that the function is injective. Basically I set $f(a)=f(b)$ for $a,b\in[0,\infty)$ and $a,b\neq 1$. ...
0
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0answers
14 views

Coffee machine exponential distribution

The amount of coffee a machine dispenses is an exponentially distributed random variable with mean 100cc. Suppose a cup will overflow if more than 120cc are dispensed. What is the probability that at ...
0
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1answer
8 views

Triple dot product relation to norm, angle and basis

So I'm asked to take the dot triple product, defined this way: $$\vec u \cdot \vec v \times \vec w $$ And I know that: $||\vec u|| = 1 $, $||\vec v|| = 2 $, $||\vec w|| = 3 $, ($\vec u$, $\vec v$, ...
1
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0answers
33 views

How do I go about showing the cardinality of two sets are the same?

How do I go about showing that the cardinality of the set of natural numbers and the cardinality of the cartesian product of integers is the same?: |N|=|Z x Z| Directly |N| = Aleph-null and I can ...
0
votes
0answers
26 views

When a measure-zero set size is bigger then another set size

Help me prove this theorem: Let $A \subseteq \mathbb{R}$ be a measure-zero set, and let $B\subseteq \mathbb{R}$ be a set. So, if $ |A| \geq |B| $ then $B$ is also a measure-zero set.
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votes
1answer
21 views

Statistics with discrete math

I am working on a homework problem and I think that I am doing this correctly but i am not sure. This is the question: An upper-level math class has 13 students: 4 of them are females. Two of the ...
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1answer
32 views

What are the solutions of the system?

There is a problem which is doing my head in :( The problem: What are the solutions of the system : Equation 1 $$ x^2 - 5xy + 6y^2= 0 $$ Equation 2 $$ x^2 - 3xy + y^2= 4$$ (I don't want the final ...
2
votes
1answer
22 views

I need help with this review question. Business Calculus/Statistics

The question is: The scores on a test have a mean of 100 and a standard deviation of 8. A personnel manager wishes to select the top 60% of applicants. Find the cutoff score. Assume the variable is ...
1
vote
2answers
50 views

Linear Algebra, Vector Space

$${ W = Sp\{{(1,3,4),(2,5,1)\}}\\ U = Sp\{{(1,1,2),(2,2,1)}} \}$$ Find a span $${U \bigcap W}$$ First time using Math latex, pretty hard.
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0answers
24 views

Linear Algebra, Vector spaces, Complex.

$W = {\rm span}\{(1,3,4),(2,5,1)\}$, $U = {\rm span}\{(1,1,2),(2,2,1)\}$. Find a set that spans $U\cup W$. Also, another question about $\Bbb C$: If $z_1 \cdot z_2 \ne -1$, $|z_1|=|z_2|=1$, is ...
1
vote
1answer
34 views

$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x$ , $x$ rational and $1-x$, $x$ irational. Prove that $f$ is injective and isn't monotone on any interval [on hold]

For injective i have to take a string with rational numbers and a string with irational numbers. Please help me!
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0answers
16 views

Pappus Locus Problem

This is a special case of the Pappus problem or the Pappus Locus Theorem. Let $L_1$, $L_2$, $L_3$, and $L_3$ be $4$ distinct lines in the plane. For a point $p$ in the plane, denote the (orthogonal) ...
1
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0answers
8 views

functional analysis findining dist(x,Z) in L2(-pi,pi)

The question in my hw was Let Z=span (1,sint,cost), x(t)=t. Find dist(x,Z) in $L_2(-\pi,\pi)$ From a lemma that we learned it says if Z is closed and $x(t)=t \notin Z$ then ...
2
votes
0answers
13 views

Finding the number of relations on set S

I know the number of reflexive relations on a finite set is: $2^{n^{2}-n}$ The number of symmetric relations is: $2^{n+1 \choose 2} $ The number of antisymmetric relations: $2^{n}3^{n \choose 2}$ ...
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1answer
25 views

Solving a system in 3 variables problem?

I need an answer for this problem, thanks in advance for the help. Find $x$, $y$, and $z$ from the problem below. \begin{eqnarray*} -2x + 1 &=& 5 \\ \\ 2x + 3y - 4z &=& 7 \\ \\ 3x ...
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votes
2answers
19 views

If f1 and f2 are 2 continous functions then f = { f1(x), x is rational and f2(x) , x is irational is continous in x0 if only if f1(x0)=f2(x0)

I have to prove that. I know that i have to take a string with rational number and a string with irational numbers but i don;t know how to do next. Please help me !
0
votes
2answers
29 views

Numbers in a list which are perfect squares and perfect cubes of numbers

How many numbers in the list $$1,2,3,...,2001$$ are perfect squares and perfect cubes of whole numbers? My progress: Well I do know $$1,4,9,16,25,36,...$$ are perfect squares and $$1,8,27,64,...$$ ...
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votes
2answers
18 views

Perfect Square and Multiple question

The population of a village is a perfect square. Later, with an increase of 100, the population was 1 more than a perfect square. Now with an additional increase of 100, the population is a perfect ...
3
votes
2answers
49 views

Number of homomorphisms $\mathbb Z_3 \times \mathbb Z_3\to\mathbb Z_9$

I had this wonderful idea: $f$ is homomorphism: $G\to H$, $|G| = |\ker f| \cdot |\operatorname{im} f|$, $\ker f$ - subgroup of $G$, and $\operatorname{im} f$ - subgroup of $H$, so their orders must be ...
2
votes
1answer
24 views

Please assist me with proving this

Prove that if $a$,$b$ and $c$ are angles in a triangle,then $$ \tan\left(\frac{b-c}{2}\right) = \frac{b-c}{b+c}\cot\left(\frac{a}{2}\right) .$$
1
vote
1answer
14 views

Integreal around a unit circle

I know that when $m \in \mathbb{Z} \backslash \{ 0 \}$, we have $$ \int_0^1 e^{2 \pi i m \beta} \ d \beta = 0. $$ I was wondering if there is a simple formula for the following similar integral, when ...
1
vote
0answers
11 views

Solving ODE numerically - getting local truncation error

Well I have NO idea how to do this or even where to start Compute the order of magnitude of the local truncation error of the following time integration scheme: $$y_{n+1} = y_{n-1} + 2h f(y_n)$$ H ...
-2
votes
1answer
13 views

Find the equation based on line segment

Suppose you draw a straight line segment between points $(a, 0)$ and $(0, 1 – a)$ for every real number $a\in (0, 1)$. All these segments taken together fill out a shape bounded by the positive ...
1
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4answers
36 views

Basic Probability Question (Expected Value)

We are given a bag of marbles containing 6 blue marbles, 7 red marbles, and 5 yellow marbles. We select 4 marbles without replacement. How can we calculate the expected value of the number of blue, ...
0
votes
3answers
64 views

How to prove $\sum_{n=1}^\infty \frac{a_n}{1+a_n}$ converges iif $\sum_{n=1}^\infty\frac{a_n}{1-a_n}$ converges?

Could you please give me some hint how to prove this statement: If $0<a_n<1$ for each n, then $\sum_{n=1}^\infty \frac{a_n}{1+a_n}$ converges iif $\sum_{n=1}^\infty\frac{a_n}{1-a_n}$ ...
0
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0answers
12 views

define the set of all affine real-valued functions

Define the set of all affine real-valued functions G := { $f$_a,b : a,b ∈ $R$ , a≠0}, where $f$_a,b : $R$ → $R$, x → ax + b. This is a group under composition ○. a) N := ...
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0answers
12 views

Bilinear Form with Constant condition show existence of bounded linear operator

The question states: Let $F:L^2(\mathbb{R}) \times L^2(\mathbb{R}) \to \mathbb{C}$ be a bilinear form (meaning that it is linear in each factor when the other is held fixed) such that there is a ...
1
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0answers
52 views

expand a rational function in a power series

$$\frac{4-x}{(2-x)(1-x)^2}$$ Expand in ascending powers of x, stating when the expansion is valid; also write down the coefficient of $x^n $
1
vote
1answer
15 views

Interest Accumulation - Geometric Sequence

Hello I have just worked a question in which I get an answer different to the answer in my book. The question states: If a person deposits 500 at the end of each month for 20 years at an AER of ...
0
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0answers
28 views

Derive three-point Gaussian quadrature formula [on hold]

Derive the three-point gaussian quadrature formula for
0
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1answer
27 views

Digit reversal arithmetic

How many three-digit odd numbers become bigger when their digits are reversed? $$abc<cba$$ and $c$ is either 1,3,5,7,9. This is the furthest I managed to reach.
2
votes
1answer
40 views

If every left coset of $H$ is a right coset the show that $H=aHa^{-1}$ for all a in G

$H$ is a subgroup of G. My attempt: $ha=ah' $ for every $h\in H$, where $h'\in H$ doesn't necessarily equal to $h$. So for each $h\in H$, $h=ah'a^{-1}\in aHa^{-1}$, so $H\subseteq aHa^{-1}$. Then how ...
3
votes
1answer
26 views

Determine $\text{Vect}_k(S^n)$

Let $\text{Vect}_k(X)$ denote the isomorphism classes of rank $k$ real vector bundles over smooth manifold $X$. Is there a rule for determining $\text{Vect}_k(X)$ over reasonably nice manifolds? ...
1
vote
2answers
53 views

Three-Digit numbers divisbile by 3

How many three digit numbers are divisible by 3 and have an additional property that the sum of of their digits is 4 times the middle digit? My approach: let the number be $abc$ so $$abc \equiv ...
0
votes
2answers
58 views

solutions of $x^2\equiv 1 \pmod p $ [duplicate]

If p is a prime, show that the only solutions of $x^2\equiv 1 \pmod p $ are $x=1$ and $x\equiv -1 \pmod p$. (from herstein's abstract algebra chapter2 section4 lagrange's theorem problem 15, this ...
2
votes
3answers
51 views

5 digit number $a6a41$ divisible by 9

In the 5-digit number $a6a41$ each of the a's represent the same number. If the number is divisible by 9, what is the digit represented by $a$? I first approached this by saying $$2a + 11$$ since ...
0
votes
0answers
15 views

supremums & functions

I'm am having some trouble with the below and was wondering if anyone would be kind enough to help me out. I have the following: $|L^n_{j}|\leq |\frac{\Delta t}{2} u_{tt}| + |\frac{ah}{2} u_{xx}|$ ...
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2answers
51 views

If $(1 + 2i)$ and $(3 - 2i)$ are two roots of $x^5 + ax^4 + bx^3 + cx^2 + dx + 4$, then $a$ =?

Consider the polynomial $x^5 + ax^4 + bx^3 + cx^2 + dx + 4$ where $a, b, c, d$ are real numbers. If $(1 + 2i)$ and $(3 - 2i)$ are two roots of this polynomial then what is the value of a? Well, I ...
6
votes
3answers
77 views

Let $a,b \in R$ where $ a < b$. Prove that there exist a rational number $c$ and an irrational number $d$ such that $ a <c<b$ and $ a<d<b$.

Question : Let $a,b \in R$ where $ a < b$. Prove that there exist a rational number $c$ and an irrational number $d$ such that $ a <c<b$ and $ a<d<b$. Hint: consider decimal expansions ...
0
votes
1answer
31 views

finite and infinite, vector space, linear transformation

I have to answer these questions for homework and I don't know if I'm answering these correctly. I think most of them are correct, but a double check would be much appreciated. a) If $S$ is a set ...
1
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0answers
8 views

Symetric powers of $sl_2$ representations

I'd like to understand some special things about representations of $sl_2$ (which is considered as a Lie algebra over $\mathbb{C}$). First, it can be shown that for each $n\in \mathbb{N}$ there is ...
1
vote
1answer
26 views

Energy Transfer in a Mechanical System - Standard Pulley Scenario

I understand that this is quite a basic question, I am new to dynamics and have trouble starting off questions, I found it quite difficult to find an example question alike to the one below thus I am ...
1
vote
0answers
40 views

How to prove convergence of $\int_0^1f\left(\sqrt x \right)dx$?

Could you please give me some hint how to prove convergence of $\int_0^1f\left(\sqrt x \right)dx$ when f(x) is continuous for $0<x\le1$ and $\lim_{x\to0^+}x^3f^2(x)=1$ ? I tried the usual way: ...
6
votes
1answer
25 views

Proof for Complex Analysis Inequality

This is a homework assignment that will be graded; so I'm not specifically asking for an answer. But I could use a hint, as it's been a few days and I'm still not sure if how I've proved it would ...
2
votes
2answers
51 views

Prove that if $y,z \in Q$ then $y^z \in A$

Question : Prove that if $y,z \in Q$ then $y^z \in A$ My attempt: Definition 2.7.8 states that a number s is an algebraic number when there exists some $p \in Z[x]$ such that $p(s) =0$. Let us ...