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
2answers
55 views

sets and finding counterexample from empty set [duplicate]

Question Find a counter-example to the claim that for all sets $A,B,C$ if $A\cap B=B\cap C=A\cap C=\emptyset$ then $A\cap B\cap C\neq\emptyset$. If i have to find a counter-example then It should be ...
2
votes
3answers
69 views

Find the remainder of $40^{314}$ divided by 91.

Here's what I have so far. $$x \equiv 40^{314} \mod{91}$$ $$\Rightarrow$$ $$x \equiv 40^{314} \mod{7}$$ $$ x \equiv 40^{314} \mod{13}$$ Then by FLT, $$40^6 ≡ 1 \mod{7}$$ $$40^{12} ≡ 1 \mod{13}$$ ...
0
votes
3answers
43 views

How to use Rolle's Theorem or the Mean Value Theorem to prove particular intersection points are the only intersection points

$$f(x) = x^{3}$$ and $$g(x) = \sqrt{x}$$ Find all of the intersection points between the graphs of $f$ and $g$. Show that these are the only intersection points I have found the intersection points ...
3
votes
2answers
71 views

If $(b-a) = (ba^2 - ab^2)$, show that $a=b$ where $a,b \in \mathbb R$

I am slightly stuck on this seemlingly simple problem that I encoutered as part of a problem to show that the orthogonality condition of $M_{2\times2}$ matrices given by $\sum_i a_{ij}a_{jk} = ...
2
votes
1answer
28 views

Is my contrapositive of this statement correct?

Proposition: If $x$ is even and $x$ is greater than $2$, then there exist prime numbers $p$ and $q$ such that $x = p + q$. Contrapositive: If for all prime numbers $p$ or $q$, $x$ does not equal $p + ...
2
votes
2answers
13 views

Determining line equation

Find the equation of the line going through the point $(2,-3,4)$ ,and which is perpendicular to the plane $ x+2y + 2z = 13$ So I tried this: the normal of the plane is $(1,2,2)$, random point on the ...
-5
votes
1answer
40 views

can any one help me with this pigeonhole question?

I try to solve it but i don't have enough time cuz it dues tomorrow. And I have no clue to solve it. hope you guy can help me out with this!
1
vote
1answer
20 views

Is my proof correct? Let $a, b, c\in\mathbb Z$. Prove that if $a\mid b$ and $b\mid c$, then $a\mid(b + c)$.

Let $a$, $b$, $c$ $\in\mathbb{Z}$. Prove that if $a\mid b$ and $b\mid c$, then $a\mid (b + c)$. My proof: since $a\mid b$, $b = k\cdot a$ for some integer $k$ since $b\mid c, c = l\cdot b$ for some ...
0
votes
1answer
20 views

I want, by the use of the equation of the line in complex plane, to find the slope and x intercept in x-y plane

$$|z-a|=|z-b|$$ $$y=mx+h$$ $$m=m(ax,ay,bx,by) \quad h=h(ax,ay,bx,by)$$ $$a=ax+iay \quad b=bx+byi$$ Find $m$ and $x$ by the use of equation of line in complex plane. I want, by the use of the equation ...
-4
votes
0answers
26 views

differentiate the given function. Simplify your answers [on hold]

In Exercise 1 through 28, differentiate the given function. Simplify your answers y=√2X
1
vote
0answers
21 views

Textbook question on variety

Suppose a variety V is defined by an infinite minimal set of identities. Show that V is a subvariety of at least continuum many varieties.
0
votes
3answers
31 views

Choose h and k such that the system has a solution, a unique solution and many solutions.

Im learning linear algebra, and im tasked with choosing $h$ and $k$ such that this system: $$ \begin{cases} x_1+hx_2=2\\ 4x_1+8x_2=k\\ \end{cases} $$ Has (a) no solution, (b) a unique solution, and ...
1
vote
1answer
29 views

Finding error variance and confidence interval

Two new types of petrol, called premium and super, are introduced in the market, and their manufacturers claim that they give extra mileage. Following data were obtained on extra mileage which is ...
3
votes
3answers
77 views

Why do we use $cm^2$?

I can't seem to wrap my head around why we should use $cm^2$ for area. According to my textbook we use it for converting units of area but I don't understand how $1cm$ is any different from $1cm^2$. ...
1
vote
1answer
16 views

population of a city based on another [hw]

I've been struggling with understanding how to solve a particular branch of population problems. The question reads as follows: City P had a population of 20,000 in the year 2005. The population ...
1
vote
1answer
22 views

Time Series Analysis.Calculate the variance mean and autocorrelation of the time series below.

For the following time series, calculate the mean, varia nce and autocorrelation function: (a) Y_t=5+Z_t+ 0.6Z_t-1
1
vote
1answer
32 views

Calculating bounds with multiple random variables.

I have this problem: Suppose there are 4 students (who we'll refer to as A, B, C, and D) in a class and each student is equally likely to have been born in any of the twelve months of the year. For ...
1
vote
1answer
28 views

Possible arrangments Letters?

How many arrangements are possible of the letters in EZPZ I CAN DO IT, which has five vowels (A, E, I, I, O) and seven consonants (C, D, N, P, T, Z, Z). a) if there are no restrictions, b) if ...
-3
votes
0answers
37 views

help me pleaaaaase! [on hold]

Cans of regular Coke are labeled as containing 12 oz}. Statistics students weighted the content of 7 randomly chosen cans, and found the mean weight to be 12.13. Assume that cans of Coke are ...
0
votes
4answers
24 views

Find a basis for the subspace of $\Bbb{R}^3$ that is spanned by the vectors

Find a basis for the subspace of $\Bbb{R}^3$ that is spanned by the vectors: $$v_1=(1,0,0), \space v_2=(1,0,1), \space v_3=(2,0,1), \space v_4=(0,0,-1)$$ I am not sure how to solve this problem. I ...
2
votes
1answer
21 views

Counterexample to “A/I is Artinian, when I is the annihilator of Artinian A-module”.

Let M be an Artinian A-module and let I be the annihilator of M in A. Is A/I necessarily an Artinian ring? I believe the answer is no since this comes off of a similar result regarding Noetherian ...
1
vote
1answer
26 views

Show that if $N$ is a normal subgroup of $G$ which contains all commuters then $G/N$ is abelian.

I am working on my proof for class and I was wondering if this look ok? Let $N$ be a normal subgroup of $G$ we want to show that $G/N$ is abelian, or $(aN)(aN) = abN = baN = (bN)(aN)$. Since $N$ ...
1
vote
1answer
16 views

2 Linear equation problems [on hold]

Write objective, constraints and graph for the following two problems: 1.A test offers 2 types of problems. Type A takes 3 Min to solve and B takes 2. You have 20 min to take the test and can only ...
-3
votes
4answers
65 views

Calculate the limit without l'hopital [on hold]

I need to prove this limit without using l'Hopital's rule: $$\lim_{x\to0} \frac{(1+ax)^{\tfrac14} - (1+bx)^{\tfrac14}}x =\frac{a-b}4$$ Thanks for the attention.
0
votes
2answers
35 views

Cardinality of two sets cross-multiplied

Let $A$ and $B$ be sets. Prove that $ \#(A \times B) = \#(B \times A)$. What I have done: There exist an element $m$ in $A$ such that the element also exists in $B$. If $\#A = \#B$, then $\#B = ...
1
vote
1answer
60 views

Vector Calculus Surface Integral (Limits of Integration)

I'm currently having trouble with the following problem. I believe that I have most of the problem set up, but I am having trouble finding what the limits of integration should be. $\int\limits_S ...
0
votes
1answer
13 views

Duality and Optimality Conditions

I have seen the solution and it involves adding a $x_5$ and $x_6$ to the inequalities. I really do not understand why this happens? I have not seen any questions like this yet. Any pointers would ...
0
votes
1answer
31 views

Simple question about a complex valued function

This is taken from an exam. One and only one of the answers is true. Let $f:\mathbb R\longrightarrow\mathbb C$ such that $\lim_{x\rightarrow0}|f(x)|=+\infty$. Hence: a)There exists ...
0
votes
2answers
27 views

Line integral over a curve in the II quadrant

I am lost here: $C = x^2 + y^2 = 4$ from $(0,2)$ to $(-2, 0)$. Calculate $ \ \int_c y^2 ds \ \ $ and give reasons the sign is correct. It's obviously the circular arc going counterclockwise from ...
0
votes
1answer
20 views

Functions (Finding Inverse)

$f(x) = x^2 + 2x$ , domain ${x ≥ 1}$ Question: find the inverse The inverse is $f(x) = 1 + \sqrt(1+x)$ (taking the positive square root only) As $f^{-1}(5) = 2$ and as 2 is an element from the ...
0
votes
1answer
23 views

Sequence of letters of length 5

How many sequences of letters are there of length 5 with exactly 2 vowels? Don't count "y" as a vowel. Pretty lost on this one. I know it involves 5 choose 2 has part, but I feel like that's not all
0
votes
1answer
24 views

calculating X, Y, Z random variables

Suppose X, Y, and Z are random variables that each take the value 0 or 1. If P(X=0,Y=1,Z=0)=1/3 and P(X=0,Y=1,Z=1)=1/4, what is the value of P(X=0,Y=1)? I am trying to calculate this but I am really ...
0
votes
1answer
19 views

integral of absolute value velocity to find total distance

$x(t)=t^3−2t+5$ $v(t)=3t^2-2$ I want to find total distance traveled from $t=0$ to $t=3$. $\int_0^3 |3t^2-2|dt$ How do I calculate this integral?
2
votes
0answers
53 views

If $\alpha$ and $\beta$ are algebraic integers then the roots of $x^2+\alpha x+\beta$ are algebraic integers

(This question is a dupplicate from If $\alpha$ and $\beta$ are algebraic integers then any solution to $x^2+\alpha x + \beta = 0$ is also an algebraic integer.) I'm trying to solve this problem with ...
-3
votes
0answers
40 views

solve this problem. using Solution of a triangle. [on hold]

solve this problem.The perimeter of right-angled triangle is 56 cm . What is the lengths of the triangle sides ?..
4
votes
0answers
69 views

Incidence variety fo Grassmmanians

Let $k$ be an algebraic closed field (say, $\text{char}(k)\neq 2$), $n \in \mathbb N\setminus \{0\}$ and $G(m, n) = G(m, \mathbb P^n(k))$ the variety of Grassmmanian of $m$-dimensional linear ...
1
vote
2answers
36 views

Find the largest $d \in \mathbb{N}$ such that for any $x \in \mathbb{N}$ the equation $16^x+10x-1 \equiv 0 \pmod d$

I interpret this problem as being finding the $gcd$ of the set of numbers generated by that given sequence. Checking by hand for a possible pattern in the sequence, I noticed instead that every term ...
-9
votes
0answers
53 views

I need a solution this problem? [on hold]

solve this problem.The perimeter of right-angled triangle is 56 cm . What is the lengths of the triangles sides ?..
2
votes
2answers
36 views

Center of Mass and Centroid

Find the centroid of the region lying between the graphs of the functions $y=\sin x$ and $y=\cos x$ over the interval $[0,\frac\pi4]$. I approached the question like this: Find the $M$ $$M = ...
0
votes
1answer
20 views

distance of position equation (basic kinematics)

A particle moves in a straight line according to the rule $x(t)=t^3-2t+5$, where $x(t)$ is given in meters and where $t$ is given in seconds. Determine the position, velocity, and acceleration of the ...
1
vote
1answer
62 views

so Thinking about induction proofs

So I'm studying some induction proofs, but I have some questions that were not clear to me when I read the book's definition. I want to know if my understanding is correct: So, for me, and ...
0
votes
1answer
38 views

Proof of integral equality

Let $f^{(n)}(x)$ be the $n$-th derivative of $f(x) = \cos(x)$. Prove that : $$ \int_0^{2\pi} f^{(n)}(x) \,\, dx = \int_0^{2\pi} f^{(n)}(kx) \,\, dx, $$ where $n$, $k$ are natural numbers equal or ...
0
votes
1answer
15 views

Interpretation of the basis and coordinates for this solution space.

I found $x_1=x_3$ and $x_2=0$. So, $x_1=t;x_2=0; x_3=t$ Therefore: $$(x_1,x_2,x_3)=t(1,0,1)$$ So, the dimension is $1$ and the basis is $(1,0,1)$. Now, I am having trouble interpreting this ...
-2
votes
3answers
59 views

I need a solution for this problem [on hold]

Abcd is a box such that an=nd=dm=mc .find sin x
0
votes
1answer
21 views

Question about vector equations of lines and planes

Find the equation of the line going through the point $(2,-3,4)$ ,and which is perpendicular to the plane $ x+2y + 2z = 13$ So I tried this: the normal of the plane is $(1,2,2)$, random point on the ...
0
votes
0answers
7 views

Asymptotic Properties of Transformation of Estimators

I'm trying to find a good explanation/proof for the following statement: If $ \sqrt{n}({\hat{\theta}} - \theta) \to^{d} N(0, \sigma^2)$, then $ \sqrt{n}({g(\hat{\theta}}) - g(\theta)) \to^{d} N(0, ...
0
votes
0answers
43 views

how far from its starting point (and in which direction!) will the pendulum be after $2.5$ sec?

The Riddler has rigged a pendulum in the clock tower with enough explosives to level the nearby elementary school. Batman has figured out that he must must snip the green wire when the pendulum has ...
0
votes
1answer
59 views

Need some help with an easy mechanics question.

The distance between a boy and the shelf is R. He wants to throw a ball of mass m with an initial speed v such that it hits the top of the shelf of a height h. 1) Show that a ball thrown at the ...
0
votes
1answer
12 views

Functions inverse + domain

Question part a): !([http://imgur.com/sKJbFKu]) Answer: !http://imgur.com/jRfeXkW Can anyone explain why the inverse must be the negative square root?
0
votes
2answers
23 views

Covariance of dependent random variables from a Poisson process

Question: Given a Poisson process $N(t),t≥0$ with rate $λ$, calculate the covariance of $N(2)$ and $N(3)$. Attempt: So clearly $N(2) \sim Po(2\lambda)$ and $N(3) \sim Po(3\lambda)$. So, ...