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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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!
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 ...
0
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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 ...
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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
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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, ...
2
votes
1answer
27 views

Using Polar Integrals to find Volume of surface

Here's the Question and the work that I've done so far to solve it: Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid $ −x^2 − y^2 + z^2 = 61$ and the plane $z ...
1
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2answers
494 views

How to find the coordinates of the intersection of median

Given the triangle $ABC$ with its vertices $A(0,1)$, $B(-2,1)$, $C(8,-8)$. Determine the intersection point of the median $AM$ and the line $l$, if $l\parallel AB$ and $C$ is element of $l$.
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1answer
254 views

Prove that set has zero Jordan content iff its closure has measure 0

Prove that set has zero Jordan content iff its closure has measure 0. I am having trouble with both directions , any tips would be great. THanks!
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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?
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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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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 ...
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0answers
37 views
1
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1answer
88 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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2answers
211 views

Statistics about unbiased estimator with an unknown parameter

Way too hard questions for me. Could anyone give me some clues or way to solve?
0
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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 ...
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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 ...
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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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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 $C$ ...
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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 ...
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, ...
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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 ...
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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, ...
1
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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 ...
2
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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 $$f:R\setminus \{-1 \}\to{R}$$ ...
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1answer
33 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 ...
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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: ...
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
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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 ...
2
votes
2answers
59 views

Dual Vector Space embedding

Is there an embedding of any vector space $V$ into $V^*$? As far as I know it is not true. The statement that I know of is that there is natural embedding of $V$ into $V^{**}$ Is there any ...
1
vote
3answers
97 views

Finding derivative of given function.

f(t) = $\int_{t^2}^{4}\sqrt{\cos(x)+12}\;dx$ Rearranging limits of integration... $f(t) = -\int_{4}^{t^2}\sqrt{\cos(x)+12}\;dx$ Taking derivative... $f'(t) = -\sqrt{\cos(t^2)+12}\; - ...
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3answers
67 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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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 ...
1
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2answers
132 views

Real analysis question involving inhomogenous linear ODE

So I had another problem like this but the ODE was homogenous, now there is a non zero right side. I completed part (i), $\large c(x) = \int \frac{b(x)}{g(x)} dx$. I am stuck on (v). (1) is the ...
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1answer
43 views

Question on sequence space (as a linear space)

Let $X$ be the space $\ell_\infty$ of all bounded sequences of real scalars. If $Y$ is the set of all $x\in X$ that have bounded partial sums (1) Can I say $Y$ is a linear space (as a subspace of ...
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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.
0
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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
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2answers
40 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
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
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4answers
89 views

If $d=\gcd(a+b,a^2+b^2)$, with $\gcd(a,b)=1$, then $d=1$ or $2$

Suppose $\gcd(a,b)=1$. Let $d=\gcd(a+b,a^2+b^2)$. I want to prove that $d$ equals $1$ or $2$. I get that $d\mid2ab$ but I can't find a linear combination that will give me some help to use the fact ...
1
vote
2answers
43 views

Solving a certain differential equation when assuming a surface of revolution is minimal

The problem is the following: Consider the surface of revolution $$ \textbf{q} (t, \mu) = (r(t)\cos(\mu),r(t)\sin(\mu),t) $$ If $\textbf{q}$ is minimal, then $r(t) = a\cosh(t)+b\sinh(t)$ for $a,b$ ...
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
vote
1answer
39 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 ...
2
votes
2answers
70 views

An application of Sylow theorems in p-groups!

If $G$ is a finite group of order $p^{n}$ (which $p$ is a prime number) and have only one subgroup of order $p^{n-1}$ ,namely $H$ ,then $G$ is cyclic ! My "proof" is as follows: suppose $$x\in G-H$$ ...
2
votes
2answers
56 views

Trigonometric substitution

Been out of touch with trigonometry for some time now. Need help proving this expression. $$\sin^{2}\left(\frac{x}{2}\right) = \frac{1}{2}(1-\cos\left(x\right))$$ Any help will be appreciated. ...
0
votes
3answers
52 views

what are the equilibrium points of the following: [on hold]

where $x$ represents susceptible individuals, $y$ represents infected individuals. Find the two biologically meaningful equilibria. $$ \frac{\mathrm{d}x}{\mathrm{d}t} =12−3xy−3x $$ $$ ...
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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 ...
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 $\equiv$ ...
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1answer
30 views

How to Find the inverse Fourier transform

How to find the inverse Fourier transform and how to transform the solution with refer to the Fourier transform table?
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10answers
2k views

How to solve $4\sin \theta +3\cos \theta = 5$

Another problem that I already wasted hours on. Given $$4\sinθ +3\cosθ = 5$$ Find $$4\cosθ -3\sinθ$$ Help me guys (PS:I'm not that good in maths)
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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 ...