# All Questions

269 views

### Value of $\frac{1}{\sqrt{3}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{11}}+\frac{1}{\sqrt{11}+\sqrt{15}}+\cdots$ ($n$ terms)

Sum $$\frac{1}{\sqrt{3}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{11}}+\frac{1}{\sqrt{11}+\sqrt{15}}+\cdots \text{ (n terms)}$$ I know how to use the telescoping series method when the terms are in ...
27 views

### Understanding what a statement means

I'm trying review for the finals by reading the text but I ran into an exercise with a sentence that I can't understand. Draw the network associated with the bipartite graph. What does that ...
47 views

### A property of polynomials in a paper by Rice

It has been suggested that a mind-reading tag be added. This is, unfortunately, a good candidate for such a tag... I was reading a paper of Rice relating to a property of integer polynomials. The ...
124 views

### Order of element in group given order of conjugacy class

What is the order of $x$ in a group of order 21 that contains a conjugacy class of order 3? I know the answer is 7 because the size of the conjugacy class of x equals the index $[G:Z(x)]$ of its ...
83 views

### Cannot understand some parts of proof for R be a countable union of closed sets

Im reading chapter9 Category, Real Analysis, Carothers, 1ed, talking about discontinuous functions of metric space. Here is a proof for a theorem that R be a countable union of closed sets,: Baire's ...
42 views

### Slope of tangent line using Wallis method

Consider the Wallis method of finding the slope of tangent lines where $x = a$. Use the method to find the slope of the line tangent to the graph of $y = x^2 + 3x + 7$. Use the method to find the ...
32 views

### True/False: Differentiablity #2

If the function $f:\mathbb{R}\rightarrow\mathbb{R}$ is differentiable and $f(x)\le f(0)$ for all $x\in[-1,1]$, then $f'(0)=0$. I think this one is false. By the definition of differentiable, ...
38 views

### How does this random vector indicate that my two random variables are independent?

I've got independent random variables $X$ and $Y$, and a random vector $\vec{V}=(h_1(X,Y),h_2(X,Y))$ where $h_1$ and $h_2$ are (specified) functions of $X$ and $Y$. I found $\vec{V}$'s density ...
77 views

### Counting/ probability

Im stuck on this question: "At a certain college, the housing office has decided to appoint, for each floor, one male and one female residential advisor. How many different pairs of advisors can be ...
58 views

### Creating a lift chart for a classification tree

This is likely a simple question but I'm new to data mining techniques and am trying to compare two different predictive models. I've created a logistic regression and a classification tree and would ...
26 views

386 views

### Proving $\left(\tan^2x +\frac{1}{\tan x}\right) \left(\sin x+\cos x\right)=\left(\frac{1}{\cos x}\right)+\left(\frac{1}{sin x}\right)$

$$\left(\tan^2x +\frac{1}{\tan x}\right) \left(\sin x+\cos x\right)=\left(\frac{1}{\cos x}\right)+\left(\frac{1}{sin x}\right)$$ Can someone show me how to solve this identity and also explain the ...
81 views

### True/False: Differentiation

If the differentiable function $f:\mathbb{R}\rightarrow\mathbb{R}$ is monotonically increasing, then $f'(x)\ge0$ for all $x$. I feel like this is true by the Mean Value Theorem, but I'm not ...
38 views

### If $U = (1, 2)$, $V = (3, -4)$, is the answer to $2U + \frac{1}{2}V$ the vector $(3.5, 2)$? Check my answer.

If $U = (1, 2)$, $V = (3, -4)$, is the answer to $2U + \frac{1}{2}V$ the vector $(3.5, 2)$? I did the following: \begin{align*} U : ( ( 2 * 1 ), ( 2 * 2 ) ) &= ( 2 , 4 )\\ V : ( ( 0.5 ...
144 views

### Generating and solving recurrence relations

I am trying to do this question but don't know where to go from here: The question: For $n\ge1$ let $t_n$ be the number of ways to tile the squares of a 2xn checkerboard using 1x2(which can be rotated ...
79 views

### Möbius Transformation of Triangles

I understand that Möbius transformations are angle preserving transformations. Knowing this, my professor asked us to think about how the image of equilateral triangle is not an equilateral triangle ...
388 views

### Optimization Word Problem, revenue

A sorority plans a bus trip to the Great Mall of America during Thanksgiving break. The bus they charter seats 44 and charge a flat rate of 350 dollars plus 35 dollars per person. However, for every ...
30 views

### A jump process as an integrand in Itô integral with respect to an Itô process

So, $X_1(s)$ is a jump process, $X_2(s)$ is another jump process, $X_2^c(s)$ is the continuous part of $X_2(s)$. And $\int_0^tX_1(s-)dX_2^c(s) = \int_0^tX_1(s)dX_2^c(s)$, is it because the ...