# Tagged Questions

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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### Inverse Trigonometry proof

Please help me prove this equation as ive been trying for days and not able to solve the $\tan^{-1}( \cot^3 x)$ part. $$\tan^{-1}(\cot x)+\tan^{-1}(\cot^3 x)+\tan^{-1}(\frac{1}{2} \tan 2x)=0$$
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### $H_I^n(R)=0$ and $H_I^n(M)\neq 0$

question: find R and M as an R-module such that $H_I^n(M)\neq 0$ and $H_I^n(R)=0$, where I an ideal of R and $n\in N$. plz give some hints to find this example.
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### How to solve this graphing question?

$\frac{|x-2|} {(x^2-4)}+\frac{(x-2)} {|x-2|} = b$ determine for which values of $b$ the equation has one and only solution. I tried sketching the graph, but was unable to do so accuratly...also, ...
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### Question about convergence in $H^1_0$

Please how to prove that if $u_n\rightarrow u$ on $H^1_0$ we have that $||u_n||\rightarrow ||u||$ ? Please i need your help Thank you
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### How to find the equation of two lines at a given point?

Here's the problem: Give the equations of two lines that meet at the point (-1, 5, 2) and which meet at right angles, but do not use that point in either of the equations. Any ideas?
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### why not applicable categorical variables using ANOVA F or Levene test?

For independent test data is a categorical variable using the Pearson chi-squared test. But, why not applicable categorical variables using ANOVA F or Levene test? Are there any theories on this ...
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### getting the slopes of the sides of an equilateral triangle given 2 points

I want to get the slopes of an equilateral triangle given the 2 vertices. Let's say they are (0, 0) and (5, 5). Graphing this would give 2 triangles forming a diamond. I tried to use distance formula ...
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### Density and convergence

I have a small question: Is it true that if the basis of a space $A$ is dense in a space $B$ ($B\subset A$) then if $u_n\rightarrow u$ in $A$ we have that $u_n\rightarrow u$ in $B$ ?
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### What is the effect of taking the sine of inverse cosine?

How can I evaluate the sine of an inverse cosine? for example: sin(arccos((x)^1/2))
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### Finding the $\cot\left(\sin^{-1}\left(-\frac12\right)\right)$

How can I calculate this value? $$\cot\left(\sin^{-1}\left(-\frac12\right)\right)$$
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### I need help finding the critical values of this function.

So $h(t)=t^{\frac{3}{4}}-7t^{\frac{1}{4}}$. So I need to set $h'(t)=0$. So for $h'(t)$ the fattest I've gotten to simplifying os $h'(t)=\frac{3}{4 \sqrt[4]{t}}-\frac{7}{4\sqrt[4]{t^3}}$ and that is as ...
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### Showing that two sums are equivalent

given \begin{gather} U_d(x,y,q\mid i_1,\ldots,i_k)=\sum\limits_{n,m\geq0}x^ny^m\sum\limits_{\sigma = i_1\ldots i_k\sigma_{k+1}\ldots\sigma_m\in C_{[d]}(n,m)}q^{v(\sigma)}. \end{gather} show ...
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### How to show this is the minimal polynomial

I'm trying to the following problem. But I can't show some irreducibility of the polynomials. Put $L=\mathbb{C}(X,Y,Z)$, $\omega=\frac{-1+\sqrt{-3}}{2}$. Define two automorphism $\sigma, \tau$ of ...
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### Polynomials that satisfy $(x-1)(p(x+1))=(x+2)(p(x))$ where $p(2)=12$?

I am taking a graduate class on Equation Theory and one of my homework questions asks me to "Determine all polynomials $p(x)$ such that $(x-1)(p(x+1))=(x+2)(p(x))$ and $p(2)=12$. A provided hint is to ...
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### Find the radius of four congruent circles inside a right triangle

Below is a homework assignment I'm working on, along with a correct method for solving it and what appears to be an incorrect method. I'm hoping someone could explain what is wrong with the second ...
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### Formula alteration

is there any way to transform the formula$\frac {1-x}{x-3}$ into something that can be easily sketched, or which will help eliminate $x$ from the denominator?
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### checking the solution of PDE

Let $u(x)$ be an entire solution of $\Delta u = 1$ on $R^{n}$, $n>1$. If $u(x)$ is also convex, that is $(D^{2}u(x))$ is non-negative definite for all $x$. Then $u(x)$ is given be a quadratic ...
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### Completing the following equation by the suitable method

i got this linear equation two variable problems for my school. I understand the basics of the normal linear equation but this seems different instead having a pure number after the "=" they got a ...
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### to prove partial derivative of a function f is bounded [duplicate]

Let$$f(x,y) = \begin{cases} 0 & (x,y)=(0,0) \\ \dfrac{x^3}{x^2+y^2} & (x,y) \neq (0,0) \end{cases}$$ Prove that $D_1 f$ and $D_2 f$ are bounded ...
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### Five apples, three pears and two bananas cost £3.18. Four apples, eight pears and three bananas cost £4.49. [closed]

Five apples, three pears and two bananas cost £3.18. Four apples, eight pears and three bananas cost £4.49. How much more expensive is an apple than a pear? A. 5p B. 6p C. 7p D. 8p E. More ...
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### Is it true that $\mathbb E[{\frac{X}{Y}]}={\frac{\mathbb E[X]}{\mathbb E[Y]}}$?

If $X$ and $Y$ are both random variables, does it hold $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
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### Optimization of a Cylindrical Can [duplicate]

I have been asked to draw a graph and use it to determine the optimum dimensions for a can. my can has a volume of 80cm3, a surface are of 230 cm2 and a radius of 3.35cm. I am assuming that the graph ...
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### $E \subset \mathbb R$ is an Interval $\iff E$ Is connected

My text gives the definition that $E$ is disconnected if there exist disjoint open sets $A, B$ such that: $A \cap E$, $B \cap E$ are nonempty. $(A \cap E) \cup (B \cap E) = E$. Then for the ...
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### Finding the size of a list given its mean, and the mean when one number is added to the list

The mean of a list of $n$ numbers is $6$. When the number $17$ is added to the list, the mean becomes $7$. What is the value of $n$?
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### How does $\frac{1}{2}\cosh(2x) -1 = \sinh^2(x)$?

Using hyperbolic trigonometric function identities is there a way to prove the following equation? $$\frac{1}{2} (\cosh(2x)-1) = \sinh^2(x)$$
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### Calculate cosh(x) given sinh(x)

Given the value of sinh(x) for example sinh(x) = 3/2 How can I calculate the value of cosh(x) ?
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### $\mathbb{Q}[x,1/x]$ is normal?

Let $x$ be a transcendental. I heard $\mathbb{Q}[x,1/x]$ is a normal domain. But I don't understand why. Help me, thanks.
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### Tangent bundle is orientable

I am having some trouble finishing a proof that the tangent bundle of any manifold is orientable. What I've done so far is calculate the transition function between two standard charts on the bundle. ...
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### Primary school math regarding circles [closed]

----------//-----------------------------------__________ Please see the figure below the question is in the ...
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### Approximating volume using differentials

A closed box with dimension $10$ cm, $8$ cm, $6$ cm, is made of $2$ mm thick plywood. Approximate the volume of material used in making the box. We have $V=xyz$ We can find what the approximate ...
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### Primary school mathematics regarding age

Mrs Lim is 40 years old and her son is twice her daughter's age. Mrs Lim will be thrice her son's age when her daughter is 12 years old. How old will mrs Lim be when her 2 children's combined age ...
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### A homework question, finding the maximum possible value of the sum of two remainders

If $a<b$ what is the maximum possible value of a mod b+ b mod a. I tried several times, the answer always came out to be 2a-2. But then it is not a choice. Am I right?
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### Stable Marriage - set of preferences such that every arrangement is stable?

This is a homework problem from the MIT OCW math for CS class, assignment 4, problem 5. Prove or disprove the following claim: for some n ≥ 3 (n boys and n girls, for a total of 2n people), there ...
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### Proving an inequality about a sequnce with Cauchy-Schwarz

show that $$\sum\limits_{i=1}^n \frac{x_i}{i^2} \geq \frac{1}{1} + \frac{1}{2} + \dots +\frac{1}{n}$$ where $x_1,x_2,\dots,x_n$ are natural numbers and all of them are different numbers(no such a ...