# All Questions

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### Determining whether a function has an image that is the entire set of reals

I am doing a textbook exercise that asks me to determine whether the function $h(x)= x$ if $x\ge0$ and $-x$ if $x\lt0$ has an image that is the entire set of real numbers. Looking at the ...
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### Finding the similarity dimension of a variation of the Cantor Set.

If we take the Cantor set and instead of removing the interval [1/3, 2/3], we remove the open interval [x,1-x], with 0
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### An strange operator in B(H)

Let $H$ be a non-separable Hilbert space and $E$ be an orthonormal basis for $H$. Let $E_0$ be a countable subset of $E$ and $\{\delta_i\}_1^{\infty}$ be a bounded sequence of $(0,\infty)$. For ...
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### How do I solve this normal distibution solving for a and b?

X ~ norm(15, 1.25). I want to find a and b, such that P(a < X < b) = .95. I've attempted this multiple times and spent like two hours and all my answers are wrong. Please help!!!!
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### Convergent, Bounded, O(1) sequences

Consider a sequence of real numbers $\{a_n\}$ and these 3 definitions: (1) $\{a_n\}$ is bounded: $\exists k>0$ s.t. $-k \leq a_n\leq k$ $\forall n \in \mathbb{N}$ (2) $a_n=O(1)$: ...
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### Tricky Residue Integration [duplicate]

Show using residues that, for all $b > 0$ and $-1 < a < 0$, $$\int_0^{\infty}\frac{x^a \log x}{x+b}dx = \frac{\pi b^a}{\sin^2 \pi a}(\pi \cos \pi a - (\log b)(\sin \pi a))$$ I'm really ...
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### Express $\frac{\sin 7\theta}{\sin \theta}$ in powers of $\sin \theta$ only

By using DeMoivre's theorm express $$\frac{\sin 7\theta}{\sin \theta}$$ in the powers of Sine only answer given in the book is $$7-56\sin ^2\theta+112\sin ^4 \theta-64\sin^6 \theta$$ can any one help ...
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### What is $x^T Ax$?

Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^T Ax$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A$? $5$ ...
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### Proving the points $P,O,N$ are collinear

In a triangle $ABC$, let $M$ be the midpoint of side $BC$ and $N$ be the midpoint of median $AM$. Let $O$ be the circumcentre of triangle $ABM$. If the circumcircle of triangle $BOM$ cuts the side ...
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### what does this sentence mean?

when the joint distribution of a set of items is different from the distributions of the individual items in the set. this is the context: Our discussion so far has focused on item-based ...
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### How big are regular (hyperbolic) polygons?

Given a hyperbolic surface of constant curvature $K=-1/a^2$ embedded in $\mathbb{R}^3$, is there a known formula for the length of the edges of a regular polygon? I know that the Gauss–Bonnet ...
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### How do i get a point from two points using a right triangle?

In the image the triangle is made up of 3 points, 2 of which are found, the third one is missing, not sure how to get this last point. [Need an Equation] triangle missing a point

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