# All Questions

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### Find the time that must elapse for the object to reach 98% of its limiting velocity?

I am given the initial value problem $$\frac{dv}{dt} = 9.8 - (\frac v5)$$ and you are given $v(0) = 0$ I was looking at the solution to this problem. They first solved the differential ...
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### How to solve $y' = -2x -y$

My thought: $\displaystyle\frac{dy}{dx}+x^0y=-2x$ Considering it as the form of linear equation, $\displaystyle\frac{dy}{dx}+P(x)y=Q(x)$ Multiplying $e^{\int1dx} = e^x$ on both sides, ...
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### Solving a system of non-linear equations with 10 equations and 10 unknowns

I'm working on a problem where I seem to have run into a system of non-linear equations. I have ten equations and ten unknowns. In the equations below, all of the $\phi_{ij}$'s are known, but all of ...
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### How do i solve this equation ${\mathbb{R}}$: $3 \sin^3x+2 \cos^3x=2 \sin x+\cos x$?

How do I solve this equation ${\mathbb{R}}$: $3 \sin^3x+2 \cos^3x=2 \sin x+\cos x$? Note : I have tried using trigonometric transformation but it seems very complicated to get the result .. may ...
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### Find angles between sides of triangle and coordinate planes (xy,yz,zx planes) using three 3d vectors .

Given the following, three vectors: a⃗ =3i−2j+5kb⃗ =i−6j+6kc⃗ =2i+3j−k, find the angles between sides of triangle and coordinate planes. I calculated the sides to be 4.58 , 11.45 and 7.87. I also ...
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### On a scale of 1 to 10 how far is this manifold from being a normal bundle?

(DIS)-CLAIMER: All the manifolds considered in this post are completely humble and have no additional structure beyond the smooth structure. Let $Y$ be a submanifold of $M$ and let $(-)^0$ denote the ...
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### Hesse matrix is negatively semidefinite if a function has a local maximum

Let $U \subset \mathbb{R}^n$ be open, and let $f: U \to \mathbb{R}$ be at least twice continuously differentiable. Also, we assume $f$ has a local maximum $a \in U$. I now want to show that the Hesse ...
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### Find recursive formula - Question from exam, check my answer

We want to demolish and move a bridge from one location to another. The bridge is made out of $m$ road segments all connected $[0,1]$, $[1,2]$, $[2,3]$...$[m-1,m]$ We have a given function $f$ which ...
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### Does this modulo formula change odds?

Good day, Consider 5 people each choosing a different number between [0 and A] randomly At the end, we add all the numbers: $n_1+n_2+n_3+n_4+n_5 =N$ Then modulo A+1: $W = N \pmod{A+1}$ My ...
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### Improving Mathmatical Skill [on hold]

I am a student of computer science and engineering. My understanding of mathematics is not very good. I am getting very hard time studying subject that require a background on mathematics. So, I ...
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### Cholesky decomposition and variance

Well, I've been reading about simulating correlated data and I've come across Cholesky decomposition. Everything seemed clear until I found a couple of posts on this site and Cross-Validated that ...
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### Solve $3^{2x} -2 \cdot 3^{x+5} + 3^{10} = 0$ for $x$

Here's the question: Solve for $x$ in $$3^{2x} - 2 \cdot 3^{x+5} + 3^{10} = 0$$ I know that you have to factor something out, I'm just not sure what that something is. Thanks in advance
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### How to show that $\int_{S}\frac{1}{z}\frac{1}{\cos(2\pi i a)-\cos(2\pi z)}dz\rightarrow 0$ as the sides of the square $S$ go to $\infty$.

I have a question where I am asked to show that the following sum is $$\sum_{k=-\infty}^\infty\frac{1}{a^2+k^2}=\frac{\pi}{a}\frac{e^{2\pi a}-e^{-2\pi a}}{e^{2\pi a}+e^{-2\pi a}-2}$$ by integrating ...
### Under what conditions does $M \oplus A \cong M \oplus B$ imply $A \cong B$?
Is it possible to find a function $x:[0,T]\to [0,x_0]$ such that, for a fixed $0<\lambda<1$ we have: \dfrac{1}{1+\lambda}\left (1-\dfrac{x(t)}{x_0}\right )^{1+\lambda} +\dfrac{1}{1-\lambda} ...