Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 105

Prove $A setminus (A setminus (A setminus B)) = A setminus B.$

$renewcommand{backslash}{setminus}$ The question is as is in the title. I am able to show that $A setminus (A setminus (A setminus B)) subseteq A setminus B$ but I...

Asked on 11/01/2021 by hk1510

2 answer

Solving a simple differential equation with DFT

I have a simple differential equation of form $frac{df(x)}{dx}=u(x)$ and u(x) is given to me in a sampled form so I need to solve this equation numerically. I decided...

Asked on 11/01/2021 by Gaganov Victor

1 answer

How do I use structural induction to show that for all $(a,b) in S$ that $(a+b) = 4k$ for some $k in Bbb Z$?

I'm given that: Let $S$ be the subset of the set of ordered pairs of integers defined recursively by: Base case: $(0,0) in S$ Recursive step: If ...

Asked on 11/01/2021 by justanotherstudent

1 answer

Initial value problem $xyz_x + x^2z_y = x^2+y^2-yz$ with initial curve

Problem Solve the initial value problem in the domain $x<0$:$$xyz_x + x^2z_y = x^2+y^2-yz$$ where $z=x$ on the line $y=1$. Attempt Edit: As...

Asked on 11/01/2021 by briemann

1 answer

Simplify $sum^{20}_{k=10} kbinom{k-1}{9}$.

Simplify $$sum^{20}_{k=10} kbinom{k-1}{9}$$ as much as possible.I feel like I could utilize the hockey stick identity, but have not found a way to do so with that extra ...

Asked on 11/01/2021

3 answer

Conjugate in $S_n$ do not imply conjugate in its subgroup.

$(12)(34)$ and $(13)(24)$ are conjugate in $S_4$, but they are not conjugate in $mathbf V_4$, the Klein four group, since $mathbf V_4$ is abelian.I know...

Asked on 11/01/2021

3 answer

Cardinality of set of $a_r$?

QuestionSo I conjectured a formula which was proven: Let $b_r = sum_{d mid r} a_dmu(frac{m}{d})$. We prove that if the $b_r$'s are small enough, the result is...

Asked on 11/01/2021

1 answer

Learn how to sketch functions intuitively

A professor told us that it is better to have an idea of the graph of a function before starting to apply the techniques of differential calculus in order to...

Asked on 11/01/2021 by q0mlm

3 answer

Definition of addition and multiplication on $ℕ$ using recursion

My book, Classic Set Theory: For Guided Independent Study, gives me this theorem:"let $y_0$ be any element of $ℕ$ and $h"ℕ×ℕ×→ℕ$ a function on pairs...

Asked on 11/01/2021

2 answer

Acceleration of a particle varies with distance as $-kx$. The particle is initially given a velocity $v_0$. Find time take to reach initial point

$newcommand{d}{mathrm{d}}$I am having a problem here because acceleration varies with distance, and I am not able to relate it with time begin{align}a &=-frac{kx}{m} \vfrac{d v}{d x}...

Asked on 11/01/2021

1 answer

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