Recent questions in Advanced Math

Laurel Yoder
2022-05-21
Answered

if I have a relation between $A\times A$

if $A=\{1,2,3\}$

if $B=\{1,2,3\}$

$R=\{(1,1),(2,2),(3,3)\}$

can I say that the Relation R is Reflexive and also a Symmetric because I have (a,b) and (b,a) and also (a,a).

Simone Werner
2022-05-21
Answered

vamosacaminarzi
2022-05-21
Answered

i. What is the probability that both balls are red?

ii. What is the probability that the second ball is red but the first ball is not?

iii. What is the probability that the second ball is green?

America Ware
2022-05-21
Answered

Assume ${a}_{1},{a}_{2},...,{a}_{n}$ are numbers $\in \mathbb{N}$ such that ${a}_{1}<{a}_{2}<...<{a}_{n}$ prove: $\sum _{i=1}^{n-1}\frac{1}{lcm({a}_{i},{a}_{i+1})}<1$

Meera Sunker
2022-05-20

Reduce the system

(D2 + 1)[x] − 2D[y] = 2t

(2D − 1)[x] + (D − 2)[y] = 7.

to an equivalent triangular system of the form

P1(D)[y] = f1(t)

P2(D)[x] + P3(D)[y] = f2(t)

and solve.

Despiniosnt
2022-05-20
Answered

the original equation was: $(x+i){y}^{\prime}+y=1+2x\mathrm{arctan}(x)$

I solved for $(x+i){y}^{\prime}+y=0$

then $(x+i){y}^{\prime}+y=1$ now I'm working on the second term ($2x\mathrm{arctan}(x)$)

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