Question and Answers Forum

AlgebraQuestion and Answers: Page 46

Question Number 205588 Answers: 2 Comments: 0

Question Number 205551 Answers: 1 Comments: 0

what is the decomposition into cycles with disjoints support of c^k , where c=(123...n) ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{into}\:\mathrm{cycles} \\ $$$$\mathrm{with}\:\mathrm{disjoints}\:\mathrm{support}\:\mathrm{of}\:\mathrm{c}^{\mathrm{k}} ,\:\mathrm{where}\:\mathrm{c}=\left(\mathrm{123}...\mathrm{n}\right)\:? \\ $$

Question Number 205559 Answers: 2 Comments: 0

Question. (math analysis) (X ,d ) is a metric space and (p_n )_(n=1) ^∞ is a sequence in X. (p_n )_(n=1) ^( ∞) is cauchy if and only if lim_(N→∞) diam (E_N )=0. where , E_N = { p_N , p_(N+1) , ...} diam E:=sup{d(x,y)∣x,y ∈E }

$$ \\ $$$$\:\:\:{Question}.\:\left({math}\:{analysis}\right) \\ $$$$\:\:\left({X}\:,{d}\:\right)\:{is}\:{a}\:{metric}\:{space}\:{and} \\ $$$$\:\:\left({p}_{{n}} \right)_{{n}=\mathrm{1}} ^{\infty} \:{is}\:{a}\:{sequence}\:{in}\:{X}. \\ $$$$\:\:\:\left({p}_{{n}} \right)_{{n}=\mathrm{1}} ^{\:\infty} {is}\:{cauchy}\:{if}\:{and}\:\:{only}\:{if} \\ $$$$\:\:\:\mathrm{lim}_{\mathrm{N}\rightarrow\infty} {diam}\:\left({E}_{\mathrm{N}} \right)=\mathrm{0}. \\ $$$$\:\:{where}\:,\:{E}_{{N}} \:=\:\left\{\:{p}_{{N}} \:,\:{p}_{{N}+\mathrm{1}} \:,\:...\right\} \\ $$$$\:\:{diam}\:{E}:={sup}\left\{{d}\left({x},{y}\right)\mid{x},{y}\:\in{E}\:\right\} \\ $$$$\:\:\:\: \\ $$

Question Number 205545 Answers: 4 Comments: 1

Question Number 205534 Answers: 1 Comments: 0

Find: lim_(n→∞) ∫_0 ^( 1) n x^n e^x^2 dx = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{n}\:\mathrm{x}^{\boldsymbol{\mathrm{n}}} \:\mathrm{e}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:=\:? \\ $$

Question Number 205528 Answers: 1 Comments: 0

Let ∀x ∈ A → x ∈ R And card(A) > card N Prove that: card(A′) > card N

$$\mathrm{Let}\:\:\:\forall\mathrm{x}\:\in\:\mathrm{A}\:\rightarrow\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{And}\:\:\:\mathrm{card}\left(\mathrm{A}\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{card}\left(\mathrm{A}'\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$

Question Number 205527 Answers: 3 Comments: 0

If the roots of ax^2 + bx + c = 0 are one another′s cube then show that (b^2 − 2ac)^2 = ac(a + c)^2 .

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{are}\:\mathrm{one} \\ $$$$\mathrm{another}'\mathrm{s}\:\mathrm{cube}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\left({b}^{\mathrm{2}} \:−\:\mathrm{2}{ac}\right)^{\mathrm{2}} \:=\:{ac}\left({a}\:+\:{c}\right)^{\mathrm{2}} . \\ $$

Question Number 205515 Answers: 0 Comments: 0

what is the decomposition into cycles with disjoints support of c^k , where c=(123...n) ?

Question Number 205514 Answers: 0 Comments: 3

Quelle est la decomposition en cycles a support disjoints de c^k , ou c=(1 2 3 ... n) ?

$$\mathrm{Quelle}\:\mathrm{est}\:\mathrm{la}\:\mathrm{decomposition}\:\mathrm{en}\:\mathrm{cycles} \\ $$$$\mathrm{a}\:\mathrm{support}\:\mathrm{disjoints}\:\mathrm{de}\:\mathrm{c}^{\mathrm{k}} \:,\:\mathrm{ou}\:\mathrm{c}=\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:...\:\mathrm{n}\right)\:? \\ $$

Question Number 205492 Answers: 2 Comments: 0

Question Number 205490 Answers: 1 Comments: 0

If,f(x)= (√(2 + x)) + a (√(x − 1)) is monotone function . find the range of ” a ”

$$ \\ $$$$\:\:\:\:{If},{f}\left({x}\right)=\:\sqrt{\mathrm{2}\:+\:{x}}\:+\:{a}\:\sqrt{{x}\:−\:\mathrm{1}}\: \\ $$$$\:\:\:\:{is}\:{monotone}\:{function}\:. \\ $$$$\:\:\:\:{find}\:{the}\:{range}\:{of}\:\:''\:{a}\:'' \\ $$$$ \\ $$

Question Number 205471 Answers: 2 Comments: 0

Solve the equation: (x/(21))+(x/(77))+(x/(165))+(x/(285))=200

$${Solve}\:{the}\:{equation}:\:\frac{{x}}{\mathrm{21}}+\frac{{x}}{\mathrm{77}}+\frac{{x}}{\mathrm{165}}+\frac{{x}}{\mathrm{285}}=\mathrm{200} \\ $$

Question Number 205460 Answers: 1 Comments: 0

If 3cosx = 8sin(30° − x) Find: tanx = ?

$$\mathrm{If}\:\:\mathrm{3cosx}\:=\:\mathrm{8sin}\left(\mathrm{30}°\:−\:\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\mathrm{tanx}\:=\:? \\ $$

Question Number 205432 Answers: 2 Comments: 0

Find: Ω = ∫_0 ^( 2𝛑) ln (sinx + (√(1 + sin^2 x))) dx

$$\mathrm{Find}:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}\boldsymbol{\pi}} \:\mathrm{ln}\:\left(\mathrm{sinx}\:+\:\sqrt{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{x}}\right)\:\mathrm{dx} \\ $$

Question Number 205431 Answers: 0 Comments: 0

Prove that in any △ABC ((cotA cotB cotC)/(sinA sinB sinC)) ≤ (8/(27))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\frac{\mathrm{cotA}\:\mathrm{cotB}\:\mathrm{cotC}}{\mathrm{sinA}\:\mathrm{sinB}\:\mathrm{sinC}}\:\leqslant\:\frac{\mathrm{8}}{\mathrm{27}} \\ $$

Question Number 205430 Answers: 0 Comments: 0

Prove that in any △ABC (1/(sinA)) + (1/(sinB)) + (1/(sinC)) ≤ (2/3) (cot(A/2) + cot(B/2) + cot(C/2))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\frac{\mathrm{1}}{\mathrm{sinA}}\:+\:\frac{\mathrm{1}}{\mathrm{sinB}}\:+\:\frac{\mathrm{1}}{\mathrm{sinC}}\:\leqslant\:\frac{\mathrm{2}}{\mathrm{3}}\:\left(\mathrm{cot}\frac{\mathrm{A}}{\mathrm{2}}\:+\:\mathrm{cot}\frac{\mathrm{B}}{\mathrm{2}}\:+\:\mathrm{cot}\frac{\mathrm{C}}{\mathrm{2}}\right) \\ $$

Question Number 205423 Answers: 1 Comments: 0

If a , b ∈ R Then: a^2 + b^2 ≥ ab + (√((a^4 + b^4 )/2))

$$\mathrm{If} \\ $$$$\mathrm{a}\:,\:\mathrm{b}\:\in\:\mathbb{R} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:\geqslant\:\mathrm{ab}\:+\:\sqrt{\frac{\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} }{\mathrm{2}}} \\ $$

Question Number 205422 Answers: 1 Comments: 0

If (a + 1)(b + 1)(c + 1) = 8 Then: a^2 + b^2 + c^2 ≥ 3

$$\mathrm{If} \\ $$$$\left(\mathrm{a}\:+\:\mathrm{1}\right)\left(\mathrm{b}\:+\:\mathrm{1}\right)\left(\mathrm{c}\:+\:\mathrm{1}\right)\:=\:\mathrm{8} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\geqslant\:\mathrm{3} \\ $$

Question Number 205420 Answers: 1 Comments: 0

If a^3 + b^3 + a^2 + b^2 = 4 Then: a^4 + b^4 ≥ 2

$$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:\geqslant\:\mathrm{2} \\ $$

Question Number 205421 Answers: 0 Comments: 0

If a,b,c>0 and abc=1 Then: (a/b^(2024) ) + (b/c^(2024) ) + (c/a^(2024) ) ≥ a + b + c

$$\mathrm{If} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}=\mathrm{1} \\ $$$$\mathrm{Then}: \\ $$$$\frac{\mathrm{a}}{\mathrm{b}^{\mathrm{2024}} }\:+\:\frac{\mathrm{b}}{\mathrm{c}^{\mathrm{2024}} }\:+\:\frac{\mathrm{c}}{\mathrm{a}^{\mathrm{2024}} }\:\geqslant\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c} \\ $$

Question Number 205380 Answers: 3 Comments: 0

Question Number 205367 Answers: 1 Comments: 0

Question Number 205353 Answers: 2 Comments: 0

If ax^2 + bx + c = 0 had two roots p and q and p^2 + q^2 = p^3 + q^3 then show that b^3 − 2a^2 c + ab^2 = 3abc.

$$\mathrm{If}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{had}\:\mathrm{two}\:\mathrm{roots}\:{p}\:\mathrm{and}\:{q} \\ $$$$\mathrm{and}\:{p}^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \:=\:{p}^{\mathrm{3}} \:+\:{q}^{\mathrm{3}} \:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${b}^{\mathrm{3}} \:−\:\mathrm{2}{a}^{\mathrm{2}} {c}\:+\:{ab}^{\mathrm{2}} \:=\:\mathrm{3}{abc}. \\ $$

Question Number 205324 Answers: 3 Comments: 0

Compare: 37^(37) and 36^(38)

$$\mathrm{Compare}: \\ $$$$\mathrm{37}^{\mathrm{37}} \:\:\:\mathrm{and}\:\:\:\mathrm{36}^{\mathrm{38}} \\ $$

Question Number 205319 Answers: 0 Comments: 0

Question Number 205297 Answers: 2 Comments: 0

Find the′′ range ′′ of : i : f (x) =⌊ (( x)/( ⌊ x ⌋)) ⌋ ii: f(x) = (( x)/(⌊ x ⌋ + ⌊ −x ⌋))

$$ \\ $$$$\:\:\:{Find}\:\:{the}''\:{range}\:''\:{of}\:\:: \\ $$$$ \\ $$$$\:\:\:{i}\::\:\:\:{f}\:\left({x}\right)\:=\lfloor\:\frac{\:{x}}{\:\lfloor\:{x}\:\rfloor}\:\rfloor \\ $$$$\:\:\:{ii}:\:{f}\left({x}\right)\:=\:\frac{\:{x}}{\lfloor\:{x}\:\rfloor\:+\:\lfloor\:−{x}\:\rfloor} \\ $$$$\:\: \\ $$

Pg 41 Pg 42 Pg 43 Pg 44 Pg 45 Pg 46 Pg 47 Pg 48 Pg 49 Pg 50

Contact: info@tinkutara.com