Question and Answers Forum

AllQuestion and Answers: Page 142

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 205517 Answers: 1 Comments: 0

Question Number 205516 Answers: 0 Comments: 0

Σ_(h=1) ^∞ ((𝛇(2h)−1)/h) = .....? Σ_(h=1) ^∞ (𝛇(2h+1)−1)=......? pls help me

$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\boldsymbol{\zeta}\left(\mathrm{2}{h}\right)−\mathrm{1}}{{h}}\:=\:.....? \\ $$$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\boldsymbol{\zeta}\left(\mathrm{2}{h}+\mathrm{1}\right)−\mathrm{1}\right)=......? \\ $$$$\mathrm{pls}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 205515 Answers: 0 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 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 205507 Answers: 1 Comments: 1

Question Number 205506 Answers: 1 Comments: 0

∫_0 ^1 (√(1−x^4 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205502 Answers: 2 Comments: 0

If two roots of ax^2 + bx + c = 0 are α and β then (1/((aα^2 + c)^2 )) + (1/((aβ^2 + c)^2 )) = ?

$$\mathrm{If}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{are}\:\alpha\:\mathrm{and}\: \\ $$$$\beta\:\mathrm{then}\:\frac{\mathrm{1}}{\left({a}\alpha^{\mathrm{2}} \:+\:{c}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({a}\beta^{\mathrm{2}} \:+\:{c}\right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 205496 Answers: 1 Comments: 0

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 205461 Answers: 2 Comments: 1

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 205457 Answers: 3 Comments: 0

Question Number 205456 Answers: 1 Comments: 0

Question Number 205479 Answers: 1 Comments: 0

Question Number 205446 Answers: 1 Comments: 0

Question Number 205451 Answers: 1 Comments: 0

lim_(x→∞) ∫_0 ^x (dt/(e^(2t) t))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{{x}} \frac{{dt}}{{e}^{\mathrm{2}{t}} {t}} \\ $$

Question Number 205448 Answers: 0 Comments: 0

A=lim_(x→0) ((sinx)/x^3 )=?

$${A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{sinx}}{{x}^{\mathrm{3}} }=? \\ $$

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 205429 Answers: 2 Comments: 0

If, ϕ = (1/2) (π −cos^( −1) ((1/4) )) ⇒ log_( 2) ( (( 1+ cos(6ϕ ))/(cos^6 (ϕ ))) ) =?

$$ \\ $$$$\:\mathrm{I}{f},\:\:\varphi\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\pi\:−{cos}^{\:−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}}\:\right)\right) \\ $$$$ \\ $$$$\:\:\:\Rightarrow\:\mathrm{log}_{\:\mathrm{2}} \left(\:\frac{\:\mathrm{1}+\:{cos}\left(\mathrm{6}\varphi\:\right)}{{cos}^{\mathrm{6}} \left(\varphi\:\right)}\:\right)\:=? \\ $$$$ \\ $$

Question Number 205428 Answers: 2 Comments: 0

Pg 137 Pg 138 Pg 139 Pg 140 Pg 141 Pg 142 Pg 143 Pg 144 Pg 145 Pg 146

Contact: info@tinkutara.com