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Question Number 164515 Answers: 0 Comments: 3

Question Number 164511 Answers: 1 Comments: 0

sin∙(π sin x) - cos∙(π sin x) = 1 find x=?

$$\mathrm{sin}\centerdot\left(\pi\:\mathrm{sin}\:\mathrm{x}\right)\:-\:\mathrm{cos}\centerdot\left(\pi\:\mathrm{sin}\:\mathrm{x}\right)\:=\:\mathrm{1} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 164582 Answers: 0 Comments: 0

Question Number 164507 Answers: 1 Comments: 2

Question Number 164497 Answers: 1 Comments: 0

Question Number 164483 Answers: 1 Comments: 1

((cos25−sin65)/(sin20+sin10))=?

$$\frac{{cos}\mathrm{25}−{sin}\mathrm{65}}{{sin}\mathrm{20}+{sin}\mathrm{10}}=? \\ $$

Question Number 164488 Answers: 0 Comments: 1

(1/(sin 30))−(cot 30)^4 −(cot 30)^2 =.... a)sin^2 30 b)(1/(sin 30)) c)2sin^2 30 d)(1/(sin^2 30))

$$\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{30}}−\left(\mathrm{cot}\:\mathrm{30}\right)^{\mathrm{4}} −\left(\mathrm{cot}\:\mathrm{30}\right)^{\mathrm{2}} =.... \\ $$$$\left.{a}\left.\right)\mathrm{sin}\:^{\mathrm{2}} \mathrm{30}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}\right)\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{30}} \\ $$$$\left.{c}\left.\right)\mathrm{2sin}\:^{\mathrm{2}} \mathrm{30}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}\right)\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{30}} \\ $$

Question Number 164478 Answers: 1 Comments: 0

Given { ((u_0 =α ∈ C)),((u_(n+1) =((u_n +∣u_n ∣)/2))) :} ; n∈ N where (u_n ) _(n∈N) is a complex sequence. Determinate the sequence (Im(u_n )) _(n∈N) and calculate its limit. NB: Im(u_n ) is the complex part of u_(n.)

$${Given}\:\begin{cases}{{u}_{\mathrm{0}} =\alpha\:\in\:\mathbb{C}}\\{{u}_{{n}+\mathrm{1}} =\frac{{u}_{{n}} +\mid{u}_{{n}} \mid}{\mathrm{2}}}\end{cases}\:;\:{n}\in\:\mathbb{N} \\ $$$${where}\:\left({u}_{{n}} \right)\:_{{n}\in\mathbb{N}} \:{is}\:{a}\:{complex}\:{sequence}. \\ $$$${Determinate}\:{the}\:{sequence}\:\left({Im}\left({u}_{{n}} \right)\right)\:_{{n}\in\mathbb{N}} \\ $$$${and}\:{calculate}\:{its}\:{limit}. \\ $$$${NB}:\:{Im}\left({u}_{{n}} \right)\:{is}\:{the}\:{complex}\:{part}\:{of}\:{u}_{{n}.} \\ $$$$ \\ $$

Question Number 164477 Answers: 0 Comments: 0

Using the definition, show that U_n =Σ_(k=1) ^n ((sin(k))/(k!)) is a sequence of Cauchy.

$${Using}\:{the}\:{definition},\:{show}\:{that}\: \\ $$$${U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{sin}\left({k}\right)}{{k}!}\:{is}\:{a}\:{sequence}\:{of}\:{Cauchy}. \\ $$

Question Number 164475 Answers: 1 Comments: 0

Etudiez la convergence de de la suite U_n =((1+cos(n)+2n)/(ni+(√((n+1)(n+2))))) ; n ∈ N. [study the convergence of U_n ]

$${Etudiez}\:\:{la}\:{convergence}\:{de}\:{de}\:{la} \\ $$$${suite}\:{U}_{{n}} =\frac{\mathrm{1}+{cos}\left({n}\right)+\mathrm{2}{n}}{{ni}+\sqrt{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}}\:;\:{n}\:\in\:\mathbb{N}. \\ $$$$\left[{study}\:{the}\:{convergence}\:{of}\:{U}_{{n}} \right] \\ $$

Question Number 164474 Answers: 0 Comments: 0

E={x ∈ Q_+ :x^2 >3}. Show that E has not lower bound in Q. [Montrez que E n′admet pas de borne inferieure dans Q]

$${E}=\left\{{x}\:\in\:\mathbb{Q}_{+} :{x}^{\mathrm{2}} >\mathrm{3}\right\}.\: \\ $$$${Show}\:{that}\:{E}\:{has}\:{not}\:{lower}\:{bound} \\ $$$${in}\:\mathbb{Q}. \\ $$$$\left[{Montrez}\:{que}\:{E}\:{n}'{admet}\:{pas}\:{de}\:{borne}\right. \\ $$$$\left.{inferieure}\:{dans}\:\mathbb{Q}\right] \\ $$

Question Number 164473 Answers: 1 Comments: 0

Show for z_1 ; z_(2 ) ∈ C that: ∣z_1 +z_2 ∣^2 +∣z_1 −z_2 ∣^2 =2(∣z_1 ∣^2 +∣z_2 ∣^2 ).

$${Show}\:{for}\:{z}_{\mathrm{1}} ;\:{z}_{\mathrm{2}\:} \:\in\:\mathbb{C}\:{that}: \\ $$$$\mid{z}_{\mathrm{1}} +{z}_{\mathrm{2}} \mid^{\mathrm{2}} +\mid{z}_{\mathrm{1}} −{z}_{\mathrm{2}} \mid^{\mathrm{2}} =\mathrm{2}\left(\mid{z}_{\mathrm{1}} \mid^{\mathrm{2}} +\mid{z}_{\mathrm{2}} \mid^{\mathrm{2}} \right). \\ $$

Question Number 164462 Answers: 2 Comments: 2

Find x, such that f(x) is minimum. f(x)={((√(c^2 −x^2 ))/(c−x))−(c−x)}^2

$${Find}\:{x},\:{such}\:{that}\:{f}\left({x}\right)\:{is}\:{minimum}. \\ $$$${f}\left({x}\right)=\left\{\frac{\sqrt{{c}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{{c}−{x}}−\left({c}−{x}\right)\right\}^{\mathrm{2}} \\ $$

Question Number 164445 Answers: 0 Comments: 1

Question Number 164447 Answers: 1 Comments: 0

Question Number 164437 Answers: 1 Comments: 0

Find the max. area of Δle witth sides a,b,c such as 0<a≤1;1≤b≤2;2≤c≤3 is a)1 b)1/2 c)2 d)3/2

$${Find}\:{the}\:{max}.\:{area}\:{of}\:\Delta{le} \\ $$$${witth}\:{sides}\:{a},{b},{c}\:{such}\:{as} \\ $$$$\mathrm{0}<{a}\leqslant\mathrm{1};\mathrm{1}\leqslant{b}\leqslant\mathrm{2};\mathrm{2}\leqslant{c}\leqslant\mathrm{3}\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\:\:\:\:\:\:\:\:{b}\right)\mathrm{1}/\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:{c}\right)\mathrm{2}\:\:\:\:\:\:\:\:{d}\right)\mathrm{3}/\mathrm{2} \\ $$

Question Number 164434 Answers: 1 Comments: 0

Question Number 164429 Answers: 1 Comments: 0

If C(2x , x) = 70 prove that x = 4

$${If}\:{C}\left(\mathrm{2}{x}\:,\:{x}\right)\:=\:\mathrm{70} \\ $$$${prove}\:{that}\:{x}\:=\:\mathrm{4} \\ $$

Question Number 164426 Answers: 1 Comments: 1

In ΔABC if { ((cot A.cot C = (1/2))),((cot B.cot C = (1/(18)))) :} then tan C = ?

$$\:\:{In}\:\Delta{ABC}\:{if}\:\begin{cases}{\mathrm{cot}\:{A}.\mathrm{cot}\:{C}\:=\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\mathrm{cot}\:{B}.\mathrm{cot}\:{C}\:=\:\frac{\mathrm{1}}{\mathrm{18}}}\end{cases} \\ $$$$\:{then}\:\mathrm{tan}\:\:{C}\:=\:? \\ $$

Question Number 164425 Answers: 1 Comments: 0

What it′s ?? 5×55×555×5555×55555.............∞=

$$\mathrm{What}\:\mathrm{it}'\mathrm{s}\:?? \\ $$$$\mathrm{5}×\mathrm{55}×\mathrm{555}×\mathrm{5555}×\mathrm{55555}.............\infty= \\ $$

Question Number 164419 Answers: 1 Comments: 0

please help me prouve that ∫_0 ^1 ((lnt)/(t^2 −1))dt=(π^2 /8)

$${please}\:{help}\:{me} \\ $$$${prouve}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{lnt}}{{t}^{\mathrm{2}} −\mathrm{1}}{dt}=\frac{\pi^{\mathrm{2}} }{\mathrm{8}} \\ $$

Question Number 164418 Answers: 2 Comments: 2

Question Number 164416 Answers: 0 Comments: 0

if a;b;c<0 and a+b+c=3 prove that: (1 + (b/a))^(1/b^2 ) ∙ (1 + (c/b))^(1/c^2 ) ∙ (1 + (a/c))^(1/a^2 ) ≥ 8

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}<\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\left(\mathrm{1}\:+\:\frac{\mathrm{b}}{\mathrm{a}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}^{\mathrm{2}} }} \centerdot\:\left(\mathrm{1}\:+\:\frac{\mathrm{c}}{\mathrm{b}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{c}}^{\mathrm{2}} }} \centerdot\:\left(\mathrm{1}\:+\:\frac{\mathrm{a}}{\mathrm{c}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} }} \geqslant\:\mathrm{8} \\ $$

Question Number 164417 Answers: 1 Comments: 0

Question Number 164405 Answers: 0 Comments: 0

let a, b, c > 0 ; a + b + c = 3 prove that; (a^2 /(b^2 + bc + c^2 )) + (b^2 /(c^2 + ac + a^2 )) + (c^2 /(b^2 +ba + a^2 )) 6 ≥ 2abc + (5/3) (a^2 + b^2 + c^2 ) ≥ 7 ^({Z.A})

$$\boldsymbol{{let}}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:>\:\mathrm{0}\:;\:\boldsymbol{{a}}\:+\:\boldsymbol{{b}}\:+\:\boldsymbol{{c}}\:=\:\mathrm{3} \\ $$$$\boldsymbol{{prove}}\:\boldsymbol{{that}};\:\frac{\boldsymbol{{a}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} \:+\:\boldsymbol{{bc}}\:+\:\boldsymbol{{c}}^{\mathrm{2}} }\:\:+\:\:\frac{\boldsymbol{{b}}^{\mathrm{2}} }{\boldsymbol{{c}}^{\mathrm{2}} \:+\:\boldsymbol{{ac}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} \:}\:\:+\:\:\frac{\boldsymbol{{c}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} \:+\boldsymbol{{ba}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} }\:\:\mathrm{6}\:\:\geqslant\:\:\mathrm{2}\boldsymbol{{abc}}\:\:+\:\:\frac{\mathrm{5}}{\mathrm{3}}\:\:\left(\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} \:+\:\boldsymbol{{c}}^{\mathrm{2}} \:\right)\:\:\geqslant\:\:\mathrm{7} \\ $$$$\:^{\left\{\boldsymbol{\mathrm{Z}}.\mathrm{A}\right\}} \\ $$

Question Number 164396 Answers: 2 Comments: 1

If f(x)=f(x−1)+x^2 +2x and f(0)=17 , find f(17).

$${If}\:\:{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{x}^{\mathrm{2}} +\mathrm{2}{x} \\ $$$${and}\:\:{f}\left(\mathrm{0}\right)=\mathrm{17}\:\:,\:\:{find}\:{f}\left(\mathrm{17}\right). \\ $$

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