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Question Number 177525 Answers: 1 Comments: 3

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Question Number 177507 Answers: 1 Comments: 0

The angle of elevetion of the top of a tower from a point A in the north is α and the angle of the top of the tower from the point B in the east of the point A is β .prove that the height of the tower is ((ABsin αsin B)/( (√(sin^2 α−sin^2 β))))

Question Number 177476 Answers: 1 Comments: 4

Question Number 177475 Answers: 1 Comments: 0

Question Number 177473 Answers: 0 Comments: 0

Question Number 178488 Answers: 1 Comments: 0

I have two children. One is a boy born on a Tuesday. What is the probbility I have two boys

$$ \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{two}\:\mathrm{children}.\:\mathrm{One}\:\mathrm{is}\:\mathrm{a}\:\mathrm{boy} \\ $$$$\mathrm{born}\:\mathrm{on}\:\mathrm{a}\:\mathrm{Tuesday}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{probbility}\:\mathrm{I}\:\mathrm{have}\:\mathrm{two}\:\mathrm{boys} \\ $$

Question Number 178487 Answers: 3 Comments: 0

∫ (dx/(cot^3 x sin^7 x)) =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{{dx}}{\mathrm{cot}\:^{\mathrm{3}} {x}\:\mathrm{sin}\:^{\mathrm{7}} {x}}\:=? \\ $$

Question Number 178486 Answers: 1 Comments: 0

Reduce (((2n)!)/(1×3×5×...×(2n−1)))

$$\:{Reduce}\:\frac{\left(\mathrm{2}{n}\right)!}{\mathrm{1}×\mathrm{3}×\mathrm{5}×...×\left(\mathrm{2}{n}−\mathrm{1}\right)}\: \\ $$

Question Number 177492 Answers: 0 Comments: 0

If 0<a≤b then: ∫_( a) ^( b) ∫_( a) ^( b) ((dx dy)/( (√(xy (x + y))))) ≤ ((b−a)/2) ∙ log ((b/a)) + log^2 ((b/a))

$$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}: \\ $$$$\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\:\frac{\mathrm{dx}\:\mathrm{dy}}{\:\sqrt{\mathrm{xy}\:\left(\mathrm{x}\:+\:\mathrm{y}\right)}}\:\:\leqslant\:\:\frac{\mathrm{b}−\mathrm{a}}{\mathrm{2}}\:\centerdot\:\mathrm{log}\:\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\:+\:\mathrm{log}^{\mathrm{2}} \:\left(\frac{\mathrm{b}}{\mathrm{a}}\right) \\ $$

Question Number 177493 Answers: 1 Comments: 2

find the laplace transform of f(t)=ln(t)

$${find}\:{the}\:{laplace}\:{transform}\:{of} \\ $$$${f}\left({t}\right)={ln}\left({t}\right) \\ $$

Question Number 181603 Answers: 0 Comments: 0

calcul Σ_(n=1) ^(+oo) U_n : U_n =(1/n)(E((√(n+1)) −E((√n) )

$${calcul}\:\:\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}{U}_{{n}} : \\ $$$${U}_{{n}} =\frac{\mathrm{1}}{{n}}\left({E}\left(\sqrt{{n}+\mathrm{1}}\:−{E}\left(\sqrt{{n}}\:\right)\right.\right. \\ $$

Question Number 177456 Answers: 2 Comments: 0

Question Number 177446 Answers: 1 Comments: 1

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Question Number 177432 Answers: 2 Comments: 10

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Question Number 177403 Answers: 2 Comments: 1

if david wears shorts and short sleeves to play outside what temperature would it most likely be?

$${if}\:{david}\:{wears}\:{shorts}\:{and}\:{short}\:{sleeves}\:{to}\:{play}\:{outside}\:{what}\:{temperature}\:{would}\:{it}\:{most}\:{likely}\:{be}? \\ $$

Question Number 177400 Answers: 3 Comments: 2

∫((√(9a^2 −1))/a)da Evaluate

$$\int\frac{\sqrt{\mathrm{9a}^{\mathrm{2}} −\mathrm{1}}}{\mathrm{a}}\mathrm{da} \\ $$$$ \\ $$$$\mathrm{Evaluate} \\ $$

Question Number 177378 Answers: 1 Comments: 0

Question Number 177451 Answers: 1 Comments: 1

Question Number 177361 Answers: 1 Comments: 0

4(16^((x+4)) × 5.2^(2x) =13

$$\mathrm{4}\left(\mathrm{16}^{\left({x}+\mathrm{4}\right)} \:×\:\mathrm{5}.\mathrm{2}^{\mathrm{2}{x}} =\mathrm{13}\right. \\ $$

Question Number 177360 Answers: 1 Comments: 0

1/2 log_4 36 ×log_6 64

$$\mathrm{1}/\mathrm{2}\:{log}_{\mathrm{4}} \mathrm{36}\:×{log}_{\mathrm{6}} \mathrm{64} \\ $$

Question Number 177375 Answers: 0 Comments: 5

soit k un entier naturel non nul ,S un nombre fini de nombres premiers impair −Demontrer qu il existe au plus une maniere(a rotation et symetrie axiale) de disposer les elements de S sur un cercle de sorte que le priduit de 2 nombres places l′un a cote de l′autre soit toujours de la forme (x^2 +x+k),x un entier naturel non nul. Extrait de Olimpiad de Mathematiques (France 2022).

$$\mathrm{soit}\:\mathrm{k}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}\:,\mathrm{S}\:\mathrm{un}\:\mathrm{nombre}\:\mathrm{fini}\:\mathrm{de}\: \\ $$$$\mathrm{nombres}\:\mathrm{premiers}\:\mathrm{impair} \\ $$$$−\mathrm{Demontrer}\:\mathrm{qu}\:\mathrm{il}\:\mathrm{existe}\:\mathrm{au}\:\mathrm{plus}\:\mathrm{une}\:\mathrm{maniere}\left(\mathrm{a}\:\mathrm{rotation}\:\mathrm{et}\:\mathrm{symetrie}\:\mathrm{axiale}\right) \\ $$$$\mathrm{de}\:\mathrm{disposer}\:\mathrm{les}\:\mathrm{elements}\:\mathrm{de}\:\mathrm{S}\:\mathrm{sur}\:\mathrm{un}\:\mathrm{cercle}\:\mathrm{de}\:\mathrm{sorte}\:\mathrm{que}\:\mathrm{le}\:\mathrm{priduit}\:\mathrm{de}\:\mathrm{2}\:\mathrm{nombres}\: \\ $$$$\mathrm{places}\:\mathrm{l}'\mathrm{un}\:\mathrm{a}\:\mathrm{cote}\:\mathrm{de}\:\mathrm{l}'\mathrm{autre}\:\mathrm{soit}\:\mathrm{toujours}\:\mathrm{de}\:\mathrm{la}\:\mathrm{forme}\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{k}}\right),\mathrm{x}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}. \\ $$$$\:\:\:\:\:\:\:{Extrait}\:{de}\:{Olimpiad}\:{de}\:{Mathematiques}\:\left({France}\:\mathrm{2022}\right). \\ $$$$ \\ $$

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