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Question Number 152111 Answers: 3 Comments: 0

∫tan^(−1) (sec x+tan x)dx

$$\int\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 152110 Answers: 3 Comments: 0

∫a^(mx) b^(nx) dx

$$\int\mathrm{a}^{\mathrm{mx}} \mathrm{b}^{\mathrm{nx}} \mathrm{dx} \\ $$

Question Number 152106 Answers: 0 Comments: 0

∫ x^n cos(nx) dx

$$\int\:\mathrm{x}^{\mathrm{n}} \:\mathrm{cos}\left(\mathrm{nx}\right)\:\mathrm{dx} \\ $$

Question Number 152094 Answers: 1 Comments: 0

Question Number 152091 Answers: 1 Comments: 0

Given tbat Arg(z+1)=(Π/6) and Arg(z−1)=((2Π)/3).Find z. please help me

$${Given}\:{tbat}\:{Arg}\left({z}+\mathrm{1}\right)=\frac{\Pi}{\mathrm{6}}\:{and}\: \\ $$$${Arg}\left({z}−\mathrm{1}\right)=\frac{\mathrm{2}\Pi}{\mathrm{3}}.{Find}\:{z}. \\ $$$${please}\:{help}\:{me} \\ $$

Question Number 152088 Answers: 2 Comments: 0

∫_0 ^(Π/2) ∣sinx−cosx∣ please help me out

$$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \mid{sinx}−{cosx}\mid \\ $$$${please}\:{help}\:{me}\:{out} \\ $$

Question Number 152186 Answers: 1 Comments: 0

∫x^n cos(nx) dx

$$\int\mathrm{x}^{\mathrm{n}} \:\mathrm{cos}\left(\mathrm{nx}\right)\:\mathrm{dx} \\ $$

Question Number 152082 Answers: 1 Comments: 0

Question Number 152101 Answers: 1 Comments: 0

Mr Bonsu an engineer walked round a cylindrical container 4m high once keeping a constant distance of 1m from the container. If he walked with a speed of 3kmh^(−1) for three minutes, calculate to the nearest whole number the: (i) radius of the circle (ii) volume of the container

$$\mathrm{Mr}\:\mathrm{Bonsu}\:\mathrm{an}\:\mathrm{engineer}\:\mathrm{walked}\:\mathrm{round} \\ $$$$\mathrm{a}\:\mathrm{cylindrical}\:\mathrm{container}\:\mathrm{4m}\:\mathrm{high}\:\mathrm{once} \\ $$$$\mathrm{keeping}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{1m}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{container}.\:\mathrm{If}\:\mathrm{he}\:\mathrm{walked}\:\mathrm{with}\:\mathrm{a}\: \\ $$$$\mathrm{speed}\:\mathrm{of}\:\mathrm{3kmh}^{−\mathrm{1}} \:\mathrm{for}\:\mathrm{three}\:\mathrm{minutes},\: \\ $$$$\mathrm{calculate}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number} \\ $$$$\mathrm{the}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{container} \\ $$

Question Number 152063 Answers: 2 Comments: 0

If x is a real number and y is equal to ((x^2 + 1)/(x^2 + x + 1)), show that ∣y − (4/3)∣ ≤ (2/3)

$$\mathrm{If}\:\:\mathrm{x}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}\:\mathrm{and}\:\:\:\mathrm{y}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{x}\:\:+\:\:\mathrm{1}}, \\ $$$$\mathrm{show}\:\mathrm{that}\:\:\:\:\:\mid\mathrm{y}\:\:\:−\:\:\:\frac{\mathrm{4}}{\mathrm{3}}\mid\:\:\:\leqslant\:\:\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 152061 Answers: 1 Comments: 0

solve Ω= ∫_0 ^( ∞) (( sin^( 3) (x).cos^( 2) (x))/x^( 3) )dx=^? ((7π)/(32))...■

$$ \\ $$$$\:\:\:{solve} \\ $$$$\:\:\:\: \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{3}} \left({x}\right).{cos}^{\:\mathrm{2}} \left({x}\right)}{{x}^{\:\mathrm{3}} }{dx}\overset{?} {=}\frac{\mathrm{7}\pi}{\mathrm{32}}...\blacksquare \\ $$

Question Number 152052 Answers: 1 Comments: 0

knowns x_2 =(2/x_1 ) , x_3 =(3/x_2 ) , x_4 =(4/x_3 ) , x_5 =(5/x_4 ) , ..., x_8 =(8/x_7 ). Find the value of x_1 ×x_2 ×x_3 ×...×x_8 .

$$\:\:\mathrm{knowns}\:\mathrm{x}_{\mathrm{2}} =\frac{\mathrm{2}}{\mathrm{x}_{\mathrm{1}} }\:,\:\mathrm{x}_{\mathrm{3}} =\frac{\mathrm{3}}{\mathrm{x}_{\mathrm{2}} }\:,\:\mathrm{x}_{\mathrm{4}} =\frac{\mathrm{4}}{\mathrm{x}_{\mathrm{3}} } \\ $$$$,\:\mathrm{x}_{\mathrm{5}} =\frac{\mathrm{5}}{\mathrm{x}_{\mathrm{4}} }\:,\:...,\:\mathrm{x}_{\mathrm{8}} =\frac{\mathrm{8}}{\mathrm{x}_{\mathrm{7}} }.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}_{\mathrm{1}} ×\mathrm{x}_{\mathrm{2}} ×\mathrm{x}_{\mathrm{3}} ×...×\mathrm{x}_{\mathrm{8}} . \\ $$

Question Number 152049 Answers: 0 Comments: 0

If a;b≥1 then prove that: (a+1+((a+1)/a^2 ))^a ∙ (b+1+((b+1)/b^2 ))^b ≥ 2^(2(1+(√(ab))))

$$\mathrm{If}\:\:\mathrm{a};\mathrm{b}\geqslant\mathrm{1}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\left(\mathrm{a}+\mathrm{1}+\frac{\mathrm{a}+\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }\right)^{\boldsymbol{\mathrm{a}}} \centerdot\:\left(\mathrm{b}+\mathrm{1}+\frac{\mathrm{b}+\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }\right)^{\boldsymbol{\mathrm{b}}} \geqslant\:\mathrm{2}^{\mathrm{2}\left(\mathrm{1}+\sqrt{\boldsymbol{\mathrm{ab}}}\right)} \: \\ $$

Question Number 152047 Answers: 0 Comments: 0

∫_0 ^( ∞) ((x^2 +1)/( (√x^x ))) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\:\sqrt{{x}^{{x}} }}\:{dx} \\ $$$$\: \\ $$

Question Number 152019 Answers: 4 Comments: 0

Ω =∫_( 0) ^( 1) Li_2 (x) log(1+x) dx = ? Li_2 (x)−polylogaritm function

$$\Omega\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{Li}_{\mathrm{2}} \left({x}\right)\:{log}\left(\mathrm{1}+{x}\right)\:{dx}\:=\:? \\ $$$${Li}_{\mathrm{2}} \left({x}\right)−{polylogaritm}\:{function} \\ $$

Question Number 152105 Answers: 1 Comments: 0

∫_0 ^( ∞) (1/(⌊x+1⌋)) − (1/(x+1)) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{1}}{\lfloor{x}+\mathrm{1}\rfloor}\:−\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:{dx} \\ $$$$\: \\ $$

Question Number 152010 Answers: 1 Comments: 1

Question Number 152001 Answers: 1 Comments: 0

Four members of a school′s first eleven criket team are also in the first fourteen rugby team. How many members play for at least one of the two teams

$$\mathrm{Four}\:\mathrm{members}\:\mathrm{of}\:\mathrm{a}\:\mathrm{school}'\mathrm{s}\:\mathrm{first}\:\mathrm{eleven} \\ $$$$\mathrm{criket}\:\mathrm{team}\:\mathrm{are}\:\mathrm{also}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{fourteen} \\ $$$$\mathrm{rugby}\:\mathrm{team}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{members}\:\mathrm{play} \\ $$$$\mathrm{for}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{teams} \\ $$

Question Number 152000 Answers: 0 Comments: 3

• Histoire de code secret Vous e^ tes un espion et vous souhaitez assister a^ une re^ union secre^ te dans une une ambassade ou le garde demande un mot de passe... Vous vous cachez et tentez d′e^ couter les personnes qui se pre^ sentent. Au premier homme, le garde dit Cinq, l′homme re^ pond Quatre et le garde le laisse entrer. Au deuxie^ me, le garde lui dit Six, il re^ pond Trois et passe. Un dernier se pre^ sente. Le garde lui dit Quatre, il re^ pond Six et entre. Vous vous pre^ sentez alors et le garde vous dit Sept. Mais que re^ pondez−vous ?

$$\bullet\:{Histoire}\:{de}\:{code}\:{secret}\: \\ $$$$ \\ $$$$\mathrm{Vous}\:\hat {\mathrm{e}tes}\:\mathrm{un}\:\mathrm{espion}\:\mathrm{et}\:\mathrm{vous}\:\mathrm{souhaitez} \\ $$$$\mathrm{assister}\:\:\grave {\mathrm{a}}\:\mathrm{une}\:\mathrm{r}\acute {\mathrm{e}union}\:\mathrm{secr}\grave {\mathrm{e}te}\:\mathrm{dans}\:\mathrm{une} \\ $$$$\mathrm{une}\:\mathrm{ambassade}\:\mathrm{ou}\:\mathrm{le}\:\mathrm{garde}\:\mathrm{demande} \\ $$$$\mathrm{un}\:\mathrm{mot}\:\mathrm{de}\:\mathrm{passe}... \\ $$$$ \\ $$$$\mathrm{Vous}\:\mathrm{vous}\:\mathrm{cachez}\:\mathrm{et}\:\mathrm{tentez}\:\mathrm{d}'\acute {\mathrm{e}couter} \\ $$$$\mathrm{les}\:\mathrm{personnes}\:\mathrm{qui}\:\mathrm{se}\:\mathrm{pr}\acute {\mathrm{e}sentent}. \\ $$$$ \\ $$$$\mathrm{Au}\:\mathrm{premier}\:\mathrm{homme},\:\mathrm{le}\:\mathrm{garde}\:\mathrm{dit}\:\mathrm{Cinq}, \\ $$$$\mathrm{l}'\mathrm{homme}\:\mathrm{r}\acute {\mathrm{e}pond}\:\mathrm{Quatre}\:\mathrm{et}\:\mathrm{le}\:\mathrm{garde}\:\mathrm{le} \\ $$$$\mathrm{laisse}\:\mathrm{entrer}. \\ $$$$ \\ $$$$\mathrm{Au}\:\mathrm{deuxi}\grave {\mathrm{e}me},\:\mathrm{le}\:\mathrm{garde}\:\mathrm{lui}\:\mathrm{dit}\:\mathrm{Six},\:\mathrm{il} \\ $$$$\mathrm{r}\acute {\mathrm{e}pond}\:\mathrm{Trois}\:\mathrm{et}\:\mathrm{passe}. \\ $$$$ \\ $$$$\mathrm{Un}\:\mathrm{dernier}\:\mathrm{se}\:\mathrm{pr}\acute {\mathrm{e}sente}.\:\mathrm{Le}\:\mathrm{garde}\:\mathrm{lui} \\ $$$$\mathrm{dit}\:\mathrm{Quatre},\:\mathrm{il}\:\mathrm{r}\acute {\mathrm{e}pond}\:\mathrm{Six}\:\mathrm{et}\:\mathrm{entre}. \\ $$$$ \\ $$$$\mathrm{Vous}\:\mathrm{vous}\:\mathrm{pr}\acute {\mathrm{e}sentez}\:\mathrm{alors}\:\mathrm{et}\:\mathrm{le}\:\mathrm{garde} \\ $$$$\mathrm{vous}\:\mathrm{dit}\:\mathrm{Sept}.\:\mathrm{Mais}\:\mathrm{que} \\ $$$$\mathrm{r}\acute {\mathrm{e}pondez}−\mathrm{vous}\:? \\ $$

Question Number 151999 Answers: 2 Comments: 0

∫((x−1)/(x^2 +x−12))

$$\int\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{12}} \\ $$

Question Number 152035 Answers: 1 Comments: 0

Show that 2sin7θcos3θ=sin10θ+sin4θ.

$${Show}\:{that}\:\mathrm{2}{sin}\mathrm{7}\theta{cos}\mathrm{3}\theta={sin}\mathrm{10}\theta+{sin}\mathrm{4}\theta. \\ $$

Question Number 152034 Answers: 2 Comments: 0

{ ((3x^2 - 2y = - ((17)/3))),((y^2 - 6x = 7)) :} ⇒ xy = ?

$$\begin{cases}{\mathrm{3x}^{\mathrm{2}} \:-\:\mathrm{2y}\:=\:-\:\frac{\mathrm{17}}{\mathrm{3}}}\\{\mathrm{y}^{\mathrm{2}} \:-\:\mathrm{6x}\:=\:\mathrm{7}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{xy}\:=\:? \\ $$

Question Number 152032 Answers: 0 Comments: 0