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Question Number 176086    Answers: 0   Comments: 1

Question Number 176076    Answers: 0   Comments: 1

Question Number 176070    Answers: 0   Comments: 3

demontrer par recurrence que pour tout n>0 appartenent a l ensemble des entier naturel 3^(2n−2^(n ) ) est multiple de 7

$${demontrer}\:{par}\:{recurrence}\:{que}\:{pour}\:{tout}\:{n}>\mathrm{0}\:{appartenent}\:{a}\:{l}\:{ensemble}\:{des}\:{entier}\:{naturel}\:\mathrm{3}^{\mathrm{2}{n}−\mathrm{2}^{{n}\:} } {est}\:{multiple}\:{de}\:\mathrm{7} \\ $$

Question Number 176058    Answers: 3   Comments: 0

22^(22) what is hte last digit?

$$\mathrm{22}^{\mathrm{22}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{hte}\:\mathrm{last}\:\mathrm{digit}? \\ $$

Question Number 176056    Answers: 1   Comments: 0

Three bags labelled R, B and W cotains Red, Blue and White balls respectively of equal sizes, the ratio of the balls in the bag are R:B=2:3 and B:W= 4:5. All the balls are removed into a big bag and properly mixed together. If two balls are picked at random one after the other with replacement, find the probability of picking a) white ball and a blue b). A blue ball first and then red ball

$$\:\mathrm{Three}\:\mathrm{bags}\:\mathrm{labelled}\:\mathrm{R},\:\mathrm{B}\:\mathrm{and}\:\mathrm{W}\: \\ $$$$\:\mathrm{cotains}\:\mathrm{Red},\:\mathrm{Blue}\:\mathrm{and}\:\mathrm{White}\:\mathrm{balls}\: \\ $$$$\:\mathrm{respectively}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{sizes},\:\mathrm{the}\:\mathrm{ratio}\: \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{are}\:\:\mathrm{R}:\mathrm{B}=\mathrm{2}:\mathrm{3}\: \\ $$$$\mathrm{and}\:\mathrm{B}:\mathrm{W}=\:\mathrm{4}:\mathrm{5}.\:\mathrm{All}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{are}\: \\ $$$$\mathrm{removed}\:\mathrm{into}\:\mathrm{a}\:\mathrm{big}\:\mathrm{bag}\:\mathrm{and}\:\mathrm{properly}\: \\ $$$$\mathrm{mixed}\:\mathrm{together}.\:\mathrm{If}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{picked} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{one}\:\mathrm{after}\:\mathrm{the}\:\mathrm{other}\:\mathrm{with}\: \\ $$$$\mathrm{replacement},\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{picking}\: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{white}\:\mathrm{ball}\:\mathrm{and}\:\mathrm{a}\:\mathrm{blue} \\ $$$$\left.\mathrm{b}\right).\:\mathrm{A}\:\mathrm{blue}\:\mathrm{ball}\:\mathrm{first}\:\mathrm{and}\:\mathrm{then}\:\mathrm{red}\:\mathrm{ball} \\ $$$$ \\ $$

Question Number 176060    Answers: 2   Comments: 0

x^2 −4x+5=0

$${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}=\mathrm{0} \\ $$

Question Number 176054    Answers: 1   Comments: 0

(1/(2!)) + (2/(3!)) + (3/(4!)) + (4/(5!)) + ............. ∞ = ?

$$\frac{\mathrm{1}}{\mathrm{2}!}\:+\:\frac{\mathrm{2}}{\mathrm{3}!}\:+\:\frac{\mathrm{3}}{\mathrm{4}!}\:+\:\frac{\mathrm{4}}{\mathrm{5}!}\:+\:.............\:\infty\:=\:? \\ $$

Question Number 176049    Answers: 1   Comments: 0

calculer (−1/2+i(√(3/2)^3 ))

$${calculer}\:\left(−\mathrm{1}/\mathrm{2}+{i}\sqrt{\left.\mathrm{3}/\mathrm{2}\right)^{\mathrm{3}} }\right. \\ $$

Question Number 176037    Answers: 2   Comments: 1

If (a−b)(a + b) = 13 Find 2a + b = ?

$$\mathrm{If}\:\:\:\left(\mathrm{a}−\mathrm{b}\right)\left(\mathrm{a}\:+\:\mathrm{b}\right)\:=\:\mathrm{13} \\ $$$$\mathrm{Find}\:\:\:\mathrm{2a}\:+\:\mathrm{b}\:=\:? \\ $$

Question Number 176035    Answers: 1   Comments: 0

lim_(x→0) ((x (√(1+x^2 )) −sin x)/((1+x^2 )^x −(√(1+x^3 )))) =

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:−\mathrm{sin}\:\mathrm{x}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{x}} −\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }}\:= \\ $$

Question Number 176022    Answers: 0   Comments: 0

Question Number 176014    Answers: 3   Comments: 1

Question Number 176090    Answers: 2   Comments: 1

determiner z tel que z=z^2 −z+2

$${determiner}\:{z}\:{tel}\:{que}\:{z}={z}^{\mathrm{2}} −{z}+\mathrm{2} \\ $$$$ \\ $$

Question Number 176005    Answers: 0   Comments: 2

Question Number 175996    Answers: 1   Comments: 0

lim_(x→0) ((a^x −1)/x)=?

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{a}^{{x}} −\mathrm{1}}{{x}}=? \\ $$

Question Number 175995    Answers: 2   Comments: 0

lim_(x→0) ((e^(3x) −1)/x)=?

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{\mathrm{3}{x}} −\mathrm{1}}{{x}}=? \\ $$

Question Number 175994    Answers: 3   Comments: 0

lim_(x→∞) ((e^x −1)/x)=?

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}=? \\ $$

Question Number 175987    Answers: 4   Comments: 0

please calculate I=∫_0 ^(π/2) (dx/(1+(tanx)^(√2) )) J=∫_0 ^π (dx/(a^2 cos^2 x+sin^2 x)) K=∫_0 ^(π/2) (dx/(3tanx+2))

$${please}\:{calculate} \\ $$$${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+\left({tanx}\right)^{\sqrt{\mathrm{2}}} } \\ $$$${J}=\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}} {x}+{sin}^{\mathrm{2}} {x}} \\ $$$${K}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{3}{tanx}+\mathrm{2}} \\ $$

Question Number 175986    Answers: 2   Comments: 0

Question Number 175976    Answers: 1   Comments: 1

Question Number 175972    Answers: 2   Comments: 0

((x^(11) +x)/(x^7 +x^5 )) = ((205)/(16)) solve for x (undecic equation )

$$\frac{{x}^{\mathrm{11}} +{x}}{{x}^{\mathrm{7}} +{x}^{\mathrm{5}} }\:=\:\frac{\mathrm{205}}{\mathrm{16}} \\ $$$${solve}\:{for}\:{x}\:\left({undecic}\:{equation}\:\right) \\ $$

Question Number 175967    Answers: 0   Comments: 0

lim_(n→∞) [tan𝚿+(1/2)tan(𝚿/2)+(1/2^2 )tan(𝚿/2^2 )+...+(1/2^n )tan(𝚿/2^n )]

$$\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\:\left[\boldsymbol{\mathrm{tan}\Psi}+\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\mathrm{2}} }+...+\frac{\mathrm{1}}{\mathrm{2}^{\boldsymbol{{n}}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\boldsymbol{{n}}} }\right]\:\:\:\:\: \\ $$

Question Number 175961    Answers: 1   Comments: 0

Given that ((2tan15^0 )/(1+tan^2 15^0 ))=sin30^0 , find tan15^0 leaving the answer in surd form (radicals)

$$\mathrm{Given}\:\mathrm{that}\:\frac{\mathrm{2tan15}^{\mathrm{0}} }{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \mathrm{15}^{\mathrm{0}} }=\mathrm{sin30}^{\mathrm{0}} ,\:\mathrm{find}\:\mathrm{tan15}^{\mathrm{0}} \\ $$$$\mathrm{leaving}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form}\:\left(\mathrm{radicals}\right) \\ $$

Question Number 175959    Answers: 3   Comments: 2

f(x) = x^6 − 100x^5 + 100x^4 − 100x^3 + 100x^2 − 100x + 100 f(99) = ?

$${f}\left({x}\right)\:=\:{x}^{\mathrm{6}} \:−\:\mathrm{100}{x}^{\mathrm{5}} \:+\:\mathrm{100}{x}^{\mathrm{4}} \:−\:\mathrm{100}{x}^{\mathrm{3}} \:+\:\mathrm{100}{x}^{\mathrm{2}} \:−\:\mathrm{100}{x}\:+\:\mathrm{100} \\ $$$${f}\left(\mathrm{99}\right)\:=\:? \\ $$

Question Number 175956    Answers: 1   Comments: 1

Question Number 175954    Answers: 0   Comments: 0

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