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Question Number 104752 Answers: 1 Comments: 1

Question Number 104751 Answers: 1 Comments: 0

Question Number 104746 Answers: 2 Comments: 0

lim_(x→∞) (((1/2))^(3x) +((1/2))^x )^(1/x^2 )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{3}{x}} +\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{x}} \right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \: \\ $$

Question Number 104744 Answers: 0 Comments: 0

ABCD is a square with center O. I is the middle of [BC]. 1) q is geometric transformation defined by q: M→M′ such that CM′^(→) =CM^(→) +3DM^(→) . a)Determinate the invariant point of q. b) show that q is a homothety and precise it ratio.

$${ABCD}\:{is}\:{a}\:{square}\:{with}\:{center}\:{O}. \\ $$$${I}\:{is}\:{the}\:{middle}\:{of}\:\left[{BC}\right]. \\ $$$$\left.\mathrm{1}\right)\:{q}\:{is}\:{geometric}\:{transformation} \\ $$$${defined}\:{by}\:{q}:\:{M}\rightarrow{M}'\:{such}\:{that} \\ $$$$\overset{\rightarrow} {{CM}'}=\overset{\rightarrow} {{CM}}+\mathrm{3}\overset{\rightarrow} {{DM}}. \\ $$$$\left.{a}\right){Determinate}\:{the}\:{invariant}\:{point} \\ $$$${of}\:{q}. \\ $$$$\left.{b}\right)\:{show}\:{that}\:{q}\:{is}\:{a}\:{homothety}\:{and}\: \\ $$$${precise}\:{it}\:{ratio}. \\ $$

Question Number 104735 Answers: 1 Comments: 2

Question Number 104732 Answers: 0 Comments: 0

∫_0 ^1 log(tanθ)dθ

$$\int_{\mathrm{0}} ^{\mathrm{1}} {log}\left({tan}\theta\right){d}\theta \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 104811 Answers: 2 Comments: 0

Given { ((a+b(√3)−2c = 1)),((3b^2 +c^2 = 2a^2 )),((a^2 +4ac = 5c^2 )) :} find b

$${Given}\:\begin{cases}{{a}+{b}\sqrt{\mathrm{3}}−\mathrm{2}{c}\:=\:\mathrm{1}}\\{\mathrm{3}{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \:=\:\mathrm{2}{a}^{\mathrm{2}} }\\{{a}^{\mathrm{2}} +\mathrm{4}{ac}\:=\:\mathrm{5}{c}^{\mathrm{2}} }\end{cases} \\ $$$${find}\:{b} \\ $$

Question Number 104727 Answers: 4 Comments: 1

Given x + (1/x) = 2cos θ find x^n +(1/x^n ) = ?

$$\mathcal{G}{iven}\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2cos}\:\theta \\ $$$${find}\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }\:=\:? \\ $$

Question Number 104718 Answers: 2 Comments: 0

∫tan^(−1) (((a(√x)+b)/c))dx

$$\int{tan}^{−\mathrm{1}} \left(\frac{{a}\sqrt{{x}}+{b}}{{c}}\right){dx}\: \\ $$

Question Number 104717 Answers: 0 Comments: 0

In the a sport camp, 65% children know playing the football,70%−in voleyball,75%−in basketball.What is least number of children who know playing all above three sport games? (Answer 10%)

$$\mathrm{In}\:\mathrm{the}\:\mathrm{a}\:\:\mathrm{sport}\:\mathrm{camp},\:\mathrm{65\%}\:\mathrm{children}\:\mathrm{know} \\ $$$$\mathrm{playing}\:\mathrm{the}\:\mathrm{football},\mathrm{70\%}−\mathrm{in}\:\mathrm{voleyball},\mathrm{75\%}−\mathrm{in} \\ $$$$\mathrm{basketball}.\mathrm{What}\:\mathrm{is}\:\mathrm{least}\:\mathrm{number}\:\mathrm{of}\:\mathrm{children}\:\mathrm{who} \\ $$$$\mathrm{know}\:\mathrm{playing}\:\mathrm{all}\:\mathrm{above}\:\mathrm{three}\:\mathrm{sport}\:\mathrm{games}? \\ $$$$\left(\mathrm{Answer}\:\mathrm{10\%}\right) \\ $$

Question Number 104708 Answers: 1 Comments: 0

A bag contains 12 white balls and 8 black balls, another contains 10 white balls and 15 black balls. If two balls are drawn wthout replacement from each bag, find the probability that: i. all the four balls are black ii. exactly one of the four balls is white

$$ \\ $$$$\:\mathrm{A}\:\mathrm{bag}\:\mathrm{contains}\:\mathrm{12}\:\mathrm{white}\:\mathrm{balls}\: \\ $$$$\mathrm{and}\:\mathrm{8}\:\mathrm{black}\:\mathrm{balls},\:\mathrm{another}\: \\ $$$$\mathrm{contains}\:\mathrm{10}\:\mathrm{white}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{15} \\ $$$$\mathrm{black}\:\mathrm{balls}.\:\mathrm{If}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{drawn} \\ $$$$\mathrm{wthout}\:\mathrm{replacement}\:\mathrm{from}\:\mathrm{each} \\ $$$$\mathrm{bag},\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}:\: \\ $$$$ \\ $$$$\mathrm{i}.\:\mathrm{all}\:\mathrm{the}\:\mathrm{four}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{black}\: \\ $$$$ \\ $$$$\mathrm{ii}.\:\mathrm{exactly}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{four}\:\mathrm{balls}\:\mathrm{is} \\ $$$$\mathrm{white} \\ $$

Question Number 104707 Answers: 0 Comments: 0