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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

Question Number 104706 Answers: 1 Comments: 2

find the value of p (pls help) 1^3 +3^3 +5^3 +...+p^3 =8128

$${find}\:{the}\:{value}\:{of}\:\:{p}\:\left({pls}\:{help}\right) \\ $$$$\mathrm{1}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\mathrm{5}^{\mathrm{3}} +...+{p}^{\mathrm{3}} =\mathrm{8128} \\ $$$$ \\ $$

Question Number 104703 Answers: 1 Comments: 1

Question Number 104701 Answers: 1 Comments: 1

Question Number 104696 Answers: 1 Comments: 0

Question Number 104694 Answers: 0 Comments: 0

Question Number 104692 Answers: 2 Comments: 0

Question Number 105301 Answers: 3 Comments: 0

Without using tables or calculator, compare 6^7 and 7^6

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{tables}\:\mathrm{or}\:\mathrm{calculator}, \\ $$$$\:{compare}\:\:\:\mathrm{6}^{\mathrm{7}} \:\mathrm{and}\:\:\:\mathrm{7}^{\mathrm{6}} \\ $$

Question Number 104676 Answers: 3 Comments: 4

Question Number 104669 Answers: 3 Comments: 0

(x^2 +y^2 ) dy = xy dx

$$\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\:{dy}\:=\:{xy}\:{dx}\: \\ $$

Question Number 104667 Answers: 1 Comments: 0

lim_(x→0) [(3^(πx) /(tan x)) − ((cos^2 x)/(sin x))] ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{3}^{\pi{x}} }{\mathrm{tan}\:{x}}\:−\:\frac{\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{sin}\:{x}}\right]\:? \\ $$

Question Number 104664 Answers: 0 Comments: 0

(1−lna)(1−lnb).......(1−lnx)(1−lny)(1−lnz)=0 ????

$$\:\:\left(\mathrm{1}−{lna}\right)\left(\mathrm{1}−{lnb}\right).......\left(\mathrm{1}−{lnx}\right)\left(\mathrm{1}−{lny}\right)\left(\mathrm{1}−{lnz}\right)=\mathrm{0}\:\:???? \\ $$

Question Number 104659 Answers: 1 Comments: 0

what is remainder of 12! in mod 17

$${what}\:{is}\:{remainder}\:{of}\:\mathrm{12}!\:{in}\:{mod}\:\mathrm{17} \\ $$

Question Number 104657 Answers: 1 Comments: 0

(x+yi)^3 = ((10(2y+8i)^2 )/(3−i)) find x & y

$$\left({x}+{yi}\right)^{\mathrm{3}} \:=\:\frac{\mathrm{10}\left(\mathrm{2}{y}+\mathrm{8}{i}\right)^{\mathrm{2}} }{\mathrm{3}−{i}} \\ $$$${find}\:{x}\:\&\:{y} \\ $$

Question Number 104655 Answers: 4 Comments: 0

lim_(x→a) (((√(2x+a))−(√(3x)))/((√(x+3a))−2(√x))) =? [a≠0]

$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\sqrt{\mathrm{2}{x}+{a}}−\sqrt{\mathrm{3}{x}}}{\sqrt{{x}+\mathrm{3}{a}}−\mathrm{2}\sqrt{{x}}}\:=?\:\:\:\:\left[{a}\neq\mathrm{0}\right]\: \\ $$

Question Number 104651 Answers: 1 Comments: 0

Consider the differential equation; x′′(t)+x(t)=t^2 cos(2t). Knowing that the Complementary Function is; y_(CF) =acos(t)+bsin(t), In what form can the particular integral be expressed so as to obtain the general solution to the given differential equation?

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}^{\mathrm{2}} \mathrm{cos}\left(\mathrm{2t}\right). \\ $$$$\mathrm{Knowing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Complementary}\:\mathrm{Function}\:\mathrm{is}; \\ $$$$\mathrm{y}_{\mathrm{CF}} =\mathrm{acos}\left(\mathrm{t}\right)+\mathrm{bsin}\left(\mathrm{t}\right), \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{form}\:\mathrm{can}\:\mathrm{the}\:\mathrm{particular}\:\mathrm{integral}\:\mathrm{be}\:\mathrm{expressed} \\ $$$$\mathrm{so}\:\mathrm{as}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{given}\: \\ $$$$\mathrm{differential}\:\mathrm{equation}? \\ $$

Question Number 104645 Answers: 1 Comments: 1

Question Number 104644 Answers: 1 Comments: 0

∫_0 ^1 ((log(1−x+x^2 −x^3 +x^4 )dx)/x) = −(π^2 /(15))

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}} \right){dx}}{{x}}\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{15}} \\ $$

Question Number 104640 Answers: 1 Comments: 0

1. What is the brief word of LCM ? 2. If x=3 and y=6 then what is the answer of ((x^2 +2xy+y^2 )/(3x+5y×9xy)) ? 3. If a∗b= ((a×b)/(a÷b)) then what is the answer of 2∗3+7∗5−9∗6 ? 4. What is the brief word of GCD ? What is the GCD of 12,56,80 ? 5. Solve that [(1,6,7),(2,8,9),(3,(−3),(−6)) ]+ [(6,7,(12)),((−6),9,(45)),((−8),6,(−3)) ].

$$\mathrm{1}.\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{brief}\:\mathrm{word}\:\mathrm{of}\:\mathrm{LCM}\:? \\ $$$$\mathrm{2}.\:\:\mathrm{If}\:\mathrm{x}=\mathrm{3}\:\mathrm{and}\:\mathrm{y}=\mathrm{6}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\mathrm{answer}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{3x}+\mathrm{5y}×\mathrm{9xy}}\:? \\ $$$$\mathrm{3}.\:\:\mathrm{If}\:\mathrm{a}\ast\mathrm{b}=\:\frac{\mathrm{a}×\mathrm{b}}{\mathrm{a}\boldsymbol{\div}\mathrm{b}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\mathrm{answer}\:\mathrm{of}\:\mathrm{2}\ast\mathrm{3}+\mathrm{7}\ast\mathrm{5}−\mathrm{9}\ast\mathrm{6}\:? \\ $$$$\mathrm{4}.\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{brief}\:\mathrm{word}\:\mathrm{of}\:\mathrm{GCD}\:? \\ $$$$\:\:\:\:\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{GCD}\:\mathrm{of}\:\mathrm{12},\mathrm{56},\mathrm{80}\:? \\ $$$$\mathrm{5}.\:\:\mathrm{Solve}\:\mathrm{that} \\ $$$$\:\:\:\:\:\begin{bmatrix}{\mathrm{1}}&{\mathrm{6}}&{\mathrm{7}}\\{\mathrm{2}}&{\mathrm{8}}&{\mathrm{9}}\\{\mathrm{3}}&{−\mathrm{3}}&{−\mathrm{6}}\end{bmatrix}+\begin{bmatrix}{\mathrm{6}}&{\mathrm{7}}&{\mathrm{12}}\\{−\mathrm{6}}&{\mathrm{9}}&{\mathrm{45}}\\{−\mathrm{8}}&{\mathrm{6}}&{−\mathrm{3}}\end{bmatrix}. \\ $$

Question Number 104624 Answers: 0 Comments: 3

Question Number 104621 Answers: 1 Comments: 0

(1/((1−x)^2 ))−(4/((1+x)^2 ))=1

$$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }−\frac{\mathrm{4}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }=\mathrm{1} \\ $$

Question Number 104609 Answers: 1 Comments: 0

prove: ∫_0 ^1 ((x^4 (1−x)^4 )/(1+x^2 ))dx=((22)/7)−π

$${prove}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{4}} \left(\mathrm{1}−{x}\right)^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{22}}{\mathrm{7}}−\pi \\ $$

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