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AllQuestion and Answers: Page 183

Question Number 196265    Answers: 2   Comments: 0

Question Number 196261    Answers: 1   Comments: 0

Question Number 196258    Answers: 0   Comments: 4

If(x_m +iy_m )^(2n+1) =1 , such that m∈{1,2,3,....,2n} ∧ x_m ,y_m ∈R p=Σ_(k=1) ^(2020) [((1−x_k +iy_k )/(1+x_k +iy_k ))] , Find ((p/(43)))

$${If}\left({x}_{{m}} +{iy}_{{m}} \right)^{\mathrm{2}{n}+\mathrm{1}} =\mathrm{1}\:,\:{such}\:{that} \\ $$$${m}\in\left\{\mathrm{1},\mathrm{2},\mathrm{3},....,\mathrm{2}{n}\right\}\:\wedge\:{x}_{{m}} ,{y}_{{m}} \in\mathbb{R} \\ $$$${p}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2020}} {\sum}}\left[\frac{\mathrm{1}−{x}_{{k}} +{iy}_{{k}} }{\mathrm{1}+{x}_{{k}} +{iy}_{{k}} }\right]\:,\:{Find}\:\left(\frac{{p}}{\mathrm{43}}\right) \\ $$

Question Number 196257    Answers: 1   Comments: 0

Question Number 197581    Answers: 1   Comments: 0

find Σ_(n=1) ^k (√n) ?

$${find}\:\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\sqrt{{n}}\:? \\ $$

Question Number 197583    Answers: 1   Comments: 0

{ ((((sin x)/(cos (x+y))) = −((√2)/2))),((((cos y)/(cos (x+y))) = ((√2)/2))) :} find the solution

$$\:\:\begin{cases}{\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\left(\mathrm{x}+\mathrm{y}\right)}\:=\:−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}\\{\frac{\mathrm{cos}\:\mathrm{y}}{\mathrm{cos}\:\left(\mathrm{x}+\mathrm{y}\right)}\:=\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}\end{cases} \\ $$$$\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$

Question Number 197582    Answers: 1   Comments: 0

Question Number 196251    Answers: 2   Comments: 0

Question Number 196249    Answers: 0   Comments: 0

log_a x=30 log_b x=70 log_(ab) x=?

$${log}_{{a}} {x}=\mathrm{30} \\ $$$${log}_{{b}} {x}=\mathrm{70} \\ $$$${log}_{{ab}} {x}=? \\ $$

Question Number 196246    Answers: 1   Comments: 1

Question Number 196242    Answers: 2   Comments: 0

Simplify (((1+cos2θ +isin2θ)/(1+cos2θ −isin2θ)))^(30)

$$\mathrm{Simplify}\:\left(\frac{\mathrm{1}+\mathrm{cos2}\theta\:+\mathrm{isin2}\theta}{\mathrm{1}+\mathrm{cos2}\theta\:−\mathrm{isin2}\theta}\right)^{\mathrm{30}} \\ $$

Question Number 196225    Answers: 2   Comments: 1

Question Number 196221    Answers: 1   Comments: 3

there is a cylinder on the horizontal plane and there is a little ball with mass m at the center of a circle on the vertical plane and there is a little hole in the wall of the cylinder on the lift of the ball which just enough for the ball to pass through the gravitational acceleration is g the collision between the ball and the cylinder wall can be regarded as an elastic coollision find all of the quondam speed

$${there}\:{is}\:{a}\:{cylinder}\:{on}\:{the}\:{horizontal}\:{plane} \\ $$$${and}\:{there}\:{is}\:{a}\:{little}\:{ball}\:{with}\:{mass}\:{m} \\ $$$${at}\:{the}\:{center}\:{of}\:{a}\:{circle}\:{on}\:{the}\:{vertical}\:{plane} \\ $$$${and}\:{there}\:{is}\:{a}\:{little}\:{hole}\:{in}\:{the}\:{wall}\:{of} \\ $$$${the}\:{cylinder}\:{on}\:{the}\:{lift}\:{of}\:{the}\:{ball}\:{which} \\ $$$${just}\:{enough}\:{for}\:{the}\:{ball}\:{to}\:{pass}\:{through} \\ $$$${the}\:{gravitational}\:{acceleration}\:{is}\:{g} \\ $$$${the}\:{collision}\:{between}\:{the}\:{ball}\:{and} \\ $$$${the}\:{cylinder}\:{wall}\:{can}\:{be}\:{regarded}\:{as} \\ $$$${an}\:{elastic}\:{coollision} \\ $$$${find}\:{all}\:{of}\:{the}\:{quondam}\:{speed} \\ $$

Question Number 196216    Answers: 0   Comments: 0

Question Number 196211    Answers: 1   Comments: 0

Show that cos((π/3)+i)=(1/4)(e+(1/e)) −((√3)/4)(e−(1/e))i

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{cos}\left(\frac{\pi}{\mathrm{3}}+\mathrm{i}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{e}+\frac{\mathrm{1}}{\mathrm{e}}\right)\:−\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\left(\mathrm{e}−\frac{\mathrm{1}}{\mathrm{e}}\right)\mathrm{i} \\ $$

Question Number 196209    Answers: 2   Comments: 0

Ω= ∫_0 ^( 1) (( (x−1)^( 2) )/(ln^2 (x))) dx= ? −−−−

$$ \\ $$$$\:\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left({x}−\mathrm{1}\right)^{\:\mathrm{2}} }{\mathrm{ln}^{\mathrm{2}} \left({x}\right)}\:{dx}=\:? \\ $$$$\:\:\:\:\:−−−− \\ $$

Question Number 196205    Answers: 1   Comments: 0

What′s the value for !7 ?

$$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:!\mathrm{7}\:? \\ $$

Question Number 196199    Answers: 1   Comments: 0

Solve: y′′′=((3y′(y′′)^2 )/(1+(y′)^2 ))

$$\mathrm{Solve}: \\ $$$${y}'''=\frac{\mathrm{3}{y}'\left({y}''\right)^{\mathrm{2}} }{\mathrm{1}+\left({y}'\right)^{\mathrm{2}} } \\ $$

Question Number 196198    Answers: 1   Comments: 0

a+b+c+d=4 prove that: (a/(a^3 +8))+(b/(b^3 +8))+(c/(c^3 +8))+(d/(d^3 +8))≤(4/9)

$${a}+{b}+{c}+{d}=\mathrm{4} \\ $$$${prove}\:{that}: \\ $$$$\frac{{a}}{{a}^{\mathrm{3}} +\mathrm{8}}+\frac{{b}}{{b}^{\mathrm{3}} +\mathrm{8}}+\frac{{c}}{{c}^{\mathrm{3}} +\mathrm{8}}+\frac{{d}}{{d}^{\mathrm{3}} +\mathrm{8}}\leq\frac{\mathrm{4}}{\mathrm{9}} \\ $$

Question Number 196185    Answers: 1   Comments: 0

$$\:\:\:\underbrace{\:} \\ $$

Question Number 196183    Answers: 2   Comments: 0

Question Number 196181    Answers: 0   Comments: 0

Question Number 196173    Answers: 1   Comments: 0

Calcul I_a =∫_a ^(1/a) ((lnx)/(1+x^2 ))dx (a>0)

$$\boldsymbol{{Calcul}}\:\boldsymbol{{I}}_{\boldsymbol{{a}}} =\int_{\boldsymbol{{a}}} ^{\frac{\mathrm{1}}{\boldsymbol{{a}}}} \frac{\boldsymbol{{lnx}}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}\:\left(\boldsymbol{{a}}>\mathrm{0}\right)\: \\ $$

Question Number 196172    Answers: 1   Comments: 2

Question Number 196166    Answers: 1   Comments: 1

for any a,b∈[−1,1] calculate: arccos(a)+arcsin(b)=? arcsin(a)+arcsin(b)=? arccos(a)+arccos(b)=?

$$\boldsymbol{{for}}\:\boldsymbol{{any}}\:\boldsymbol{{a}},\boldsymbol{{b}}\in\left[−\mathrm{1},\mathrm{1}\right]\:\:\boldsymbol{{calculate}}:\: \\ $$$$\boldsymbol{{arccos}}\left(\boldsymbol{{a}}\right)+\boldsymbol{{arcsin}}\left(\boldsymbol{{b}}\right)=? \\ $$$$\boldsymbol{{arcsin}}\left(\boldsymbol{{a}}\right)+\boldsymbol{{arcsin}}\left(\boldsymbol{{b}}\right)=? \\ $$$$\boldsymbol{{arccos}}\left(\boldsymbol{{a}}\right)+\boldsymbol{{arc}}{cos}\left(\boldsymbol{{b}}\right)=? \\ $$

Question Number 196164    Answers: 2   Comments: 0

calcul: lim_(n→+∞ ) Un=((((2n)!)/(n!n^n )))^(1/n)

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{calcul}: \\ $$$$ \\ $$$$\:\:\:{lim}_{{n}\rightarrow+\infty\:\:\:\:} {Un}=\sqrt[{{n}}]{\frac{\left(\mathrm{2}{n}\right)!}{{n}!{n}^{{n}} }} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

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