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AllQuestion and Answers: Page 211

Question Number 195900 Answers: 1 Comments: 0

Question Number 195898 Answers: 1 Comments: 0

Question Number 195896 Answers: 2 Comments: 0

Question Number 195895 Answers: 1 Comments: 0

Calcul ∫^( (π/2)) _( 0) t(√(tan(t))) dt

$$\mathrm{Calcul}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{t}\sqrt{\mathrm{tan}\left(\mathrm{t}\right)}\:\mathrm{dt} \\ $$

Question Number 195892 Answers: 1 Comments: 0

Question Number 195885 Answers: 2 Comments: 0

(dy/dx) + (√((1−y^2 )/(1−x^2 ))) = 0

$$\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\sqrt{\frac{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:=\:\mathrm{0}\: \\ $$

Question Number 195884 Answers: 0 Comments: 0

solve the integral by the method of Differentiation ∫_0 ^1 ((x^2 −1)/(log_2 (x)))dx

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{by}\:\mathrm{the}\:\mathrm{method}\: \\ $$$$\mathrm{of}\:\mathrm{Differentiation} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)}\mathrm{dx} \\ $$

Question Number 195883 Answers: 0 Comments: 0

The speed of a boat is given by, V=k((l/t)−at), where k is the constant and l is the distance travel by boat in time t and a is the acceleration of water. If there is a change in l from 2cm to 1cm in time 2sec. to 1sec. If the acceleration of water changes from 0.95m/s^2 to 2m/s^2 . Find the motion of boat.

$$\mathrm{The}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{a}\:\mathrm{boat}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by},\:\mathrm{V}=\mathrm{k}\left(\frac{\mathrm{l}}{\mathrm{t}}−\mathrm{at}\right), \\ $$$$\mathrm{where}\:\mathrm{k}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{and}\:\mathrm{l}\:\mathrm{is}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{travel}\:\mathrm{by}\:\mathrm{boat}\:\mathrm{in}\:\mathrm{time}\:\mathrm{t}\:\mathrm{and}\:\mathrm{a}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{water}.\: \\ $$$$\mathrm{If}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{change}\:\mathrm{in}\:\mathrm{l}\:\mathrm{from}\:\mathrm{2cm}\:\mathrm{to}\:\mathrm{1cm}\:\mathrm{in}\:\mathrm{time}\:\mathrm{2sec}.\:\mathrm{to}\:\mathrm{1sec}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{water}\:\mathrm{changes}\:\mathrm{from}\:\mathrm{0}.\mathrm{95m}/\mathrm{s}^{\mathrm{2}} \:\mathrm{to}\:\mathrm{2m}/\mathrm{s}^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{motion}\:\mathrm{of}\:\mathrm{boat}. \\ $$

Question Number 195880 Answers: 1 Comments: 1

Question Number 195878 Answers: 0 Comments: 0

Question Number 195874 Answers: 1 Comments: 0

Question Number 195872 Answers: 1 Comments: 0

z_1 , z_2 , z_3 ∈C.∣z_1 ∣=∣z_2 ∣=∣z_3 ∣=1. Prove that (((z_1 +z_2 )(z_2 +z_3 )(z_3 +z_1 ))/(z_1 z_2 z_3 ))∈R.

$${z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} \in\mathbb{C}.\mid{z}_{\mathrm{1}} \mid=\mid{z}_{\mathrm{2}} \mid=\mid{z}_{\mathrm{3}} \mid=\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)\left({z}_{\mathrm{2}} +{z}_{\mathrm{3}} \right)\left({z}_{\mathrm{3}} +{z}_{\mathrm{1}} \right)}{{z}_{\mathrm{1}} {z}_{\mathrm{2}} {z}_{\mathrm{3}} }\in\mathbb{R}. \\ $$

Question Number 195870 Answers: 1 Comments: 4

Question Number 195860 Answers: 0 Comments: 0

Question Number 195855 Answers: 1 Comments: 0

{ ((3(√(((12))^(1/3) −(3)^(1/3) ))=(x)^(1/3) +(y)^(1/3) −(z)^(1/3) )),((x,y,z ∈ N)) :} ⇒ x,y,z =? please help me

$$\begin{cases}{\mathrm{3}\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{12}}−\sqrt[{\mathrm{3}}]{\mathrm{3}}}=\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{y}}−\sqrt[{\mathrm{3}}]{{z}}}\\{{x},{y},{z}\:\in\:{N}}\end{cases}\:\:\Rightarrow\:{x},{y},{z}\:=? \\ $$$${please}\:{help}\:{me} \\ $$

Question Number 195854 Answers: 3 Comments: 2

Question Number 195848 Answers: 2 Comments: 0

Please how did ∣z−a∣=r became z= a + re^(iθ) ?

$$\mathrm{Please}\:\mathrm{how}\:\mathrm{did}\:\mid\mathrm{z}−\mathrm{a}\mid=\mathrm{r}\:\mathrm{became}\: \\ $$$$\mathrm{z}=\:\mathrm{a}\:+\:\mathrm{re}^{\mathrm{i}\theta} ? \\ $$

Question Number 195846 Answers: 1 Comments: 0

{ (( Ω_1 = ∫_0 ^( (π/2)) (( x^( 2) )/(sin^( 2) (x))) dx )),(( ⇒ (Ω_1 /Ω_( 2) ) = ? )),(( Ω_( 2) = ∫_0 ^( (π/2)) (x/(tan(x))) dx)) :}

$$ \\ $$$$\:\:\:\:\:\:\begin{cases}{\:\:\:\Omega_{\mathrm{1}} \:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{x}^{\:\mathrm{2}} }{{sin}^{\:\mathrm{2}} \left({x}\right)}\:{dx}\:}\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\frac{\Omega_{\mathrm{1}} }{\Omega_{\:\mathrm{2}} }\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\\{\:\:\Omega_{\:\mathrm{2}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tan}\left({x}\right)}\:{dx}}\end{cases} \\ $$$$ \\ $$

Question Number 195840 Answers: 0 Comments: 4

find the valur lim_(→0) ((x−sinx)/x^3 )

$${find}\:{the}\:{valur} \\ $$$$\:\:{li}\underset{\rightarrow\mathrm{0}} {{m}}\:\frac{{x}−{sinx}}{{x}^{\mathrm{3}} } \\ $$

Question Number 195838 Answers: 1 Comments: 0

Question Number 195833 Answers: 1 Comments: 1

how does the d get max

$${how}\:{does}\:\:{the}\:{d}\:{get}\:{max} \\ $$

Question Number 195823 Answers: 1 Comments: 0

Question Number 195820 Answers: 1 Comments: 0

a,b,c>0 &abc=1,prove that (1/(1+a+b))+(1/(1+b+c))+(1/(1+c+a))≤1

$${a},{b},{c}>\mathrm{0}\:\&{abc}=\mathrm{1},{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{a}+{b}}+\frac{\mathrm{1}}{\mathrm{1}+{b}+{c}}+\frac{\mathrm{1}}{\mathrm{1}+{c}+{a}}\leqslant\mathrm{1} \\ $$

Question Number 195815 Answers: 0 Comments: 0

Question Number 195814 Answers: 1 Comments: 0

Question Number 195813 Answers: 0 Comments: 0

{ ((3(√(((12))^(1/3) −(3)^(1/3) )) = (x)^(1/3) + (y)^(1/3) −(z)^(1/3) )),((x,y,z ∈ N)) :} ⇒ x,y,z =? mr.W please help me and other my friends please help me

$$\begin{cases}{\mathrm{3}\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{12}}−\sqrt[{\mathrm{3}}]{\mathrm{3}}}\:\:=\:\sqrt[{\mathrm{3}}]{{x}}\:+\:\sqrt[{\mathrm{3}}]{{y}}\:−\sqrt[{\mathrm{3}}]{{z}}}\\{{x},{y},{z}\:\in\:{N}}\end{cases}\:\Rightarrow\:{x},{y},{z}\:=? \\ $$$${mr}.{W}\:{please}\:{help}\:{me} \\ $$$${and}\:{other}\:{my}\:{friends}\:{please}\:{help}\:{me} \\ $$

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