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Question Number 82057 Answers: 2 Comments: 1

Question Number 82056 Answers: 0 Comments: 0

g(M)=2MB^→ .MC^→ +MC^→ .MA^→ +MA^→ .MB^→ g(G)=4MA^2 +3MA^→ (AB^→ +AC^→ ) 1) show that ∀ M ∈ plan g(M)=g(G)+4MG^2 2) Determine the set of point M of plan such as g(M)=g(A) 2) Construct this set of point M in the case where g(G)=5.

$${g}\left({M}\right)=\mathrm{2}{M}\overset{\rightarrow} {{B}}.{M}\overset{\rightarrow} {{C}}+{M}\overset{\rightarrow} {{C}}.{M}\overset{\rightarrow} {{A}}+{M}\overset{\rightarrow} {{A}}.{M}\overset{\rightarrow} {{B}} \\ $$$${g}\left({G}\right)=\mathrm{4}{MA}^{\mathrm{2}} +\mathrm{3}{M}\overset{\rightarrow} {{A}}\left({A}\overset{\rightarrow} {{B}}+{A}\overset{\rightarrow} {{C}}\right) \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{show}\:{that}\:\forall\:{M}\:\in\:{plan} \\ $$$${g}\left({M}\right)={g}\left({G}\right)+\mathrm{4}{MG}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{Determine}\:{the}\:{set}\:{of}\:{point}\:{M}\:{of}\:{plan} \\ $$$${such}\:{as}\:{g}\left({M}\right)={g}\left({A}\right) \\ $$$$\left.\mathrm{2}\right)\:{Construct}\:{this}\:{set}\:{of}\:{point}\:{M} \\ $$$${in}\:{the}\:{case}\:{where}\:{g}\left({G}\right)=\mathrm{5}. \\ $$

Question Number 82042 Answers: 0 Comments: 4

Question Number 82041 Answers: 1 Comments: 4

show that π^(ie) +(1/2)=0

$${show}\:{that} \\ $$$$\pi^{{ie}} +\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$

Question Number 82034 Answers: 0 Comments: 1

Prove by maths induction tbat n^5 − n^3 is divisible by 24.

$$\boldsymbol{{P}}{rove}\:\:{by}\:\:{maths}\:\:{induction}\:\:{tbat} \\ $$$$\boldsymbol{{n}}^{\mathrm{5}} \:−\:\boldsymbol{{n}}^{\mathrm{3}} \:\:\boldsymbol{{is}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{24}. \\ $$

Question Number 82026 Answers: 1 Comments: 0

(√x)+y = 7 x+(√(y )) =11 find x and y

$$\sqrt{{x}}+{y}\:=\:\mathrm{7} \\ $$$${x}+\sqrt{{y}\:}\:=\mathrm{11}\: \\ $$$${find}\:{x}\:{and}\:{y} \\ $$$$ \\ $$

Question Number 82022 Answers: 0 Comments: 0

Question Number 82020 Answers: 0 Comments: 2

Question Number 82019 Answers: 1 Comments: 0

Question Number 82018 Answers: 2 Comments: 2

Differentiate y = 2^x from the first principle.

$$\mathrm{Differentiate}\:\:\:\:\:\mathrm{y}\:\:=\:\:\mathrm{2}^{\mathrm{x}} \:\:\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle}. \\ $$

Question Number 81996 Answers: 0 Comments: 0

calculate I_n =∫∫_([(1/n),n[) e^(−x^2 −3y^2 ) dxdy and find lim_(n→+∞) I_n conclude that ∫_0 ^∞ e^(−x^2 ) dx=((√π)/2)

$${calculate}\:{I}_{{n}} =\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.} \:\:{e}^{−{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} } {dxdy} \\ $$$${and}\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:{I}_{{n}} \\ $$$${conclude}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{2}} } {dx}=\frac{\sqrt{\pi}}{\mathrm{2}} \\ $$

Question Number 81994 Answers: 0 Comments: 0

calculate ∫∫_W (x+y)e^(x−y) dxdy with W is the triangle limited by o,A(1,0)and B(0,1)

$${calculate}\:\int\int_{{W}} \left({x}+{y}\right){e}^{{x}−{y}} {dxdy} \\ $$$${with}\:{W}\:{is}\:{the}\:{triangle}\:{limited}\:{by} \\ $$$${o},{A}\left(\mathrm{1},\mathrm{0}\right){and}\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$

Question Number 81993 Answers: 0 Comments: 0

calculate ∫∫_D ln(1+x+y)dxdy with D is the triangle limited by points 0,A(1,0) and B(0,1)

$${calculate}\:\int\int_{{D}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy} \\ $$$${with}\:{D}\:{is}\:{the}\:{triangle}\:{limited}\:{by} \\ $$$${points}\:\mathrm{0},{A}\left(\mathrm{1},\mathrm{0}\right)\:{and}\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$

Question Number 81983 Answers: 0 Comments: 4

Question Number 81980 Answers: 1 Comments: 2

Question Number 82031 Answers: 1 Comments: 0

find x,y { ((5(√(2x^2 −y^4 )) =4x−3y)),((4(√(2x^2 −y^4 )) =3x−2y)) :}

$${find}\:{x},{y} \\ $$$$\begin{cases}{\mathrm{5}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{4}{x}−\mathrm{3}{y}}\\{\mathrm{4}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{3}{x}−\mathrm{2}{y}}\end{cases} \\ $$

Question Number 82030 Answers: 1 Comments: 0

a − b + c − d = 2 a^2 − b^2 + c^2 − d^2 = 6 a^3 − b^3 + c^3 − d^3 = 20 a^4 − b^4 + c^4 − d^4 = 66 a + b + c + d = ?

$${a}\:−\:{b}\:+\:{c}\:−\:{d}\:\:=\:\:\mathrm{2} \\ $$$${a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:−\:{d}^{\mathrm{2}} \:\:=\:\:\mathrm{6} \\ $$$${a}^{\mathrm{3}} \:−\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:−\:{d}^{\mathrm{3}} \:\:=\:\:\mathrm{20} \\ $$$${a}^{\mathrm{4}} \:−\:{b}^{\mathrm{4}} \:+\:{c}^{\mathrm{4}} \:−\:{d}^{\mathrm{4}} \:\:=\:\:\mathrm{66} \\ $$$${a}\:+\:{b}\:+\:{c}\:+\:{d}\:\:=\:\:? \\ $$

Question Number 81975 Answers: 2 Comments: 5

Question Number 81972 Answers: 1 Comments: 1

Question Number 81971 Answers: 1 Comments: 0

Question Number 81970 Answers: 0 Comments: 1

find the limit as n −>∞ lim(2−^n (√x))^n

$${find}\:{the}\:{limit}\:{as}\:{n}\:−>\infty \\ $$$$ \\ $$$${lim}\left(\mathrm{2}−\:^{{n}} \sqrt{{x}}\right)^{{n}} \\ $$$$ \\ $$

Question Number 81968 Answers: 1 Comments: 1

Question Number 81966 Answers: 1 Comments: 0

(((1 + i(√3))/2) )^(2020) + (((1 − i(√3))/2) )^(2020) = A A^4 = ?

$$\left(\frac{\mathrm{1}\:+\:{i}\sqrt{\mathrm{3}}}{\mathrm{2}}\:\right)^{\mathrm{2020}} \:+\:\:\left(\frac{\mathrm{1}\:−\:{i}\sqrt{\mathrm{3}}}{\mathrm{2}}\:\right)^{\mathrm{2020}} \:\:=\:\:\:{A} \\ $$$${A}^{\mathrm{4}} \:\:=\:\:? \\ $$

Question Number 81963 Answers: 1 Comments: 2

if tan (x)+sec (x) = (7/8) find cot (x)+cosec (x) =

$${if}\:\mathrm{tan}\:\left({x}\right)+\mathrm{sec}\:\left({x}\right)\:=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$$${find}\:\mathrm{cot}\:\left({x}\right)+\mathrm{cosec}\:\left({x}\right)\:=\: \\ $$

Question Number 82130 Answers: 0 Comments: 5

In an arrangement of the word VIOLENT, find the chances that the vowels I, O, E occupy the odd positions.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{arrangement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\:\mathrm{VIOLENT},\:\mathrm{find}\:\mathrm{the}\:\mathrm{chances} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{vowels}\:\:\:\mathrm{I},\:\mathrm{O},\:\mathrm{E}\:\:\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{positions}. \\ $$

Question Number 81954 Answers: 0 Comments: 6

soit α∈]0;π[. determiner: 1)le module et l′argument de: a)1−e^(iα) ,b)1+e^(i𝛂) 2)deduire le module et l′argument de a) ((1−e^(iα) )/(1+e^(iα) )), b)(1−e^(iα) )(1+e^(iα) ) rochinel930@gmail.c

$$\left.\:{soit}\:\alpha\in\right]\mathrm{0};\pi\left[.\:{determiner}:\right. \\ $$$$\left.\mathrm{1}\right){le}\:{module}\:{et}\:{l}'{argument}\:{de}: \\ $$$$\left.\boldsymbol{{a}}\left.\right)\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{i}}\alpha} ,\boldsymbol{{b}}\right)\mathrm{1}+\boldsymbol{{e}}^{\boldsymbol{{i}\alpha}} \\ $$$$\left.\mathrm{2}\right)\boldsymbol{{deduire}}\:\boldsymbol{{le}}\:\boldsymbol{{module}}\:\boldsymbol{{et}}\:\boldsymbol{{l}}'\boldsymbol{{argument}}\:\boldsymbol{{de}} \\ $$$$\left.\:\left.\boldsymbol{{a}}\right)\:\frac{\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{i}}\alpha} }{\mathrm{1}+{e}^{{i}\alpha} },\:{b}\right)\left(\mathrm{1}−{e}^{{i}\alpha} \right)\left(\mathrm{1}+{e}^{{i}\alpha} \right) \\ $$$$\:\boldsymbol{{rochinel}}\mathrm{930}@{gmail}.\boldsymbol{{c}} \\ $$

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