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Question Number 82082    Answers: 0   Comments: 4

Evaluate: (((√(30 + (√8) + (√5)))/((√8) + (√5))))^(1/4)

$$\mathrm{Evaluate}:\:\:\:\:\:\:\left(\frac{\sqrt{\mathrm{30}\:+\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}}{\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}\right)^{\mathrm{1}/\mathrm{4}} \\ $$

Question Number 82073    Answers: 1   Comments: 3

Show that: j_(3/2) (x) = ((√2)/(πx)) (((sin x)/x) − cos x)

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\mathrm{j}_{\mathrm{3}/\mathrm{2}} \left(\mathrm{x}\right)\:\:=\:\:\frac{\sqrt{\mathrm{2}}}{\pi\mathrm{x}}\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:−\:\mathrm{cos}\:\mathrm{x}\right) \\ $$

Question Number 82071    Answers: 2   Comments: 0

x≠ y ≠z ≠ 0 xy + xz + yz = 0 prove that ((x+y)/z)+((x+z)/y)+((y+z)/x) = −3

$${x}\neq\:{y}\:\neq{z}\:\neq\:\mathrm{0} \\ $$$${xy}\:+\:{xz}\:+\:{yz}\:=\:\mathrm{0} \\ $$$${prove}\:{that}\:\frac{{x}+{y}}{{z}}+\frac{{x}+{z}}{{y}}+\frac{{y}+{z}}{{x}}\:=\:−\mathrm{3} \\ $$$$ \\ $$

Question Number 82067    Answers: 1   Comments: 5

{ ((∣x∣ −((y+3 ))^(1/(3 )) = 1)),(((−x(√(−x)))^2 = y +10)) :} find solution

$$\begin{cases}{\mid{x}\mid\:−\sqrt[{\mathrm{3}\:}]{{y}+\mathrm{3}\:}\:=\:\mathrm{1}}\\{\left(−{x}\sqrt{−{x}}\right)^{\mathrm{2}} \:=\:{y}\:+\mathrm{10}}\end{cases} \\ $$$${find}\:{solution} \\ $$

Question Number 82066    Answers: 0   Comments: 1

log_(3+2x−x^2 ) (((sin x+(√3)cos x)/(sin 3x))) = (1/(log_2 (3+2x−x^2 )))

$$\mathrm{log}_{\mathrm{3}+\mathrm{2}{x}−{x}^{\mathrm{2}} } \:\left(\frac{\mathrm{sin}\:{x}+\sqrt{\mathrm{3}}\mathrm{cos}\:{x}}{\mathrm{sin}\:\mathrm{3}{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \left(\mathrm{3}+\mathrm{2}{x}−{x}^{\mathrm{2}} \right)}\: \\ $$

Question Number 82078    Answers: 1   Comments: 1

f(10^x ) = (√x) what is f^(−1) (x)=?

$${f}\left(\mathrm{10}^{{x}} \right)\:=\:\sqrt{{x}}\: \\ $$$${what}\:{is}\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 82059    Answers: 2   Comments: 0

what is derivative of h = (√(ln(x))) by first principle method

$${what}\:{is}\:{derivative}\:{of}\:\:{h}\:=\:\sqrt{{ln}\left({x}\right)} \\ $$$${by}\:{first}\:{principle}\:{method}\: \\ $$

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

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