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Question Number 51250 Answers: 1 Comments: 0

Given that z_1 = R_1 + R + jωL ; z_2 = R_2 ; z_3 = (1/(jωC_3 )) and z_4 = R_4 + (1/(jωC_4 )) and also that z_1 z_3 = z_2 z_4 , express R and L in terms of the real constants R_1 , R_2 , R_4 , C_3 and C_4 Answer: R = ((R_2 C_3 − R_1 C_4 )/C_4 ) , L = R_2 R_4 C_3

Question Number 51248 Answers: 1 Comments: 0

If ((R_1 + jωL)/R_3 ) = (R_2 /(R_4 − j (1/(ωC)))) , where R_1 , R_2 , R_3 , R_4 , ω, L and C are real , show that L = ((C R_2 R_3 )/(ω^2 C^2 R_4 ^2 + 1))

$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{j}\omega\mathrm{L}}{\mathrm{R}_{\mathrm{3}} }\:\:=\:\:\frac{\mathrm{R}_{\mathrm{2}} }{\mathrm{R}_{\mathrm{4}} \:−\:\mathrm{j}\:\frac{\mathrm{1}}{\omega\mathrm{C}}}\:\:,\:\:\:\mathrm{where}\:\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} ,\:\mathrm{R}_{\mathrm{3}} ,\:\mathrm{R}_{\mathrm{4}} ,\:\omega,\:\mathrm{L}\:\mathrm{and}\:\mathrm{C} \\ $$$$\mathrm{are}\:\mathrm{real}\:,\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\mathrm{L}\:=\:\frac{\mathrm{C}\:\mathrm{R}_{\mathrm{2}} \mathrm{R}_{\mathrm{3}} }{\omega^{\mathrm{2}} \mathrm{C}^{\mathrm{2}} \mathrm{R}_{\mathrm{4}} ^{\mathrm{2}} \:+\:\mathrm{1}} \\ $$

Question Number 51245 Answers: 2 Comments: 0

Question Number 51228 Answers: 1 Comments: 1

Question Number 51227 Answers: 1 Comments: 4

How many odd numbers with different digits are there from 2019 to 9102?

$${How}\:{many}\:{odd}\:{numbers}\:{with}\:{different} \\ $$$${digits}\:{are}\:{there}\:{from}\:\mathrm{2019}\:{to}\:\mathrm{9102}? \\ $$

Question Number 51220 Answers: 1 Comments: 1

Question Number 51218 Answers: 0 Comments: 0

show each of the following functions a entire functions a. f(z)=e^(−y) sin x−i e^(−y) cos x b. f(z)=(z^2 −2)e^(−x) e^(−iy)

$$\mathrm{show}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{functions}\:\mathrm{a}\:\mathrm{entire}\:\mathrm{functions} \\ $$$$\mathrm{a}.\:{f}\left({z}\right)={e}^{−{y}} \mathrm{sin}\:{x}−{i}\:{e}^{−{y}} \mathrm{cos}\:{x} \\ $$$${b}.\:{f}\left({z}\right)=\left({z}^{\mathrm{2}} −\mathrm{2}\right){e}^{−{x}} {e}^{−{iy}} \\ $$

Question Number 51217 Answers: 0 Comments: 0

show that f(z)=z^2 continuous at z=z_0

$$\mathrm{show}\:\mathrm{that}\:{f}\left({z}\right)={z}^{\mathrm{2}} \:\mathrm{continuous}\:\mathrm{at}\:{z}={z}_{\mathrm{0}} \\ $$

Question Number 51216 Answers: 1 Comments: 0

show lim f(z) for z→0 along the line y=x where: f(z)=((2xy)/(x^2 +y^2 ))−i(y^2 /x^2 )

$$\mathrm{show}\:\mathrm{lim}\:{f}\left({z}\right)\:\mathrm{for}\:{z}\rightarrow\mathrm{0}\:\mathrm{along}\:\mathrm{the}\:\mathrm{line}\:{y}={x} \\ $$$$\mathrm{where}:\:{f}\left({z}\right)=\frac{\mathrm{2}{xy}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }−{i}\frac{{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} } \\ $$

Question Number 51215 Answers: 1 Comments: 0

∫_0 ^π e^((1+i)x) dx=...

$$\int_{\mathrm{0}} ^{\pi} {e}^{\left(\mathrm{1}+{i}\right){x}} {dx}=... \\ $$

Question Number 51199 Answers: 0 Comments: 0

Question Number 51236 Answers: 2 Comments: 0

Prove that line y=mx+(3/(4 ))m+(1/m) touches the parabola y^2 =4x+3 whatever the value of m

$${Prove}\:{that}\:{line}\:{y}={mx}+\frac{\mathrm{3}}{\mathrm{4}\:\:}{m}+\frac{\mathrm{1}}{{m}} \\ $$$${touches}\:{the}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}+\mathrm{3}\:{whatever}\:{the} \\ $$$${value}\:{of}\:{m} \\ $$

Question Number 51235 Answers: 2 Comments: 0

Without using tables, find tha value of ((((√5) +2)^6 −((√5)−2)^6 )/(8(√5) ))

$${Without}\:{using}\:{tables}, \\ $$$${find}\:{tha}\:{value}\:{of} \\ $$$$\frac{\left(\sqrt{\mathrm{5}}\:+\mathrm{2}\right)^{\mathrm{6}} −\left(\sqrt{\mathrm{5}}−\mathrm{2}\right)^{\mathrm{6}} }{\mathrm{8}\sqrt{\mathrm{5}}\:}\:\: \\ $$

Question Number 51190 Answers: 0 Comments: 0

find lim_(ξ→0^+ ) ^ ∫_0 ^ξ (x/(sinx −(√(sin^2 x +ξ^2 ))))dx

$${find}\:{lim}_{\xi\rightarrow\mathrm{0}^{+} } ^{} \:\:\:\:\:\int_{\mathrm{0}} ^{\xi} \:\:\:\:\:\:\frac{{x}}{{sinx}\:−\sqrt{{sin}^{\mathrm{2}} {x}\:+\xi^{\mathrm{2}} }}{dx} \\ $$

Question Number 51188 Answers: 0 Comments: 0

find ∫ ((cos^2 x)/(cosx +2sinx))dx

$${find}\:\:\int\:\:\:\:\:\frac{{cos}^{\mathrm{2}} {x}}{{cosx}\:+\mathrm{2}{sinx}}{dx} \\ $$

Question Number 51186 Answers: 1 Comments: 1

calculate ∫_0 ^1 (([nx])/(2x+1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\left[{nx}\right]}{\mathrm{2}{x}+\mathrm{1}}{dx} \\ $$

Question Number 51185 Answers: 0 Comments: 1

calculate Σ_(n=0) ^∞ (n/((n+1)^4 (2n+1)^2 ))

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{n}}{\left({n}+\mathrm{1}\right)^{\mathrm{4}} \left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 51181 Answers: 2 Comments: 1

Question Number 51174 Answers: 0 Comments: 7

please can you make arabic app like this ? or add arabic language to this great app ?

$$\mathrm{please} \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{make}\:\mathrm{arabic}\:\mathrm{app} \\ $$$$\mathrm{like}\:\mathrm{this}\:? \\ $$$$\mathrm{or}\:\mathrm{add}\:\mathrm{arabic}\:\mathrm{language} \\ $$$$\mathrm{to}\:\mathrm{this}\:\mathrm{great}\:\mathrm{app}\:? \\ $$

Question Number 51167 Answers: 3 Comments: 0

Prove that: (a) If ∣z_1 + z_2 ∣ = ∣z_1 − z_2 ∣, the difference of the arguements of z_1 and z_2 is (π/2) (b) If arg{((z_1 + z_2 )/(z_1 − z_2 ))} = (π/2) , then ∣z_1 ∣ = ∣z_2 ∣

Question Number 51163 Answers: 0 Comments: 0

Question Number 51156 Answers: 2 Comments: 0

Show that the equation of tangent to the ellipse (x^2 /a^2 )+(y^2 /b^2 )=1 at the end of lactus rectum which lie in the 1^(st) quadrant is xe+y−a=0 ∗merry X−mas and happy new year∗

$${Show}\:{that}\:{the}\:{equation} \\ $$$${of}\:{tangent}\:{to}\:{the}\:{ellipse} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:{at}\:{the}\:{end}\:{of} \\ $$$${lactus}\:{rectum}\:{which} \\ $$$${lie}\:{in}\:{the}\:\mathrm{1}^{{st}} {quadrant}\:{is} \\ $$$${xe}+{y}−{a}=\mathrm{0} \\ $$$$ \\ $$$$\ast{merry}\:{X}−{mas}\:{and}\:{happy}\:{new}\:{year}\ast \\ $$

Question Number 51153 Answers: 3 Comments: 1

Question Number 51214 Answers: 3 Comments: 0

1.lim_(x→−(i/2)) (((z−i)^2 )/((2z−i)(3−z))) 2.lim_(x→e^((πi)/4) ) ((2z^2 )/(z^3 −z−1)) 3.lim_(x→2i) ((2z^2 +8)/((√z^4 )−^3 (√(64)))) 4.lim_(x→0) ((cos 4z−1)/(z sin z))

$$\mathrm{1}.\underset{{x}\rightarrow−\frac{\mathrm{i}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\left({z}−{i}\right)^{\mathrm{2}} }{\left(\mathrm{2}{z}−{i}\right)\left(\mathrm{3}−{z}\right)} \\ $$$$\mathrm{2}.\underset{{x}\rightarrow{e}^{\frac{\pi{i}}{\mathrm{4}}} } {\mathrm{lim}}\:\frac{\mathrm{2}{z}^{\mathrm{2}} }{{z}^{\mathrm{3}} −{z}−\mathrm{1}} \\ $$$$\mathrm{3}.\underset{{x}\rightarrow\mathrm{2}{i}} {\mathrm{lim}}\:\frac{\mathrm{2}{z}^{\mathrm{2}} +\mathrm{8}}{\sqrt{{z}^{\mathrm{4}} }−^{\mathrm{3}} \sqrt{\mathrm{64}}} \\ $$$$\mathrm{4}.\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4}{z}−\mathrm{1}}{{z}\:\mathrm{sin}\:{z}} \\ $$$$ \\ $$

Question Number 51151 Answers: 1 Comments: 0

Find the equation of tangent to the ellipse x^2 +4y^2 =4 which are perpendicular to the line 2x−3y=1 ∗merry X−mas and happy new year∗

$${Find}\:{the}\:{equation}\:{of} \\ $$$${tangent}\:{to}\:{the}\:\:{ellipse} \\ $$$${x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} =\mathrm{4}\:{which}\:{are} \\ $$$${perpendicular}\:{to}\:{the}\: \\ $$$${line}\:\mathrm{2}{x}−\mathrm{3}{y}=\mathrm{1} \\ $$$$ \\ $$$$\ast{merry}\:{X}−{mas}\:{and}\:{happy}\:{new}\:{year}\ast \\ $$

Question Number 51150 Answers: 2 Comments: 0

from left hand sides prove that ((sinαsin β)/(cos α+cos β))=((2tan(α/2) tan (β/2))/(1−tan^2 (α/2)tan^2 (β/2)))

$${from}\:{left}\:{hand}\:{sides} \\ $$$${prove}\:{that} \\ $$$$\frac{{sin}\alpha\mathrm{sin}\:\beta}{\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta}=\frac{\mathrm{2tan}\frac{\alpha}{\mathrm{2}}\:\mathrm{tan}\:\frac{\beta}{\mathrm{2}}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \frac{\alpha}{\mathrm{2}}\mathrm{tan}^{\mathrm{2}} \:\frac{\beta}{\mathrm{2}}} \\ $$

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