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Question Number 59975    Answers: 1   Comments: 0

Question Number 59872    Answers: 1   Comments: 0

solve the o d e (1+siny)dx={2ycos y−x(secy+tany)}dy

$${solve}\:{the}\:{o}\:{d}\:{e} \\ $$$$\left(\mathrm{1}+{siny}\right){dx}=\left\{\mathrm{2}{y}\mathrm{cos}\:{y}−{x}\left({secy}+{tany}\right)\right\}{dy} \\ $$

Question Number 59870    Answers: 2   Comments: 7

Question Number 59861    Answers: 2   Comments: 2

(√(a+b(√c)))=(√((a+(√(a^2 −b^2 c)))/2))+(√((a−(√(a^2 −b^2 c)))/2)). prove

$$\sqrt{\boldsymbol{{a}}+\boldsymbol{{b}}\sqrt{\boldsymbol{{c}}}}=\sqrt{\frac{\boldsymbol{{a}}+\sqrt{\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{b}}^{\mathrm{2}} \boldsymbol{{c}}}}{\mathrm{2}}}+\sqrt{\frac{\boldsymbol{{a}}−\sqrt{\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{b}}^{\mathrm{2}} \boldsymbol{{c}}}}{\mathrm{2}}}. \\ $$$$\boldsymbol{{prove}} \\ $$

Question Number 59858    Answers: 0   Comments: 0

P(1)=(1/i) P_(n+1) P_n =1−P_(n+1) lim_(n→∞) Im(P_n ) =?

$$\mathrm{P}\left(\mathrm{1}\right)=\frac{\mathrm{1}}{{i}}\: \\ $$$$\mathrm{P}_{\mathrm{n}+\mathrm{1}} \mathrm{P}_{\mathrm{n}} =\mathrm{1}−\mathrm{P}_{\mathrm{n}+\mathrm{1}} \\ $$$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}Im}\left(\mathrm{P}_{\mathrm{n}} \right)\:=? \\ $$

Question Number 59846    Answers: 0   Comments: 8

Question Number 59842    Answers: 1   Comments: 3

Question Number 59838    Answers: 1   Comments: 1

What is the nth derivative of sinx in terms of the sine function?

$${What}\:{is}\:{the}\:{nth}\:{derivative}\:{of}\:{sinx}\:{in} \\ $$$${terms}\:{of}\:{the}\:{sine}\:{function}? \\ $$

Question Number 59835    Answers: 1   Comments: 0

Question Number 59834    Answers: 1   Comments: 0

Question Number 59833    Answers: 1   Comments: 0

Question Number 59832    Answers: 0   Comments: 0

Question Number 59829    Answers: 2   Comments: 2

Question Number 59825    Answers: 0   Comments: 0

Question Number 59814    Answers: 1   Comments: 1

Question Number 59812    Answers: 1   Comments: 1

(6/(3+(3)^(1/3) +(9)^(1/3) )) simplify.

$$\frac{\mathrm{6}}{\mathrm{3}+\sqrt[{\mathrm{3}}]{\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{9}}}\:\:\:\boldsymbol{\mathrm{simplify}}. \\ $$

Question Number 59811    Answers: 1   Comments: 2

(((tg^2 (590°))/(cos^2 (320°)))+((sin(111°))/(cos(159°))))(((cos(279°))/(sin(549°)))+((ctg(950°))/(sin^2 (400°)))) simplify.

$$\left(\frac{\boldsymbol{\mathrm{tg}}^{\mathrm{2}} \left(\mathrm{590}°\right)}{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \left(\mathrm{320}°\right)}+\frac{\boldsymbol{\mathrm{sin}}\left(\mathrm{111}°\right)}{\boldsymbol{\mathrm{cos}}\left(\mathrm{159}°\right)}\right)\left(\frac{\boldsymbol{\mathrm{cos}}\left(\mathrm{279}°\right)}{\boldsymbol{\mathrm{sin}}\left(\mathrm{549}°\right)}+\frac{\boldsymbol{\mathrm{ctg}}\left(\mathrm{950}°\right)}{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \left(\mathrm{400}°\right)}\right) \\ $$$$\boldsymbol{\mathrm{simplify}}. \\ $$

Question Number 59803    Answers: 0   Comments: 3

Question Number 59802    Answers: 0   Comments: 1

Question Number 59800    Answers: 2   Comments: 0

find the general solution y(t) of the ordinary differential equation y′′ + ω^2 y=cos ωt ,where w>0

$${find}\:{the}\:{general}\:{solution}\:{y}\left({t}\right)\:{of}\:{the} \\ $$$${ordinary}\:{differential}\:{equation} \\ $$$${y}''\:+\:\omega^{\mathrm{2}} {y}=\mathrm{cos}\:\omega{t}\:,{where}\:{w}>\mathrm{0} \\ $$

Question Number 59788    Answers: 2   Comments: 4

find the local minimum and maximum value a^2 y=x^2 (a−x) f(x)=(4/(2−x))+(9/(x−3))

$${find}\:{the}\:{local}\:{minimum}\:{and}\:{maximum}\:{value} \\ $$$$ \\ $$$${a}^{\mathrm{2}} {y}={x}^{\mathrm{2}} \left({a}−{x}\right) \\ $$$${f}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{2}−{x}}+\frac{\mathrm{9}}{{x}−\mathrm{3}} \\ $$

Question Number 59787    Answers: 2   Comments: 0

Question Number 59781    Answers: 0   Comments: 0

Question Number 59780    Answers: 1   Comments: 0

An earth-based observer sees rocket A moving at 0.70c directly towards rocket B,which is moving towards A at 0.80c. How fast does rocket A sees rocket B approaching?

$${An}\:{earth}-{based}\:{observer}\:{sees}\:{rocket}\:{A} \\ $$$${moving}\:{at}\:\mathrm{0}.\mathrm{70}{c}\:{directly}\:{towards}\:{rocket} \\ $$$${B},{which}\:{is}\:{moving}\:{towards}\:{A}\:{at}\:\mathrm{0}.\mathrm{80}{c}. \\ $$$${How}\:{fast}\:{does}\:{rocket}\:{A}\:{sees}\:{rocket}\:{B} \\ $$$${approaching}? \\ $$$$ \\ $$

Question Number 59777    Answers: 0   Comments: 4

Question Number 59764    Answers: 1   Comments: 0

((2+(√3))/((√2)+(√(2+(√3)))))+((2−(√3))/((√2)−(√(2−(√3))))). simplify.

$$\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}+\frac{\mathrm{2}−\sqrt{\mathrm{3}}}{\sqrt{\mathrm{2}}−\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}}. \\ $$$$\boldsymbol{\mathrm{simplify}}. \\ $$

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