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Question Number 59595    Answers: 1   Comments: 1

Question Number 59588    Answers: 1   Comments: 1

find x,y in R (x+yi)^3 =((1+(√(15)) i)/((√5) − (√3) i))

$${find}\:{x},{y}\:{in}\:{R} \\ $$$$\left({x}+{yi}\right)^{\mathrm{3}} =\frac{\mathrm{1}+\sqrt{\mathrm{15}}\:{i}}{\sqrt{\mathrm{5}}\:−\:\sqrt{\mathrm{3}}\:{i}} \\ $$

Question Number 59581    Answers: 2   Comments: 0

Determine a , b , c in terms of α , β , γ. ab+c=γ bc+a=α ca+b=β

$$\mathcal{D}{etermine}\:{a}\:,\:{b}\:,\:{c}\:{in}\:{terms}\:{of}\:\alpha\:,\:\beta\:,\:\gamma. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}+{c}=\gamma\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{bc}+{a}=\alpha \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ca}+{b}=\beta \\ $$

Question Number 59580    Answers: 1   Comments: 1

decompose at simple element the fraction F(x) =(1/(x^7 (x^2 −1)^2 ))

$${decompose}\:{at}\:{simple}\:{element}\:{the}\:{fraction}\: \\ $$$${F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{7}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 59576    Answers: 0   Comments: 4

let f(x) =∫ (dt/((x+t)(√(t^2 −x^2 )))) 1) determine a explicit form of f(x) 2) determine ∫ (dt/((x+2)(√(t^2 −4)))) and ∫ (dt/((x+1)(√(t^2 −1))))

$${let}\:{f}\left({x}\right)\:=\int\:\:\:\:\:\:\:\frac{{dt}}{\left({x}+{t}\right)\sqrt{{t}^{\mathrm{2}} −{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\int\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{2}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{4}}}\:\:{and}\:\:\int\:\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}} \\ $$

Question Number 59575    Answers: 1   Comments: 0

find ∫ ((sin(2x))/(1+cos^2 x))dx

$${find}\:\int\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 59562    Answers: 1   Comments: 0

Derive the equations of motion 1)Vu+at

$$\left.\mathrm{Derive}\:\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{motion}\:\mathrm{1}\right)\mathrm{Vu}+\mathrm{at} \\ $$

Question Number 59552    Answers: 1   Comments: 0

(1/4)+((1/4)+(1/8))

$$\frac{\mathrm{1}}{\mathrm{4}}+\left(\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}}\right) \\ $$

Question Number 59551    Answers: 1   Comments: 0

1.8×1.6

$$\mathrm{1}.\mathrm{8}×\mathrm{1}.\mathrm{6} \\ $$

Question Number 59550    Answers: 1   Comments: 0

9+(5×4+5^3 )

$$\mathrm{9}+\left(\mathrm{5}×\mathrm{4}+\mathrm{5}^{\mathrm{3}} \right) \\ $$

Question Number 59549    Answers: 2   Comments: 0

(1/5)×i i=7

$$\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{i}\:\:\mathrm{i}=\mathrm{7} \\ $$

Question Number 59547    Answers: 1   Comments: 0

4+t×c t=3 c=6

$$\mathrm{4}+\mathrm{t}×\mathrm{c}\:\mathrm{t}=\mathrm{3}\:\mathrm{c}=\mathrm{6} \\ $$

Question Number 59542    Answers: 0   Comments: 4

lim_(x→0) ((ln(cosx))/x^2 ) I have a doubt

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\mathrm{ln}\left(\mathrm{cosx}\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$$${I}\:{have}\:{a}\:{doubt} \\ $$

Question Number 59563    Answers: 2   Comments: 1

Question Number 59528    Answers: 0   Comments: 5

let f(x) =∫_0 ^1 (dt/(1+xch(t))) with x real 1) determine a explicit form of f(x) 2)find also g(x)=∫_0 ^1 (dt/((1+xch(t))^2 )) 3) calculate ∫_0 ^1 (dt/(1+3ch(t))) and ∫_0 ^1 (dt/((1+3ch(t))^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{1}+{xch}\left({t}\right)}\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left(\mathrm{1}+{xch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{ch}\left({t}\right)}\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+\mathrm{3}{ch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$

Question Number 59526    Answers: 1   Comments: 1

calculate ∫_0 ^1 (dx/(2sh(x)+3ch(x)))

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\mathrm{2}{sh}\left({x}\right)+\mathrm{3}{ch}\left({x}\right)} \\ $$

Question Number 59518    Answers: 1   Comments: 1

if x+y+z=1 x^2 +y^2 +z^2 =2 x^3 +y^3 +z^3 =3 calculste x^5 +y^5 +z^5

$${if}\:\:{x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{3}} \:+{y}^{\mathrm{3}} \:+{z}^{\mathrm{3}} =\mathrm{3}\:\:{calculste} \\ $$$${x}^{\mathrm{5}} +{y}^{\mathrm{5}} \:+{z}^{\mathrm{5}} \\ $$

Question Number 59516    Answers: 1   Comments: 0

Question Number 59515    Answers: 0   Comments: 0

Question Number 59509    Answers: 2   Comments: 0

Question Number 59506    Answers: 1   Comments: 4

Question Number 59505    Answers: 2   Comments: 0

Two particles P and Q move towards each other along a straight line MN, 51 meters long. P starts fromM with velocity 5 ms^(−1) and constant acceleration of 1 ms^(−2) . Q starts from N at the same time with velocity 6 ms^(−1) and at a constant acceleration of 3 ms^(−2) . Find the time when the: (a) particles are 30 metres apart; (b) particles meet; (c) velocity of P is (3/4) os the velocity of Q.

$$\mathrm{Two}\:\mathrm{particles}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:{MN},\:\mathrm{51}\:\mathrm{meters} \\ $$$$\mathrm{long}.\:\mathrm{P}\:\mathrm{starts}\:\mathrm{from}{M}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{5}\:\mathrm{ms}^{−\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{constant}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{1}\:\mathrm{ms}^{−\mathrm{2}} .\:\mathrm{Q}\:\mathrm{starts} \\ $$$$\mathrm{from}\:\mathrm{N}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{6}\:\mathrm{ms}^{−\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{3}\:\mathrm{ms}^{−\mathrm{2}} . \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{time}\:\mathrm{when}\:\mathrm{the}: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{particles}\:\mathrm{are}\:\mathrm{30}\:\mathrm{metres}\:\mathrm{apart}; \\ $$$$\left(\mathrm{b}\right)\:\mathrm{particles}\:\mathrm{meet}; \\ $$$$\left(\mathrm{c}\right)\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{P}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{os}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{Q}. \\ $$

Question Number 59503    Answers: 0   Comments: 1

∫_a ^b (e^(−x^2 ) )dx=?

$$\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}\left(\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } \right)\boldsymbol{{dx}}=? \\ $$

Question Number 59499    Answers: 1   Comments: 3

Question Number 59483    Answers: 0   Comments: 0

Question Number 59482    Answers: 0   Comments: 0

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