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Question Number 79373 Answers: 0 Comments: 0

find ∫_0 ^∞ e^(−(x^3 +(1/x^3 ))) dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({x}^{\mathrm{3}} \:+\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)} {dx} \\ $$

Question Number 79368 Answers: 2 Comments: 6

Question Number 79365 Answers: 1 Comments: 1

Question Number 79361 Answers: 1 Comments: 1

Question Number 79359 Answers: 0 Comments: 1

Question Number 79357 Answers: 0 Comments: 1

Question Number 79352 Answers: 1 Comments: 2

∫(dx/(1−(√(cos(x)))))

$$\int\frac{{dx}}{\mathrm{1}−\sqrt{{cos}\left({x}\right)}} \\ $$

Question Number 79351 Answers: 0 Comments: 1

Physic A generator(E=230V ; r≠0) supplies two receivers connected in parallel (E′_1 =180V ; r′_1 =5Ω and E′_2 =0V ;r′_2 =150Ω) 1. calculate the currents I_(1 ) and I_(2 ) passing through each receptor. 2.calculate the total delivred cur− rent I by the generator. which type is the second receiptor? Thank you for helping me sirs! For more details, E represents the electromotive force of generator ; r represents his internal resistance. E′ and r′ caracterise receiptors.

$$\mathrm{Physic} \\ $$$$ \\ $$$$\mathrm{A}\:\mathrm{generator}\left(\mathrm{E}=\mathrm{230V}\:;\:\mathrm{r}\neq\mathrm{0}\right)\:\mathrm{supplies} \\ $$$$\mathrm{two}\:\mathrm{receivers}\:\mathrm{connected}\:\mathrm{in}\:\mathrm{parallel} \\ $$$$\left(\mathrm{E}'_{\mathrm{1}} =\mathrm{180V}\:;\:\mathrm{r}'_{\mathrm{1}} =\mathrm{5}\Omega\:\mathrm{and}\:\mathrm{E}'_{\mathrm{2}} =\mathrm{0V}\:;\mathrm{r}'_{\mathrm{2}} =\mathrm{150}\Omega\right) \\ $$$$ \\ $$$$\mathrm{1}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{currents}\:\mathrm{I}_{\mathrm{1}\:} \mathrm{and}\:\mathrm{I}_{\mathrm{2}\:} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{each}\:\mathrm{receptor}. \\ $$$$\mathrm{2}.\mathrm{calculate}\:\mathrm{the}\:\mathrm{total}\:\mathrm{delivred}\:\mathrm{cur}− \\ $$$$\mathrm{rent}\:\mathrm{I}\:\mathrm{by}\:\mathrm{the}\:\mathrm{generator}. \\ $$$$\mathrm{which}\:\mathrm{type}\:\mathrm{is}\:\mathrm{the}\:\mathrm{second}\:\mathrm{receiptor}? \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{for}\:\mathrm{helping}\:\mathrm{me}\:\mathrm{sirs}! \\ $$$$ \\ $$$$\mathrm{For}\:\mathrm{more}\:\mathrm{details},\:\mathrm{E}\:\mathrm{represents}\:\mathrm{the} \\ $$$$\mathrm{electromotive}\:\mathrm{force}\:\mathrm{of}\:\mathrm{generator} \\ $$$$;\:\mathrm{r}\:{represents}\:{his}\:{internal}\:{resistance}. \\ $$$$\mathrm{E}'\:\mathrm{and}\:\mathrm{r}'\:\mathrm{caracterise}\:\mathrm{receiptors}. \\ $$

Question Number 79360 Answers: 0 Comments: 0

Question Number 79340 Answers: 1 Comments: 3

Question Number 79325 Answers: 0 Comments: 2

Convergence of : 1) I=∫_1 ^( ∞) ((e^(−t/5) ∣sin(lnt)∣)/((t−1)^(3/2) ))dt 2) I=∫_1 ^∞ ((√(lnx))/((x−1)(√x)))dx

$$\:\boldsymbol{{Convergence}}\:\:\boldsymbol{{of}}\:: \\ $$$$\left.\:\:\mathrm{1}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\:\infty} \frac{\boldsymbol{{e}}^{−\boldsymbol{{t}}/\mathrm{5}} \mid\boldsymbol{{sin}}\left(\boldsymbol{{lnt}}\right)\mid}{\left(\boldsymbol{{t}}−\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\boldsymbol{{dt}} \\ $$$$\left.\:\:\mathrm{2}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\infty} \frac{\sqrt{\boldsymbol{{lnx}}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\sqrt{\boldsymbol{{x}}}}\boldsymbol{{dx}} \\ $$

Question Number 79311 Answers: 0 Comments: 2

Question Number 79309 Answers: 1 Comments: 3

Question Number 79308 Answers: 1 Comments: 3

Question Number 79306 Answers: 1 Comments: 7

(√(3−x))−(√(x+1))>(1/2)

$$ \\ $$$$\sqrt{\mathrm{3}−\mathrm{x}}−\sqrt{\mathrm{x}+\mathrm{1}}>\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 79290 Answers: 1 Comments: 0

What is the area of one petal of r=2cos(3θ)

$${What}\:{is}\:{the}\:{area}\:{of}\:{one}\:{petal}\:{of} \\ $$$${r}=\mathrm{2cos}\left(\mathrm{3}\theta\right) \\ $$

Question Number 79289 Answers: 0 Comments: 1

m^2 +n^2 =2(a^2 +b^2 ) What is 2(a+b) in terms of m and n

$${m}^{\mathrm{2}} +{n}^{\mathrm{2}} =\mathrm{2}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$$${What}\:{is}\:\mathrm{2}\left({a}+{b}\right)\:{in}\:{terms}\:{of}\:{m}\:{and}\:{n} \\ $$

Question Number 79320 Answers: 0 Comments: 3

what the minimum value of y = sec (x)+cosec (x)?

$$\mathrm{what}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{sec}\:\left(\mathrm{x}\right)+\mathrm{cosec}\:\left(\mathrm{x}\right)? \\ $$

Question Number 79279 Answers: 1 Comments: 4

solve ∣x∣^3 −7x^2 +7∣x∣+15<0

$$\mathrm{solve}\: \\ $$$$\mid\mathrm{x}\mid^{\mathrm{3}} −\mathrm{7x}^{\mathrm{2}} +\mathrm{7}\mid\mathrm{x}\mid+\mathrm{15}<\mathrm{0} \\ $$

Question Number 79266 Answers: 0 Comments: 3

let ABC be a escalene triangle of area 7. Let A_1 be a point on the side BC, and let B_1 and C_1 be points on the sides AC and AB, such that AA_1 , BB_1 and CC_1 are parallel. Find the area of triangle A_1 B_1 C_1 .

$${let}\:{ABC}\:{be}\:{a}\:{escalene}\:{triangle}\:{of} \\ $$$${area}\:\mathrm{7}.\:{Let}\:{A}_{\mathrm{1}} \:{be}\:{a}\:{point}\:{on}\:{the}\:{side} \\ $$$${BC},\:{and}\:{let}\:{B}_{\mathrm{1}} \:{and}\:{C}_{\mathrm{1}} \:{be}\:{points}\:{on} \\ $$$${the}\:{sides}\:{AC}\:{and}\:{AB},\:{such}\:{that} \\ $$$${AA}_{\mathrm{1}} ,\:{BB}_{\mathrm{1}} \:{and}\:{CC}_{\mathrm{1}} \:{are}\:{parallel}.\:{Find} \\ $$$${the}\:{area}\:{of}\:{triangle}\:{A}_{\mathrm{1}} {B}_{\mathrm{1}} {C}_{\mathrm{1}} . \\ $$

Question Number 79264 Answers: 0 Comments: 0

Question Number 79263 Answers: 0 Comments: 4

4^(2x−1) +(1/4)^2 log^2 (2x)>^2 log(x) {^2 log((1/x))−2^(2x) }

$$\mathrm{4}^{\mathrm{2x}−\mathrm{1}} +\frac{\mathrm{1}}{\mathrm{4}}\:^{\mathrm{2}} \mathrm{log}^{\mathrm{2}} \left(\mathrm{2x}\right)>\:^{\mathrm{2}} \mathrm{log}\left(\mathrm{x}\right) \\ $$$$\left\{^{\mathrm{2}} \mathrm{log}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{2}^{\mathrm{2x}} \right\} \\ $$

Question Number 79256 Answers: 1 Comments: 0

3s^2 −2ps−3cp−1=0 and 3s−2p−sp^2 −3cp^2 =0 find s and p both real in terms of c ∈R.

$$\mathrm{3}{s}^{\mathrm{2}} −\mathrm{2}{ps}−\mathrm{3}{cp}−\mathrm{1}=\mathrm{0}\:\:\:{and} \\ $$$$\mathrm{3}{s}−\mathrm{2}{p}−{sp}^{\mathrm{2}} −\mathrm{3}{cp}^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:{s}\:{and}\:{p}\:{both}\:{real}\:{in}\:{terms} \\ $$$${of}\:{c}\:\in\mathbb{R}. \\ $$

Question Number 79249 Answers: 1 Comments: 3

Question Number 79254 Answers: 4 Comments: 2

Question Number 79236 Answers: 1 Comments: 3

lim_(x→+∞) x{e−(1+(1/x))^x }=?

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\mathrm{x}\left\{\mathrm{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \right\}=? \\ $$

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