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AllQuestion and Answers: Page 1378

Question Number 74560 Answers: 0 Comments: 1

Question Number 74522 Answers: 0 Comments: 3

A rope inclined at angle 37° to the horizontal is used to drag a 50kg block along a level floor with an acceleration of 1m/s^2 .The coefficient of friction between the block and the floor is 0.2. What is the tension in the rope?

$${A}\:{rope}\:{inclined}\:{at}\:{angle}\:\mathrm{37}°\:{to}\:{the}\: \\ $$$${horizontal}\:{is}\:{used}\:{to}\:{drag}\:{a}\:\mathrm{50}{kg}\:{block} \\ $$$${along}\:{a}\:{level}\:{floor}\:{with}\:{an}\:{acceleration} \\ $$$${of}\:\mathrm{1}{m}/{s}^{\mathrm{2}} \:.{The}\:{coefficient}\:{of}\:{friction} \\ $$$${between}\:{the}\:{block}\:{and}\:{the}\:{floor}\:{is}\:\mathrm{0}.\mathrm{2}. \\ $$$${What}\:{is}\:{the}\:{tension}\:{in}\:{the}\:{rope}? \\ $$

Question Number 74520 Answers: 1 Comments: 0

Question Number 74515 Answers: 0 Comments: 0

Question Number 74508 Answers: 0 Comments: 0

li=x^− −t_v ,(α/2).((s/(√n))) ls=x^− +t_v ,(α/2).((s/(√n)))

$${li}=\overset{−} {{x}}−{t}_{{v}} ,\frac{\alpha}{\mathrm{2}}.\left(\frac{{s}}{\sqrt{{n}}}\right) \\ $$$${ls}=\overset{−} {{x}}+{t}_{{v}} ,\frac{\alpha}{\mathrm{2}}.\left(\frac{{s}}{\sqrt{{n}}}\right) \\ $$$$ \\ $$

Question Number 74502 Answers: 1 Comments: 4

let f(x)=e^(−nx) ln(1+x^2 ) 1)determine f^((n)) (x) and f^((n)) (0) 2)developp f at integr serie (n integr natural)

$${let}\:{f}\left({x}\right)={e}^{−{nx}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right){determine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie}\:\:\:\left({n}\:{integr}\:{natural}\right) \\ $$

Question Number 74501 Answers: 0 Comments: 1

let P(x)=(1/(n!))(x^2 −1)^n calculate P^((n)) (x) and P^( (n)) (0)

$$\:{let}\:{P}\left({x}\right)=\frac{\mathrm{1}}{{n}!}\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} \\ $$$${calculate}\:{P}^{\left({n}\right)} \left({x}\right)\:\:{and}\:{P}^{\:\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 74500 Answers: 0 Comments: 0

1) decompose the fraction F(x)=((x^3 −2)/((x+1)^4 (x−2)^3 )) 2)find ∫_3 ^(+∞) F(x)dx

$$\left.\mathrm{1}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{{x}^{\mathrm{3}} −\mathrm{2}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} \left({x}−\mathrm{2}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right){find}\:\:\:\int_{\mathrm{3}} ^{+\infty} \:{F}\left({x}\right){dx} \\ $$

Question Number 74499 Answers: 0 Comments: 1

decompose inside C(x) the fraction f(x)=(1/((x^2 +1)^n ))

$${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} } \\ $$

Question Number 74498 Answers: 1 Comments: 1

1) calculte A_n =∫_0 ^∞ e^(−nx) [e^x ] dx with n integr and n≥2 2)find lim_(n→+∞) n^n A_n

$$\left.\mathrm{1}\right)\:{calculte}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{nx}} \left[{e}^{{x}} \right]\:{dx}\:\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{{n}} \:{A}_{{n}} \\ $$

Question Number 74503 Answers: 0 Comments: 1

Question Number 74492 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(x^2 ))/(x^2 +9))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 74474 Answers: 1 Comments: 1

Question Number 74473 Answers: 1 Comments: 2

Question Number 74456 Answers: 1 Comments: 2

Question Number 74484 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(2x))/(x^2 +3))dx

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

Question Number 74483 Answers: 1 Comments: 2

Question Number 74446 Answers: 1 Comments: 0

Question Number 74431 Answers: 0 Comments: 11

Question Number 74429 Answers: 0 Comments: 2

Question Number 74455 Answers: 1 Comments: 0

if K=(x∈R 2x−1+∣2x−1∣=0 )and J=(x∈R −x(2x+1)≤−1) find J−K.

$${if}\:{K}=\left({x}\in\mathbb{R}\:\mathrm{2}{x}−\mathrm{1}+\mid\mathrm{2}{x}−\mathrm{1}\mid=\mathrm{0}\:\right){and} \\ $$$${J}=\left({x}\in\mathbb{R}\:−{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\leqslant−\mathrm{1}\right)\:{find}\:{J}−{K}. \\ $$

Question Number 74423 Answers: 0 Comments: 1

Question Number 74419 Answers: 0 Comments: 1

Question Number 74418 Answers: 1 Comments: 0

Question Number 74415 Answers: 1 Comments: 1

Question Number 74412 Answers: 0 Comments: 0

a,b,c are given real constants. p,q,r,t are unknowns from which we can choose values of two of them (non zero) and have to determine the other two (non zero), obeying two equations given below p^2 +q(1+bq)t^2 +q(ap+br)t +r(1+bq)t+r(ap+br) = 0 pt+q(a+cq)t^2 +r(a+cq)t +cqrt+cr^2 = 0 Can this be done solving a quadratic eq. and none higher..?

$${a},{b},{c}\:{are}\:{given}\:{real}\:{constants}. \\ $$$${p},{q},{r},{t}\:{are}\:{unknowns}\:{from}\:{which} \\ $$$${we}\:{can}\:{choose}\:{values}\:{of}\:{two}\:{of} \\ $$$${them}\:\left({non}\:{zero}\right)\:{and}\:{have}\:{to}\: \\ $$$${determine}\:{the}\:{other}\:{two}\:\left({non}\:{zero}\right), \\ $$$${obeying}\:\:{two}\:{equations}\:{given}\:{below} \\ $$$$\:{p}^{\mathrm{2}} +{q}\left(\mathrm{1}+{bq}\right){t}^{\mathrm{2}} +{q}\left({ap}+{br}\right){t} \\ $$$$\:\:\:\:\:+{r}\left(\mathrm{1}+{bq}\right){t}+{r}\left({ap}+{br}\right)\:=\:\mathrm{0} \\ $$$${pt}+{q}\left({a}+{cq}\right){t}^{\mathrm{2}} +{r}\left({a}+{cq}\right){t} \\ $$$$\:\:\:\:+{cqrt}+{cr}^{\mathrm{2}} =\:\mathrm{0} \\ $$$${Can}\:{this}\:{be}\:{done}\:{solving}\:{a} \\ $$$${quadratic}\:{eq}.\:{and}\:{none}\:{higher}..? \\ $$

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