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Question Number 175028 Answers: 0 Comments: 1

Question Number 175032 Answers: 0 Comments: 0

Question Number 175017 Answers: 0 Comments: 2

Question Number 175012 Answers: 1 Comments: 0

prove: Use the residus form ∫_0 ^(+∞) ((xsinx)/((x^2 +1)^2 ))dx=(π/(4e))

$${prove}:\:{Use}\:{the}\:{residus}\:{form} \\ $$$$\int_{\mathrm{0}} ^{+\infty} \frac{{xsinx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{4}{e}} \\ $$

Question Number 175011 Answers: 0 Comments: 2

A large lot of tires contain 5% defectives. 4 tires are to be chosen for a car. Find the probability that you find (a) 2 defective tires before 4 good ones (b) at most 2 defective tires before 4 good ones.

$$\mathrm{A}\:\mathrm{large}\:\mathrm{lot}\:\mathrm{of}\:\mathrm{tires}\:\mathrm{contain}\:\mathrm{5\%}\:\mathrm{defectives}. \\ $$$$\mathrm{4}\:\mathrm{tires}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be}\:\mathrm{chosen}\:\mathrm{for}\:\mathrm{a}\:\mathrm{car}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{you}\:\mathrm{find} \\ $$$$\:\left(\mathrm{a}\right)\:\mathrm{2}\:\mathrm{defective}\:\mathrm{tires}\:\mathrm{before}\:\mathrm{4}\:\mathrm{good}\:\mathrm{ones} \\ $$$$\:\left(\mathrm{b}\right)\:\mathrm{at}\:\mathrm{most}\:\mathrm{2}\:\mathrm{defective}\:\mathrm{tires}\:\mathrm{before}\:\mathrm{4}\:\mathrm{good}\:\mathrm{ones}. \\ $$

Question Number 175010 Answers: 1 Comments: 1

A ball of p of mass 0.25kg losses (1/3) of its velocity when it makes an head on collision with an identical ball q at rest. After collision, q moves off with a velocity of 2ms^(−1) in the original direction of p. Calculate the initial velocity of p.

$$\:\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{25kg}\:\mathrm{losses}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{of}\: \\ $$$$\mathrm{its}\:\mathrm{velocity}\:\mathrm{when}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{head}\:\mathrm{on} \\ $$$$\mathrm{collision}\:\mathrm{with}\:\mathrm{an}\:\mathrm{identical}\:\mathrm{ball}\:\boldsymbol{\mathrm{q}}\:\mathrm{at}\:\mathrm{rest}. \\ $$$$\mathrm{After}\:\mathrm{collision},\:\boldsymbol{\mathrm{q}}\:\mathrm{moves}\:\mathrm{off}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{2ms}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{original}\:\mathrm{direction}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$

Question Number 175008 Answers: 0 Comments: 2

Find The Centroid Coordinate If Trapezoid With B_1 =4, B_2 =3 And Height=5 With Positions Like This

$${Find}\:{The}\:{Centroid}\:{Coordinate}\: \\ $$$${If}\:{Trapezoid}\:{With}\:{B}_{\mathrm{1}} =\mathrm{4},\:{B}_{\mathrm{2}} =\mathrm{3} \\ $$$${And}\:{Height}=\mathrm{5}\:{With}\:{Positions}\: \\ $$$${Like}\:{This} \\ $$

Question Number 175023 Answers: 0 Comments: 0

𝚺_(n=0) ^∞ (((−1)^n )/(7+6n))[𝛙^((0)) (((9+6n)/2))−𝛙^((0)) (((7+6n)/2))]

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{7}+\mathrm{6}\boldsymbol{\mathrm{n}}}\left[\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\frac{\mathrm{9}+\mathrm{6}\boldsymbol{\mathrm{n}}}{\mathrm{2}}\right)−\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\frac{\mathrm{7}+\mathrm{6}\boldsymbol{\mathrm{n}}}{\mathrm{2}}\right)\right] \\ $$

Question Number 175004 Answers: 0 Comments: 1