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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

Question Number 175000 Answers: 1 Comments: 1

Question Number 174983 Answers: 0 Comments: 3

Question Number 174982 Answers: 2 Comments: 0

Question Number 174981 Answers: 0 Comments: 1

Question Number 174975 Answers: 1 Comments: 0

Question Number 174974 Answers: 1 Comments: 0

Question Number 174965 Answers: 1 Comments: 0

∫ ((x+sin x)/(1+cos x)) dx =?

$$\:\:\:\:\:\:\int\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$

Question Number 174963 Answers: 3 Comments: 1

Question Number 174960 Answers: 1 Comments: 0

solve for all x ⌊x^2 ⌋ − ⌊x⌋^2 = 100

$${solve}\:{for}\:{all}\:{x}\: \\ $$$$\lfloor{x}^{\mathrm{2}} \rfloor\:−\:\lfloor{x}\rfloor^{\mathrm{2}} \:=\:\mathrm{100} \\ $$

Question Number 174951 Answers: 1 Comments: 0

lim_(n→∞) (1/n)[1+(√2)+^3 (√3)+...^n (√n)]

$$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\left[\mathrm{1}+\sqrt{\mathrm{2}}+^{\mathrm{3}} \sqrt{\mathrm{3}}+...^{{n}} \sqrt{{n}}\right] \\ $$

Question Number 174950 Answers: 1 Comments: 0

Have you seen this method of solving quadratic problem? x^2 −x−12=0 y′=±(√(b^2 −4ac))

$$\mathrm{Have}\:\mathrm{you}\:\mathrm{seen}\:\mathrm{this}\:\mathrm{method}\:\mathrm{of}\:\mathrm{solving} \\ $$$$\mathrm{quadratic}\:\mathrm{problem}? \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{12}=\mathrm{0} \\ $$$$\mathrm{y}'=\pm\sqrt{\mathrm{b}^{\mathrm{2}} −\mathrm{4ac}} \\ $$

Question Number 174933 Answers: 1 Comments: 0

Question Number 174928 Answers: 3 Comments: 0

How many digits does 1000^(1000) have? Mastermind

$$\mathrm{How}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{does}\:\mathrm{1000}^{\mathrm{1000}} \:\mathrm{have}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174915 Answers: 1 Comments: 0

Find the value of a for which the limit lim_(x→0) ((sin (ax)−arctan x−x)/(x^3 +x^4 )) is finite and then evaluate the limit

$$\:{Find}\:{the}\:{value}\:{of}\:{a}\:{for}\:{which}\: \\ $$$$\:{the}\:{limit}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({ax}\right)−\mathrm{arctan}\:{x}−{x}}{{x}^{\mathrm{3}} +{x}^{\mathrm{4}} } \\ $$$${is}\:{finite}\:{and}\:{then}\:{evaluate}\:{the}\:{limit} \\ $$

Question Number 174939 Answers: 1 Comments: 0

sum of the all proper factors of 360 ?

$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{all}\:\mathrm{proper}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{360}\:? \\ $$

Question Number 174938 Answers: 0 Comments: 0

let u_n = ∫_0 ^1 x^n artan(nx)dx 1)lim u_n ? 2)nature of Σ u_n 3) calculate u_n 4)equivalent of u_n ?

$${let}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} {artan}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right){lim}\:{u}_{{n}} ? \\ $$$$\left.\mathrm{2}\right){nature}\:{of}\:\Sigma\:{u}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{u}_{{n}} \\ $$$$\left.\mathrm{4}\right){equivalent}\:{of}\:{u}_{{n}} ? \\ $$

Question Number 174940 Answers: 0 Comments: 1

f(x)=(log3^x −2log3).(x^2 −1) let

$${f}\left({x}\right)=\left({log}\mathrm{3}^{{x}} −\mathrm{2}{log}\mathrm{3}\right).\left({x}^{\mathrm{2}} −\mathrm{1}\right) \\ $$$${let} \\ $$

Question Number 174902 Answers: 1 Comments: 0

Question Number 174896 Answers: 0 Comments: 0

prove that ∫_(−∞) ^( ∞) ((x csch((x/2)))/(x^2 +π^2 ))dx=π−2

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{−\infty} ^{\:\infty} \frac{\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{csch}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\pi^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=\pi−\mathrm{2} \\ $$

Question Number 174888 Answers: 1 Comments: 0

Question Number 174884 Answers: 1 Comments: 0

Question Number 174883 Answers: 2 Comments: 0

lim_(n→∞) ∫_0 ^1 e^x^2 sin(nx)dx

$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{x}^{\mathrm{2}} } \mathrm{sin}\left({nx}\right){dx}\: \\ $$

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