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Question Number 223720    Answers: 1   Comments: 1

One end of a string is attached to a solid wall and the other end is hanging from a smooth pulley 2 m away fromthe wall. A point mass M of mass 2 kg is attached to the string 1 m away from the wall and an object m of mass 0.5 kg is attached to the hanging end of the string. The object is fixed in such a way that the part of the string inside the wall and pully is horizontal and the rest is vertical. If mass m is released, with what speed will mass M hit the wall?

$$ \\ $$$$\mathrm{One}\:\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{string}\:\mathrm{is} \\ $$$$\mathrm{attached}\:\mathrm{to}\:\mathrm{a}\:\mathrm{solid}\:\mathrm{wall}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{smooth}\:\mathrm{pulley}\:\mathrm{2}\:\mathrm{m}\:\mathrm{away}\: \\ $$$$\mathrm{fromthe}\:\mathrm{wall}.\:\mathrm{A}\:\mathrm{point}\:\mathrm{mass}\: \\ $$$$\mathrm{M}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{string}\:\mathrm{1}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{wall}\:\mathrm{and}\:\mathrm{an}\:\mathrm{object}\:\mathrm{m}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{0}.\mathrm{5}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{hanging}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}.\: \\ $$$$\mathrm{The}\:\mathrm{object}\:\mathrm{is}\:\mathrm{fixed}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a} \\ $$$$\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{string}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{and} \\ $$$$\mathrm{pully}\:\mathrm{is}\:\mathrm{horizontal}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{rest}\:\mathrm{is}\:\mathrm{vertical}.\:\mathrm{If}\:\mathrm{mass}\:\mathrm{m}\:\mathrm{is} \\ $$$$\mathrm{released},\:\mathrm{with}\:\mathrm{what}\:\mathrm{speed}\:\mathrm{will} \\ $$$$\mathrm{mass}\:\mathrm{M}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{wall}? \\ $$

Question Number 223712    Answers: 3   Comments: 1

Question Number 223703    Answers: 2   Comments: 0

Question Number 223700    Answers: 1   Comments: 0

$$\:\underline{\underbrace{\:}} \\ $$

Question Number 223899    Answers: 0   Comments: 0

Question Number 223896    Answers: 0   Comments: 2

Question Number 223875    Answers: 0   Comments: 1

Question Number 223905    Answers: 1   Comments: 4

ABCD is a square EL=LF FN=ND O is the center of square Prove that points K, L, O, N and C are concyclic

$${ABCD}\:{is}\:{a}\:{square} \\ $$$${EL}={LF} \\ $$$${FN}={ND} \\ $$$${O}\:{is}\:{the}\:{center}\:{of}\:{square} \\ $$$${Prove}\:{that}\:{points}\:{K},\:{L},\:{O},\:{N}\:{and}\:{C}\:{are}\:{concyclic} \\ $$

Question Number 223685    Answers: 1   Comments: 0

25^x −8.5^x =−16

$$\mathrm{25}^{{x}} −\mathrm{8}.\mathrm{5}^{{x}} =−\mathrm{16} \\ $$

Question Number 223673    Answers: 1   Comments: 0

Question Number 223666    Answers: 2   Comments: 0

Question Number 223655    Answers: 3   Comments: 4

Question Number 223653    Answers: 1   Comments: 1

Question Number 223636    Answers: 0   Comments: 0

Factor the following expression: (((arctan(x^5 +1)))^(1/5) )^x^(−x^2 )

$$\mathrm{Factor}\:\mathrm{the}\:\mathrm{following}\:\mathrm{expression}: \\ $$$$\left(\sqrt[{\mathrm{5}}]{\mathrm{arctan}\left({x}^{\mathrm{5}} +\mathrm{1}\right)}\right)^{{x}^{−{x}^{\mathrm{2}} } } \\ $$

Question Number 223631    Answers: 2   Comments: 1

Question Number 223626    Answers: 1   Comments: 6

{ ((x^2 +y^2 +xy=25)),((y^2 +z^2 +yz=49)),((z^2 +x^2 +zx=64)) :} (x+y+z)^2 −100=??

$$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{25}}\\{{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{yz}=\mathrm{49}}\\{{z}^{\mathrm{2}} +{x}^{\mathrm{2}} +{zx}=\mathrm{64}}\end{cases} \\ $$$$\left({x}+{y}+{z}\right)^{\mathrm{2}} −\mathrm{100}=?? \\ $$

Question Number 223619    Answers: 2   Comments: 0

Question Number 223615    Answers: 3   Comments: 0

40^(x−1) =2^(2x+1)

$$\mathrm{40}^{{x}−\mathrm{1}} =\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} \\ $$

Question Number 223595    Answers: 1   Comments: 1

Question Number 223591    Answers: 1   Comments: 12

Question Number 223585    Answers: 1   Comments: 1

Question Number 223580    Answers: 3   Comments: 0

∫_0 ^(1 ) ((e^(−r^2 ) sin(1/r^2 )ln(r+1))/r^2 ) dr

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}\:} \:\frac{{e}^{−\boldsymbol{{r}}^{\mathrm{2}} } \boldsymbol{\mathrm{sin}}\left(\mathrm{1}/\boldsymbol{{r}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{ln}}\left(\boldsymbol{{r}}+\mathrm{1}\right)}{\boldsymbol{{r}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{d}{r}} \\ $$$$ \\ $$

Question Number 223571    Answers: 2   Comments: 0

S_1 = 1∙1! + 2∙2! + 3∙3! +...+ 16∙16! S_2 = 1∙1! + 2∙2! + 3∙3! +...+ 14∙14! Find: (S_1 /S_2 ) = ?

$$\mathrm{S}_{\mathrm{1}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+...+\:\mathrm{16}\centerdot\mathrm{16}! \\ $$$$\mathrm{S}_{\mathrm{2}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+...+\:\mathrm{14}\centerdot\mathrm{14}! \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{S}_{\mathrm{1}} }{\mathrm{S}_{\mathrm{2}} }\:=\:? \\ $$

Question Number 223560    Answers: 0   Comments: 15

Question Number 223570    Answers: 0   Comments: 0

demontrer que quelque soit k appartenant N l

$${demontrer}\:{que}\:{quelque}\:{soit}\:{k}\:{appartenant}\:{N}\:\:{l} \\ $$

Question Number 223569    Answers: 2   Comments: 0

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