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Question Number 205685    Answers: 2   Comments: 0

Question Number 205684    Answers: 0   Comments: 0

Figure Shows that Object A is connected to Object B by thread along the Slope it shows a costant acceleration motion the mass of A of B are 3m , 2m respectively and when A communicates from point P to Q B′s the decrease in potential energy is 10 times the decrease in Kinetic energy of B find accerate of A (3 point)

$$\mathrm{Figure}\:\mathrm{Shows}\:\mathrm{that}\:\mathrm{Object}\:\boldsymbol{\mathrm{A}}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{to} \\ $$$$\mathrm{Object}\:\boldsymbol{\mathrm{B}}\:\mathrm{by}\:\mathrm{thread}\:\mathrm{along}\:\mathrm{the}\:\mathrm{Slope} \\ $$$$\mathrm{it}\:\mathrm{shows}\:\mathrm{a}\:\mathrm{costant}\:\mathrm{acceleration}\:\mathrm{motion} \\ $$$$\mathrm{the}\:\mathrm{mass}\:\mathrm{of}\:\boldsymbol{\mathrm{A}}\:\mathrm{of}\:\boldsymbol{\mathrm{B}}\:\mathrm{are}\:\mathrm{3m}\:,\:\mathrm{2m} \\ $$$$\mathrm{respectively}\:\mathrm{and}\:\mathrm{when}\:\boldsymbol{\mathrm{A}}\:\mathrm{communicates}\:\mathrm{from}\:\mathrm{point}\:\boldsymbol{\mathrm{P}}\:\mathrm{to}\:\boldsymbol{\mathrm{Q}}\: \\ $$$$\boldsymbol{\mathrm{B}}'{s}\:\mathrm{the}\:\mathrm{decrease}\:\mathrm{in}\:\mathrm{potential}\:\mathrm{energy}\:\mathrm{is}\:\mathrm{10}\:\:\mathrm{times} \\ $$$$\mathrm{the}\:\mathrm{decrease}\:\mathrm{in}\:\mathrm{Kinetic}\:\mathrm{energy}\:\mathrm{of}\:\boldsymbol{\mathrm{B}}\: \\ $$$$\mathrm{find}\:\mathrm{accerate}\:\mathrm{of}\:\boldsymbol{\mathrm{A}}\:\left(\mathrm{3}\:\mathrm{point}\right) \\ $$

Question Number 205683    Answers: 1   Comments: 1

$$\:\:\:\:\: \\ $$

Question Number 205682    Answers: 0   Comments: 0

Question Number 205681    Answers: 2   Comments: 0

Question Number 205680    Answers: 1   Comments: 0

solve ⌊x ⌋ + ⌊ x^2 ⌋ = ⌊ x^3 ⌋

$$ \\ $$$$\:\:\:\:\:\:\:\:\:{solve}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\lfloor{x}\:\rfloor\:+\:\lfloor\:{x}^{\mathrm{2}} \rfloor\:=\:\lfloor\:{x}^{\mathrm{3}} \:\rfloor \\ $$$$ \\ $$

Question Number 205690    Answers: 0   Comments: 6

Question Number 205673    Answers: 0   Comments: 0

Question Number 205672    Answers: 1   Comments: 0

Question Number 205671    Answers: 1   Comments: 0

Question Number 205670    Answers: 1   Comments: 0

Question Number 205669    Answers: 1   Comments: 0

Question Number 205660    Answers: 1   Comments: 0

Question Number 205657    Answers: 1   Comments: 0

Question Number 205656    Answers: 0   Comments: 0

Question Number 205654    Answers: 0   Comments: 0

We define a domino as being and ordered pair of distinct integers. A suitable sequence of dominos is a list of distinct dominoes in which the first coordonate of each pair after the first is equal to the second coordonate of the immediately preceding pair, and in which the pairs (i;j) and (j;i) do not both appear for all i and j. Let D_(40) the set of all dominoes whose coordonate are not greater than 40. Find the length of the longest suitable sequence of dominoes that can be formed using the dominoes of D_(40) .

$${We}\:{define}\:{a}\:{domino}\:{as}\:{being}\:{and}\:{ordered}\:{pair}\:{of}\:{distinct} \\ $$$${integers}.\:{A}\:{suitable}\:{sequence}\:{of}\:{dominos}\:{is}\:{a}\:{list}\:{of}\:{distinct} \\ $$$${dominoes}\:{in}\:{which}\:{the}\:{first}\:{coordonate}\:{of}\:{each}\:{pair}\:{after} \\ $$$${the}\:{first}\:{is}\:{equal}\:{to}\:{the}\:{second}\:{coordonate}\:{of}\:{the}\:{immediately} \\ $$$${preceding}\:{pair},\:{and}\:{in}\:{which}\:{the}\:{pairs}\:\left({i};{j}\right)\:{and}\:\left({j};{i}\right) \\ $$$${do}\:{not}\:{both}\:{appear}\:{for}\:{all}\:{i}\:{and}\:{j}.\:{Let}\:{D}_{\mathrm{40}} \:{the} \\ $$$${set}\:{of}\:{all}\:{dominoes}\:{whose}\:{coordonate}\:{are}\:{not}\:{greater} \\ $$$${than}\:\mathrm{40}.\:{Find}\:{the}\:{length}\:{of}\:{the}\:{longest}\:{suitable}\:{sequence} \\ $$$${of}\:{dominoes}\:{that}\:{can}\:{be}\:{formed}\:{using}\:{the}\:{dominoes}\:{of}\:{D}_{\mathrm{40}} . \\ $$

Question Number 205645    Answers: 1   Comments: 0

Find: Ω = ∫_0 ^( (𝛑/2)) ((sin^2 x)/(2 cosx + 3 sinx)) dx = ?

$$\mathrm{Find}:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}{\mathrm{2}\:\mathrm{cosx}\:+\:\mathrm{3}\:\mathrm{sinx}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 205643    Answers: 0   Comments: 0

If a,b,c>0 and a^2 + b^2 + c^2 = abc Prove that: (a/(a^2 + bc)) + (b/(b^2 + ac)) + (c/(c^2 + ab)) ≤ (1/2)

$$\mathrm{If}\:\:\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:=\:\mathrm{abc} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{a}}{\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{bc}}\:+\:\frac{\mathrm{b}}{\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{ac}}\:+\:\frac{\mathrm{c}}{\mathrm{c}^{\mathrm{2}} \:+\:\mathrm{ab}}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 205640    Answers: 0   Comments: 0

If a,b,c>0 and abc≥1 Prove that: a + b + c ≥ ((1+a)/(1+b)) + ((1+b)/(1+c)) + ((1+c)/(1+a))

$$\mathrm{If}\:\:\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{abc}\geqslant\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\geqslant\:\frac{\mathrm{1}+\mathrm{a}}{\mathrm{1}+\mathrm{b}}\:+\:\frac{\mathrm{1}+\mathrm{b}}{\mathrm{1}+\mathrm{c}}\:+\:\frac{\mathrm{1}+\mathrm{c}}{\mathrm{1}+\mathrm{a}} \\ $$

Question Number 205639    Answers: 2   Comments: 0

Question Number 205631    Answers: 1   Comments: 0

Question Number 205627    Answers: 1   Comments: 0

Question Number 205626    Answers: 2   Comments: 0

if a+b+c=(1/(a+1))+(1/(b+2))+(1/(c+3))=0, find (a+1)^2 +(b+2)^2 +(c+3)^2 =?

$${if}\:{a}+{b}+{c}=\frac{\mathrm{1}}{{a}+\mathrm{1}}+\frac{\mathrm{1}}{{b}+\mathrm{2}}+\frac{\mathrm{1}}{{c}+\mathrm{3}}=\mathrm{0}, \\ $$$${find}\:\left({a}+\mathrm{1}\right)^{\mathrm{2}} +\left({b}+\mathrm{2}\right)^{\mathrm{2}} +\left({c}+\mathrm{3}\right)^{\mathrm{2}} =? \\ $$

Question Number 205625    Answers: 1   Comments: 0

∫_0 ^1 (√(1−x^4 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205614    Answers: 2   Comments: 0

Question Number 205607    Answers: 1   Comments: 0

soit H espace de Hilbert montrez que: d(x,{a})^⌊ = ((∣<x,a>∣)/(∣∣a∣∣))

$${soit}\:{H}\:{espace}\:{de}\:{Hilbert} \\ $$$${montrez}\:{que}: \\ $$$${d}\left({x},\left\{{a}\right\}\right)^{\lfloor} \:=\:\frac{\mid<{x},{a}>\mid}{\mid\mid{a}\mid\mid} \\ $$

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