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Author: Tinku Tara

Is-the-section-marked-correct-i-1-x-i-x-n-1-x-i-1-n-i-1-2-x-1-1-2-1-2-3-1-2-x-1-x-2-x-1-3-x-2-x-1-2-x-1-m-1-x-n-1-m-i-1-

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Question Number 4639 by FilupSmith last updated on 17/Feb/16 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{section}\:\mathrm{marked}\:\left(\ast\right)\:{correct}? \\ $$$$ \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{x}} {\prod}}{i}={x}! \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{{x}} {\prod}}\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{i}\right)=\mathrm{1}!×\mathrm{2}!×…×{x}! \\…

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Let-P-1-p-1-p-2-p-1-1-p-2-a-1-1-a-1-2-a-2-1-a-2-2-and-that-P-n-be-the-nth-power-of-P-evaluated-as-P-n-P-P-n-1-i-e-by-successive-pre-multiplication-of-P-to-P-2

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Question Number 4638 by Yozzii last updated on 17/Feb/16 $${Let}\:\boldsymbol{\mathrm{P}}=\begin{pmatrix}{\mathrm{1}−{p}_{\mathrm{1}} }&{{p}_{\mathrm{2}} }\\{{p}_{\mathrm{1}} }&{\mathrm{1}−{p}_{\mathrm{2}} }\end{pmatrix}=\begin{pmatrix}{{a}_{\mathrm{1},\mathrm{1}} }&{{a}_{\mathrm{1},\mathrm{2}} }\\{{a}_{\mathrm{2},\mathrm{1}} }&{{a}_{\mathrm{2},\mathrm{2}} }\end{pmatrix} \\ $$$${and}\:{that}\:\boldsymbol{\mathrm{P}}^{{n}} \:{be}\:{the}\:{nth}\:{power}\:{of}\:\boldsymbol{\mathrm{P}}\:{evaluated} \\ $$$${as}\:\boldsymbol{\mathrm{P}}^{{n}} =\boldsymbol{\mathrm{P}}×\boldsymbol{\mathrm{P}}^{{n}−\mathrm{1}} ;{i}.{e}\:{by}\:{successive}\:…

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Y-1-Asin-6x-10t-Y-2-Asin-3x-9t-Show-that-the-medium-is-dispersive-If-this-two-waves-superpose-obtain-both-the-phase-velocity-and-group-velocity-of-a-combine-disturbance-

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Question Number 4634 by sanusihammed last updated on 16/Feb/16 $${Y}^{\mathrm{1}} \:=\:{Asin}\left(\mathrm{6}{x}\:−\:\mathrm{10}{t}\right) \\ $$$$ \\ $$$${Y}^{\mathrm{2}} \:=\:{Asin}\left(\mathrm{3}{x}\:−\:\mathrm{9}{t}\right) \\ $$$$ \\ $$$${Show}\:{that}\:{the}\:{medium}\:{is}\:{dispersive}.\:{If}\:{this}\:{two}\:{waves}\:\: \\ $$$${superpose}\:{obtain}\:{both}\:{the}\:{phase}\:{velocity}\:{and}\:{group}\:{velocity}\: \\ $$$${of}\:{a}\:{combine}\:{disturbance}. \\…

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The-volume-V-in-liters-of-petrol-in-a-car-tank-is-decreasing-at-the-rate-of-1-5-m-2000-liters-km-After-travelling-m-kilometers-Assuming-that-V-4

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Question Number 4633 by sanusihammed last updated on 16/Feb/16 $${The}\:{volume}\:{V}\:\left({in}\:{liters}\right)\:\:{of}\:{petrol}\:{in}\:{a}\:{car}\:{tank}\:{is}\:{decreasing}\: \\ $$$${at}\:{the}\:{rate}\:{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\frac{\mathrm{1}}{\mathrm{5}}\:−\:\frac{{m}}{\mathrm{2000}}\right)\:{liters}/{km} \\ $$$$ \\ $$$${After}\:{travelling}\:{m}\:{kilometers}.\:{Assuming}\:{that}\:{V}\:=\:\mathrm{40} \\ $$$${when}\:{m}\:=\:\mathrm{0}.\:{Find}\:{an}\:{expression}\:{for}\:{V}\:\:{in}\:{terms}\:{of}\:{m}. \\ $$$$ \\ $$ Answered…

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