Question Number 135723 by Algoritm last updated on 15/Mar/21 Answered by liberty last updated on 15/Mar/21 $$\left(\mathrm{1}\right)\:\sqrt{{x}+\mathrm{3}}\:+\sqrt[{\mathrm{4}}]{\mathrm{9}−{x}}\:\leqslant\:\sqrt{\mathrm{3}}\:\wedge\:{x}^{\mathrm{2}} −\mathrm{16}>\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\sqrt{{x}+\mathrm{3}}\:+\sqrt[{\mathrm{4}}]{\mathrm{9}−{x}}\:\geqslant\sqrt{\mathrm{3}}\:\wedge\:{x}^{\mathrm{2}} −\mathrm{16}>\mathrm{0} \\ $$$${solution}\::\:\left(\mathrm{1}\right)\cup\left(\mathrm{2}\right) \\ $$$$…
Question Number 4645 by FilupSmith last updated on 18/Feb/16 $${S}=\underset{{i}=\mathrm{1}} {\overset{{x}} {\prod}}\left({i}^{\frac{\mathrm{1}}{\mathrm{2}}\left({x}−{i}+\mathrm{1}\right)\left({x}−{i}+\mathrm{2}\right)} \right),\:\left({x},\:{i}\right)\in\mathbb{Z} \\ $$$$ \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{S}\in\mathbb{Z} \\ $$ Answered by Yozzii last updated on…
Question Number 135718 by liberty last updated on 15/Mar/21 Answered by dhgt last updated on 04/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135712 by Dwaipayan Shikari last updated on 15/Mar/21 Commented by Dwaipayan Shikari last updated on 15/Mar/21 $${Smaller}\:{circle}\:{has}\:{half}\:{of}\:{the}\:{radius}\:{of}\:{the}\:{larger}\:{circle}. \\ $$$${Prove}\:{that},\:{irrespective}\:{of}\:{any}\:{position}\:{oc}\:{the}\:{smaller}\:{circle}\: \\ $$$${that}\:{blue}\:{point}\:{will}\:{always}\:{stay}\:{on}\:{the}\:{diametre}\:{of}\:{that}\: \\ $$$${larger}\:{circle}…
Question Number 135709 by Algoritm last updated on 15/Mar/21 Commented by mr W last updated on 15/Mar/21 $${x}_{{i}} =−\pi\:{or}\:\pi−\mathrm{1} \\ $$$${x}_{\mathrm{2021}} +\pi=\mathrm{0}\:{or}\:\mathrm{2}\pi−\mathrm{1} \\ $$ Answered…
Question Number 4639 by FilupSmith last updated on 17/Feb/16 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{section}\:\mathrm{marked}\:\left(\ast\right)\:{correct}? \\ $$$$ \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{x}} {\prod}}{i}={x}! \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{{x}} {\prod}}\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{i}\right)=\mathrm{1}!×\mathrm{2}!×…×{x}! \\…
Question Number 4638 by Yozzii last updated on 17/Feb/16 $${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} \\ $$$${and}\:{that}\:\boldsymbol{\mathrm{P}}^{{n}} \:{be}\:{the}\:{nth}\:{power}\:{of}\:\boldsymbol{\mathrm{P}}\:{evaluated} \\ $$$${as}\:\boldsymbol{\mathrm{P}}^{{n}} =\boldsymbol{\mathrm{P}}×\boldsymbol{\mathrm{P}}^{{n}−\mathrm{1}} ;{i}.{e}\:{by}\:{successive}\:…
Question Number 4634 by sanusihammed last updated on 16/Feb/16 $${Y}^{\mathrm{1}} \:=\:{Asin}\left(\mathrm{6}{x}\:−\:\mathrm{10}{t}\right) \\ $$$$ \\ $$$${Y}^{\mathrm{2}} \:=\:{Asin}\left(\mathrm{3}{x}\:−\:\mathrm{9}{t}\right) \\ $$$$ \\ $$$${Show}\:{that}\:{the}\:{medium}\:{is}\:{dispersive}.\:{If}\:{this}\:{two}\:{waves}\:\: \\ $$$${superpose}\:{obtain}\:{both}\:{the}\:{phase}\:{velocity}\:{and}\:{group}\:{velocity}\: \\ $$$${of}\:{a}\:{combine}\:{disturbance}. \\…
Question Number 70168 by Askash last updated on 01/Oct/19 Commented by Askash last updated on 01/Oct/19 Please solve ���� Commented by MJS last updated on 01/Oct/19 $$\mathrm{zillions}\:\mathrm{of}\:\mathrm{possibilities}…
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…