Question Number 19215 by Tinkutara last updated on 07/Aug/17 $$\mathrm{STATEMENT}-\mathrm{1}\::\:\mathrm{For}\:\mathrm{every}\:\mathrm{natural} \\ $$$$\mathrm{number}\:{n}\:\geqslant\:\mathrm{2},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:…..\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\:>\:\sqrt{{n}} \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{For}\:\mathrm{every}\:\mathrm{natural} \\ $$$$\mathrm{number}\:{n}\:\geqslant\:\mathrm{2},\:\sqrt{{n}\left({n}\:+\:\mathrm{1}\right)}\:<\:{n}\:+\:\mathrm{1} \\ $$ Answered by 433 last updated…
Question Number 150277 by mathdanisur last updated on 10/Aug/21 $$\mathrm{Laplace}\:\mathrm{Metodu}\:\left(\mathrm{solution}\right) \\ $$$$\mathrm{y}^{''} \:+\:\mathrm{5y}^{'} \:+\:\mathrm{6y}\:=\:\mathrm{cos}\left(\mathrm{t}\right) \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$ Commented by amin96 last updated on…
Question Number 84740 by Rio Michael last updated on 15/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:−\mathrm{18}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{4} \\ $$ Commented by mr W last updated on 15/Mar/20 $$−\mathrm{18}=\left(−\mathrm{5}\right)×\mathrm{4}+\mathrm{2} \\ $$$$\Rightarrow{remainder}\:=\:\mathrm{2} \\…
Question Number 19204 by malwaan last updated on 06/Aug/17 $$\mathrm{If}\:\mathrm{L}=\begin{bmatrix}{\mathrm{1}\:\:\mathrm{0}\:\:\mathrm{0}}\\{\mathrm{3}\:\:\mathrm{1}\:\:\mathrm{0}}\\{\mathrm{2}\:\:\mathrm{4}\:\:\mathrm{1}}\end{bmatrix}\mathrm{and}\:\mathrm{B}=\begin{bmatrix}{\mathrm{3}}\\{\mathrm{2}}\\{\mathrm{1}}\end{bmatrix} \\ $$$$\mathrm{x}_{\mathrm{1}} =−\mathrm{2}\:;\:\mathrm{x}_{\mathrm{2}} =\mathrm{1}\:;\:\mathrm{x}_{\mathrm{3}} =\mathrm{5} \\ $$$$\mathrm{find}\:\mathrm{U} \\ $$$$\left(\mathrm{numerical}\:\mathrm{analysis}\right) \\ $$$$ \\ $$ Commented by…
Question Number 84739 by Rio Michael last updated on 15/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{unit}\:\mathrm{digit}\:\mathrm{in}\:\mathrm{the}\:\mathrm{number} \\ $$$$\:\mathrm{15}^{\mathrm{1789}} \:+\:\mathrm{17}^{\mathrm{1789}} \:+\:\mathrm{19}^{\mathrm{1789}} \\ $$ Answered by TANMAY PANACEA last updated on 15/Mar/20…
Question Number 19200 by Tinkutara last updated on 06/Aug/17 $$\mathrm{A}\:\mathrm{river}\:\mathrm{of}\:\mathrm{width}\:{d}\:\mathrm{is}\:\mathrm{flowing}\:\mathrm{with}\:\mathrm{speed} \\ $$$${u}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{figure}.\:\mathrm{John}\:\mathrm{can}\:\mathrm{swim} \\ $$$$\mathrm{with}\:\mathrm{maximum}\:\mathrm{speed}\:{v}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{river}\:\mathrm{and}\:\mathrm{can}\:\mathrm{cross}\:\mathrm{it}\:\mathrm{in}\:\mathrm{shortest}\:\mathrm{time} \\ $$$${T}.\:\mathrm{John}\:\mathrm{starts}\:\mathrm{at}\:{A}.\:{B}\:\mathrm{is}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{directly}\:\mathrm{opposite}\:\mathrm{to}\:{A}\:\mathrm{on}\:\mathrm{the}\:\mathrm{other} \\ $$$$\mathrm{bank}\:\mathrm{of}\:\mathrm{the}\:\mathrm{river}.\:\mathrm{If}\:{t}\:\mathrm{be}\:\mathrm{the}\:\mathrm{time}\:\mathrm{John} \\ $$$$\mathrm{takes}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{the}\:\mathrm{opposite}\:\mathrm{bank},\:\mathrm{match} \\…
Question Number 19199 by priyankavarma094@gmail.com last updated on 06/Aug/17 $$\mathrm{y}=\mathrm{tan}\:\mathrm{x}^{\mathrm{tan}\:\mathrm{x}^{\mathrm{tan}\:\mathrm{x}} } \\ $$ Answered by NEC last updated on 06/Aug/17 $${let}\:{u}=\mathrm{tan}\:{x} \\ $$$$ \\ $$$${y}={u}^{{u}^{{u}}…
Question Number 19198 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{integer}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{system}: \\ $$$$\mathrm{35}{x}\:+\:\mathrm{63}{y}\:+\:\mathrm{45}{z}\:=\:\mathrm{1},\:\mid{x}\mid\:<\:\mathrm{9},\:\mid{y}\mid\:<\:\mathrm{5}, \\ $$$$\mid{z}\mid\:<\:\mathrm{7}. \\ $$ Commented by mrW1 last updated on 09/Aug/17 $$\left(−\mathrm{10},\mathrm{2},\mathrm{5}\right) \\…
Question Number 84733 by manr last updated on 15/Mar/20 $$\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx} \\ $$ Answered by TANMAY PANACEA last updated on 15/Mar/20 $$ \\ $$$$\int\frac{\left({x}^{\mathrm{2}}…
Question Number 19195 by vivek last updated on 06/Aug/17 $$\int\frac{\mathrm{5}{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{5}} }{\left({x}^{\mathrm{5}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }\:\:\:{solve}\:{the}\:{intgration} \\ $$ Commented by vivek last updated on 07/Aug/17 $${please}\:{solve}\:{quetion} \\…