Question Number 10487 by Saham last updated on 13/Feb/17 $$\mathrm{A}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{numbers}\:\mathrm{T}_{\mathrm{1}} ,\mathrm{T}_{\mathrm{2}} ,\mathrm{T}_{\mathrm{3}} ,…….\:\mathrm{T}_{\mathrm{n}\:} \mathrm{satisfies} \\ $$$$\mathrm{the}\:\mathrm{relation}\:\mathrm{T}_{\mathrm{n}\:+\:\mathrm{1}} \:+\:\mathrm{n}^{\mathrm{2}} \:=\:\mathrm{nT}_{\mathrm{n}} \:+\:\mathrm{2}\:\mathrm{for}\:\mathrm{all}\:\mathrm{integers} \\ $$$$\mathrm{n}\geqslant\mathrm{1}.\:\mathrm{if}\:\mathrm{T}_{\mathrm{1}} \:=\:\mathrm{2}.\:\mathrm{find}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{values}\:\mathrm{of}\:\mathrm{T}_{\mathrm{2}} ,\:\mathrm{T}_{\mathrm{3}}…
Question Number 10485 by Saham last updated on 13/Feb/17 $$\mathrm{A}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{numbers}\:\mathrm{T}_{\mathrm{1}} ,\:\mathrm{T}_{\mathrm{2}} ,\:\mathrm{T}_{\mathrm{3}} ,\:…\:\:\mathrm{Satisfies}\:\mathrm{the} \\ $$$$\mathrm{relation}\:\mathrm{3T}_{\mathrm{n}} =\:\mathrm{T}_{\mathrm{n}\:−\:\mathrm{1}} \:+\:\mathrm{6},\:\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all}\:\mathrm{values}\: \\ $$$$\mathrm{of}\:\mathrm{n}\:\geqslant\:\mathrm{1},\:\mathrm{T}_{\mathrm{n}} −\:\mathrm{3}\:\:=\:\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{T}_{\mathrm{n}\:−\:\mathrm{3}} \:−\:\mathrm{3}\right).\:\mathrm{Hence}\:\mathrm{or}\:\mathrm{otherwise} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{T}_{\mathrm{1}} \:=\:\mathrm{4},\:\mathrm{T}_{\mathrm{n}} \:=\:\mathrm{3}\:+\:\mathrm{3}^{\mathrm{1}\:−\:\mathrm{n}}…
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Question Number 10480 by ssparasmani@gmail.com last updated on 13/Feb/17 $${d}/{dx}\left(\mathrm{cos}\:^{\mathrm{2}} {xdy}/{dx}\right)=\mathrm{0} \\ $$$$ \\ $$ Answered by mrW1 last updated on 13/Feb/17 $${d}/{dx}\left(\mathrm{cos}\:^{\mathrm{2}} {xdy}/{dx}\right)=\mathrm{0} \\…
Question Number 76014 by Master last updated on 22/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76015 by Master last updated on 22/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141551 by sarkor last updated on 20/May/21 Commented by mr W last updated on 20/May/21 $${you}\:{have}\:{posted}\:{alot}\:{of}\:{posts}\:{which} \\ $$$${are}\:{meaningless},\:{because}\:{it}\:{is}\:{not} \\ $$$${clear}\:{what}\:{your}\:{question}\:{is}. \\ $$ Commented…
Question Number 76012 by mathocean1 last updated on 22/Dec/19 $$\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{1}−\mathrm{3sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}=\frac{\mathrm{5}}{\mathrm{8}}+\frac{\mathrm{3}}{\mathrm{8}}\boldsymbol{\mathrm{cos}}\mathrm{4}\boldsymbol{{x}} \\ $$ Answered by benjo last updated on 22/Dec/19 $$\mathrm{1}−\mathrm{3}/\mathrm{4}\left({sin}^{\mathrm{2}} \mathrm{2}{x}\right)=…
Question Number 10477 by ABCDEFGH last updated on 14/Feb/17 $${maximum}\:{and}\:{minimum}\:{value}\:{of}\: \\ $$$$\mathrm{12}{x}^{\mathrm{5}−\mathrm{5}{x}^{\mathrm{4}_{+\mathrm{40}{x}^{\mathrm{3}_{+\mathrm{6}} } } } } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76013 by vishalbhardwaj last updated on 22/Dec/19 Answered by som(math1967) last updated on 22/Dec/19 $$\left({y}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{4}.\mathrm{3}\left({x}−\mathrm{9}\right) \\ $$$$\therefore{Vertex}\:\left(\mathrm{9},\mathrm{4}\right)\:\:{focus}\left(\mathrm{3}+\mathrm{9}\:,\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\mathrm{12},\mathrm{4}\right) \\ $$$${equation}\:{of}\:{directrix}\:{x}+\mathrm{3}=\mathrm{9} \\…