Question Number 23253 by ajfour last updated on 28/Oct/17 Commented by ajfour last updated on 28/Oct/17 $${Q}.\mathrm{23251}\:\left({solution}\right) \\ $$ Commented by math solver last updated…
Question Number 88789 by M±th+et£s last updated on 12/Apr/20 $$\int\int{ln}\left({x}+\mathrm{1}\right)\:{dx}\:{dy} \\ $$ Commented by mr W last updated on 13/Apr/20 $$\int\:\mathrm{ln}\left(\mathrm{x}+\mathrm{1}\right)\:\mathrm{dx}\:=\:\int\:\mathrm{ln}\:\mathrm{u}\:\mathrm{du} \\ $$$$….. \\ $$$$=\:\left({x}+\mathrm{1}\right)\:\mathrm{ln}\left({x}+\mathrm{1}\right)−\left({x}+\mathrm{1}\right)+{c}\left({y}\right)…
Question Number 154321 by DELETED last updated on 17/Sep/21 Answered by DELETED last updated on 17/Sep/21 $$\bullet\mathrm{pK}_{\mathrm{1}} =\mathrm{6},\mathrm{08}\:\rightarrow−\mathrm{log}\:\mathrm{K}_{\mathrm{1}} =−\mathrm{log}\:\mathrm{10}^{−\mathrm{6},\mathrm{08}} \\ $$$$\rightarrow\mathrm{K}_{\mathrm{1}} =\mathrm{10}^{−\mathrm{6},\mathrm{08}} \\ $$$$\bullet\mathrm{pK}_{\mathrm{2}} =\mathrm{9},\mathrm{28}\:\rightarrow−\mathrm{log}\:\mathrm{K}_{\mathrm{2}}…
Question Number 23251 by math solver last updated on 28/Oct/17 Commented by math solver last updated on 28/Oct/17 $$\mathrm{q}.\mathrm{19}\:? \\ $$ Terms of Service Privacy…
Question Number 154320 by mathdanisur last updated on 17/Sep/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{2}\:\:\mathrm{then}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}\left(\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \right)}{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{2}} \mathrm{c}\:+\:\mathrm{bc}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$ Answered by ghimisi last…
Question Number 23250 by Tinkutara last updated on 28/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} ,\:{then}\:{prove}\:{that} \\ $$$$\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left(\frac{{i}}{\:^{{n}} {C}_{{i}} }\:+\:\frac{{j}}{\:^{{n}}…
Question Number 154316 by mathdanisur last updated on 17/Sep/21 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} }\:=\:\mathrm{y}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{xyz}\right)^{\mathrm{2025}} \:-\:\mathrm{1}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 154318 by liberty last updated on 17/Sep/21 Answered by MJS_new last updated on 17/Sep/21 $$\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}\:=\sqrt{\mathrm{2}}\mathrm{sin}\:\frac{\mathrm{4}{x}+\pi}{\mathrm{4}}\:= \\ $$$$\:\:\:\:\:\left[\mathrm{sin}\:\theta\:=\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:\frac{\mathrm{2}\theta−\pi}{\mathrm{4}}\right] \\ $$$$=\sqrt{\mathrm{2}}\left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:\frac{\mathrm{4}{x}−\pi}{\mathrm{8}}\right) \\ $$$$\int\sqrt{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{dx}=…
Question Number 88778 by mathocean1 last updated on 12/Apr/20 Commented by mathocean1 last updated on 13/Apr/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}. \\ $$ Commented by mathmax by abdo last…
Question Number 23243 by paro123 last updated on 27/Oct/17 $$\mathrm{2}^{\mathrm{n}−\mathrm{1}} \mathrm{sin}\:\mathrm{a}×\mathrm{sin}\:\mathrm{2a}×\mathrm{sin}\:\mathrm{3a}×……×\mathrm{sin}\:\left(\mathrm{n}−\mathrm{1}\right)\mathrm{a}=\mathrm{n}\:\mathrm{why}? \\ $$ Commented by mrW1 last updated on 28/Oct/17 $$\mathrm{this}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{wrong}! \\ $$$$ \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{find}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{of}\:\mathrm{examples}:…