Question Number 189506 by Rupesh123 last updated on 18/Mar/23 Answered by HeferH last updated on 18/Mar/23 Commented by HeferH last updated on 18/Mar/23 $$\mathrm{Area}\:=\:\mathrm{12}×\mathrm{14}\:−\:\left(\frac{\mathrm{12}×\mathrm{7}+\mathrm{7}×\mathrm{6}+\mathrm{14}×\mathrm{6}}{\mathrm{2}}\right) \\…
Question Number 189464 by Rupesh123 last updated on 17/Mar/23 Answered by Rasheed.Sindhi last updated on 17/Mar/23 $$\mathrm{4}{a}_{{n}+\mathrm{1}} ^{\mathrm{2}} −\mathrm{4}{a}_{{n}} {a}_{{n}+\mathrm{1}} +{a}_{{n}} ^{\mathrm{2}} −\mathrm{1}=\mathrm{0} \\ $$$${n}=\mathrm{1}:…
Question Number 58362 by peter frank last updated on 22/Apr/19 $$\int\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:\mathrm{3}{x}}{dx} \\ $$ Answered by mr W last updated on 22/Apr/19 $$=\int\frac{\mathrm{sin}\:{x}}{\mathrm{3}\:\mathrm{sin}\:{x}−\mathrm{4}\:\mathrm{sin}^{\mathrm{3}} \:{x}}\:{dx} \\ $$$$=\int\frac{\mathrm{1}}{\mathrm{3}−\mathrm{4}\:\mathrm{sin}^{\mathrm{2}}…
Question Number 123869 by benjo_mathlover last updated on 28/Nov/20 Answered by liberty last updated on 29/Nov/20 $${let}\::{a}\:,{ar},{ar}^{\mathrm{2}} ,{ar}^{\mathrm{3}} \:{the}\:{four}\:{consecutive}\:{terms}\:{in}\:{GP} \\ $$$${given}\:{the}\:{condition}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}{u}_{{i}} \:=\:{a}+{ar}+{ar}^{\mathrm{2}} +{ar}^{\mathrm{3}}…
Question Number 189357 by BaliramKumar last updated on 15/Mar/23 $$ \\ $$How many pairs of positive integers x, y exist such that HCF (x, y)…
Question Number 189267 by Rupesh123 last updated on 14/Mar/23 Commented by Rupesh123 last updated on 14/Mar/23 Find the 5-digit number ABCDE such that Answered by HeferH last updated on 14/Mar/23 $$\:\bullet\:\mathrm{E}\:=\:\mathrm{7}…
Question Number 189126 by Mingma last updated on 12/Mar/23 Answered by mr W last updated on 12/Mar/23 $${if}\:\mathrm{6}{k}\leqslant{n}<\mathrm{6}{k}+\mathrm{2}: \\ $$$$\mathrm{3}{k}+\mathrm{2}{k}+{k}={n}\:\Rightarrow{n}=\mathrm{6}{k}\:\checkmark \\ $$$${if}\:\mathrm{6}{k}+\mathrm{2}\leqslant{n}<\mathrm{6}{k}+\mathrm{3}: \\ $$$$\mathrm{3}{k}+\mathrm{1}+\mathrm{2}{k}+{k}={n}\:\Rightarrow{n}=\mathrm{6}{k}+\mathrm{1}\:\rightarrow{bad} \\…
Question Number 123488 by peter frank last updated on 25/Nov/20 Answered by MJS_new last updated on 25/Nov/20 $${x}=\mathrm{sech}\:{y}\:=\frac{\mathrm{1}}{\mathrm{cosh}\:{y}}=\frac{\mathrm{2e}^{{y}} }{\mathrm{e}^{\mathrm{2}{y}} +\mathrm{1}} \\ $$$$\Rightarrow\:{y}=\mathrm{ln}\:\frac{\mathrm{1}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{x}}\:=\mathrm{sech}^{−\mathrm{1}} \:{x} \\…
Question Number 188970 by BaliramKumar last updated on 09/Mar/23 $$\mathrm{LCM}\left({x},\:\mathrm{144},\:\mathrm{150}\right)\:=\:\mathrm{10800}\:{how}\:{many}\:{value}\:{of}\:\:{x}. \\ $$$$ \\ $$ Answered by mr W last updated on 10/Mar/23 $$\mathrm{10800}=\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{3}} ×\mathrm{5}^{\mathrm{2}}…
Question Number 188881 by mnjuly1970 last updated on 08/Mar/23 $$ \\ $$$$\:\:\:\:\mathrm{Q}\::\:\:\mathrm{the}\:\mathrm{non}−\mathrm{zero}\:\mathrm{vector}\:\overset{\rightarrow} {{a}}\:=\:\left({a}_{\mathrm{1}} \:,\:{a}_{\:\mathrm{2}} \:,\:{a}_{\:\mathrm{3}} \:\right)\:\mathrm{with} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{the}\:\:\mathrm{coordinate}\:\mathrm{axes}\:\mathrm{makes}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{angles}\:\:,\:\:\alpha\:\:\:,\:\:\beta\:\:\mathrm{and}\:\:\:\gamma\:.\:\:\mathrm{prove} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{that}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{equality}. \\ $$$$\:\: \\…