Question Number 220745 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $${cosx}+{cosy}={a} \\ $$$$\Rightarrow\mathrm{2}{cos}\left(\frac{{x}+{y}}{\mathrm{2}}\right){cos}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={a}…\left(\mathrm{1}\right) \\ $$$$\:{sinx}+{siny}={b} \\ $$$$\Rightarrow\mathrm{2}{sin}\left(\frac{{x}+{y}}{\mathrm{2}}\right){cos}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={b}\:\:….\left(\mathrm{2}\right) \\ $$$$\therefore\:{tan}\left(\frac{{x}+{y}}{\mathrm{2}}\right)=\frac{{b}}{{a}}\:\:\:\:\:\left[\:\:\left(\mathrm{2}\right)\boldsymbol{\div}\left(\mathrm{1}\right)\:\right]…
Question Number 220715 by Noorzai last updated on 18/May/25 Commented by Noorzai last updated on 18/May/25 $${do}\:{you}\:{help}\:{me} \\ $$$$ \\ $$ Answered by SdC355 last…
Question Number 220740 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $$\mathrm{52}\:{cards}:\:\mathrm{26}\:{red}\:{and}\:\mathrm{26}\:{black} \\ $$$${to}\:{select}\:\mathrm{13}\:{cards}\:{there}\:{are}\:{totally} \\ $$$${C}_{\mathrm{13}} ^{\mathrm{52}} \:{possibilities} \\…
Question Number 220741 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $$\:\:^{\mathrm{9}} {P}_{\mathrm{4}} =\mathrm{3024} \\ $$ Commented by Spillover last…
Question Number 220743 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $$\:{No}\:{of}\:{way}\:\mathrm{4}\:{soldiers}\:{can}\:{be}\:{chosen} \\ $$$$=\:^{\mathrm{9}} {C}_{\mathrm{4}} =\mathrm{126} \\ $$$${when}\:{particular}\:{soldier}\:{included} \\ $$$$=\:^{\mathrm{8}}…
Question Number 220769 by hardmath last updated on 18/May/25 Answered by mr W last updated on 18/May/25 Commented by mr W last updated on 18/May/25…
Question Number 220737 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $$\:\mathrm{0}.\overset{.} {\mathrm{6}}=\mathrm{0}.\mathrm{6}+\mathrm{0}.\mathrm{06}+\mathrm{0}.\mathrm{006}+… \\ $$$$=\frac{\mathrm{0}.\mathrm{6}}{\mathrm{1}−.\mathrm{1}}=\frac{\mathrm{6}}{\mathrm{9}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$ Commented by Spillover…
Question Number 220770 by mnjuly1970 last updated on 18/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{sin}\left({x}\right)}{\:\sqrt{\mathrm{1}\:+\sqrt{{sin}\left(\mathrm{2}{x}\right)}}}{dx}\: \\ $$ Answered by Ghisom last updated on 21/May/25 $${F}\left({x}\right)=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}}…
Question Number 220738 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $${a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{n}} +…=\frac{{a}_{\mathrm{1}} }{\mathrm{1}−{q}}={k} \\ $$$${a}_{\mathrm{1}} ^{\mathrm{2}}…
Question Number 220739 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $$\left.\mathrm{1}\right) \\ $$$$\frac{\mathrm{7}!}{\mathrm{2}!\mathrm{2}!}=\mathrm{1260} \\ $$$$\left.\mathrm{2}\right) \\ $$$$\mathrm{1260}−\mathrm{2}×\frac{\mathrm{6}!}{\mathrm{2}!\mathrm{2}!}=\mathrm{1260}−\mathrm{360}=\mathrm{900} \\…