Question Number 224146 by hardmath last updated on 22/Aug/25 $$\boldsymbol{\mathrm{a}}\:=\:\mathrm{12}^{\mathrm{223}} \:\centerdot\:\mathrm{7}^{\mathrm{56}} \:+\:\mathrm{19}^{\mathrm{25}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}? \\ $$ Answered by Ghisom_ last updated on 23/Aug/25 $$\mathrm{12}^{\mathrm{223}} \:\mathrm{has}\:\mathrm{the}\:\mathrm{same}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{as}\:\mathrm{2}^{\mathrm{223}}…
Question Number 224124 by klipto last updated on 21/Aug/25 $$\int_{−\mathrm{2}} ^{\mathrm{2}} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}}{\:\sqrt{\mathrm{4}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }} \\ $$ Answered by klipto last updated on 21/Aug/25 $$ \\…
Question Number 224108 by MirHasibulHossain last updated on 21/Aug/25 Answered by mr W last updated on 21/Aug/25 $${i}\:{think}\:{if}\:{the}\:{three}\:{big}\:{blue}\:{circles}\: \\ $$$${have}\:{different}\:{radii}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\: \\ $$$${generally}\:{we}\:{have}…
Question Number 224121 by fantastic last updated on 21/Aug/25 Answered by mr W last updated on 21/Aug/25 $${R}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\frac{\mathrm{1}}{\mathrm{10}×\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}×\mathrm{10}}}−\frac{\mathrm{1}}{\mathrm{10}}−\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{2}}}=\mathrm{15} \\ $$$$\pi{R}^{\mathrm{2}} =\mathrm{225}\pi\:\checkmark \\ $$ Commented by…
Question Number 224122 by fantastic last updated on 21/Aug/25 Commented by fantastic last updated on 21/Aug/25 $${Three}\:{circles}\:{in}\:{a}\:{big}\:{circle} \\ $$$${A}\:{pointed}\:{circle}\:{r}_{\mathrm{1}} \\ $$$${B}\:{pointed}\:{circle}\:{r}_{\mathrm{2}} \\ $$$${C}\:{pointed}\:{circle}\:{r}_{\mathrm{3}} \\ $$$${R}=?…
Question Number 224118 by fantastic last updated on 21/Aug/25 Answered by mr W last updated on 22/Aug/25 $${R}=\mathrm{12} \\ $$$$\mathrm{2}{b}={R}\:\Rightarrow{b}=\frac{{R}}{\mathrm{2}} \\ $$$$\left({a}+{b}\right)^{\mathrm{2}} ={b}^{\mathrm{2}} +\left({R}−{a}\right)^{\mathrm{2}} \\…
Question Number 224113 by fantastic last updated on 21/Aug/25 $${Guys}\:{my}\:{exams}\:{are}\:{finished}\:! \\ $$$${I}\:{will}\:{be}\:{active}\:{as}\:{usual}! \\ $$$$\left.:\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 224106 by OmoloyeMichael last updated on 20/Aug/25 Commented by OmoloyeMichael last updated on 20/Aug/25 $$\boldsymbol{{how}}\:\boldsymbol{{to}}\:\boldsymbol{{prove}}\:\boldsymbol{{this}}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 224095 by fitraha last updated on 19/Aug/25 $${how}\:{to}\:{prove}\:{that}\:\:{x}\:+\:\mathrm{9}\:=\:{x}\:{is}\:{not}\:{has}\:{solution} \\ $$$${because}\: \\ $$$$\left({x}\:+\:\mathrm{9}\right)^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{18}{x}\:+\:\mathrm{81}\:=\:{x}^{\mathrm{2}} \\ $$$$\mathrm{18}{x}\:=\:−\mathrm{81} \\ $$$${x}\:=\:−\:\frac{\mathrm{81}}{\mathrm{18}}\:=\:−\frac{\mathrm{9}}{\mathrm{2}} \\ $$ Commented…