Question Number 104260 by Anindita last updated on 20/Jul/20 $$\mathrm{You}\:\mathrm{bought}\:\mathrm{3g}\:\mathrm{rice},\:\mathrm{5g}\:\mathrm{flour}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{market}.\:\mathrm{At}\:\mathrm{first}\:\mathrm{you}\:\mathrm{had}\:\mathrm{500}\:\mathrm{rupees}. \\ $$$$\mathrm{Now}\:\mathrm{you}\:\mathrm{have}\:\mathrm{300}\:\mathrm{rupees}.\:\mathrm{How}\:\mathrm{much} \\ $$$$\mathrm{rupees}\:\mathrm{you}\:\mathrm{wasted}?\:\mathrm{Suppose}\:\mathrm{you} \\ $$$$\mathrm{distribute}\:\mathrm{the}\:\mathrm{300}\:\mathrm{rupees}\:\mathrm{among} \\ $$$$\mathrm{your}\:\mathrm{4}\:\mathrm{sons}.\:\mathrm{Now}\:\mathrm{how}\:\mathrm{much}\:\mathrm{rupees} \\ $$$$\mathrm{does}\:\mathrm{your}\:\mathrm{one}\:\mathrm{son}\:\mathrm{get}? \\ $$ Commented…
Question Number 104251 by Anindita last updated on 20/Jul/20 $$\mathrm{If}\:{x}=\mathrm{8}\:\mathrm{and}\:{y}=\mathrm{5}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\:\frac{{x}+{y}+\mathrm{6}}{{x}^{\mathrm{2}} −{y}^{\mathrm{3}} }\:? \\ $$ Answered by mathmax by abdo last updated on 20/Jul/20…
Question Number 104253 by Anindita last updated on 20/Jul/20 $$\mathrm{When}\:{a}\ast{b}=\:\frac{{a}+{b}}{{a}−{b}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\mathrm{2}\ast\mathrm{3}×\mathrm{9}\ast\mathrm{10}\:? \\ $$ Commented by som(math1967) last updated on 20/Jul/20 $$\frac{\mathrm{2}+\mathrm{3}}{\mathrm{2}−\mathrm{3}}×\frac{\mathrm{9}+\mathrm{10}}{\mathrm{9}−\mathrm{10}}=\frac{\mathrm{5}}{−\mathrm{1}}×\frac{\mathrm{19}}{−\mathrm{1}}=\mathrm{95} \\ $$ Answered…
Question Number 104246 by Anindita last updated on 20/Jul/20 $$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)….\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{99}}\right)\:=? \\ $$ Answered by mathmax by abdo last updated on 20/Jul/20 $$\mathrm{let}\:\mathrm{A}_{\mathrm{n}} =\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)….\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{n}}\right)\:\Rightarrow\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{4}}{\mathrm{5}}×…\frac{\mathrm{n}−\mathrm{2}}{\mathrm{n}−\mathrm{1}}×\frac{\mathrm{n}−\mathrm{1}}{\mathrm{n}} \\…
Question Number 104243 by M±th+et+s last updated on 20/Jul/20 $${prove}\:{that} \\ $$$$\pi=\mathrm{2}×\frac{\mathrm{2}}{\:\sqrt{\mathrm{2}}}×\frac{\mathrm{2}}{\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}×\frac{\mathrm{2}}{\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}}×….. \\ $$ Answered by OlafThorendsen last updated on 20/Jul/20 $$\mathrm{sin}{x}\:=\:\mathrm{2sin}\frac{{x}}{\mathrm{2}}\mathrm{cos}\frac{{x}}{\mathrm{2}} \\ $$$$\mathrm{sin}{x}\:=\:\mathrm{2}^{\mathrm{2}} \mathrm{sin}\frac{{x}}{\mathrm{4}}\mathrm{cos}\frac{{x}}{\mathrm{4}}\mathrm{cos}\frac{{x}}{\mathrm{2}}…
Question Number 169768 by mnjuly1970 last updated on 08/May/22 $$\:\:\: \\ $$$$\:\:\:\left[{x}\right]+\left[{x}+\frac{\mathrm{1}}{\mathrm{2}}\right]+\left[{x}−\frac{\mathrm{1}}{\mathrm{3}}\right]=\:\mathrm{8} \\ $$$$\:\:\:\:\:\left[\mathrm{2}{x}\right]=\mathrm{8}−\left[{x}−\frac{\mathrm{1}}{\mathrm{3}}\right]={k} \\ $$$$\:\:\:\:\:\:\:\:\:\frac{{k}}{\mathrm{2}}\leqslant{x}<\frac{{k}+\mathrm{1}}{\mathrm{2}}\:,\:\:\:\:\:\mathrm{8}−{k}+\frac{\mathrm{1}}{\mathrm{3}}\leqslant{x}\:<\mathrm{9}−{k}+\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{{k}}{\mathrm{2}}\:<\:\frac{\mathrm{28}−\mathrm{3}{k}}{\mathrm{3}}\:\:\Rightarrow\:\mathrm{9}{k}\:<\:\mathrm{56} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{k}\:<\frac{\mathrm{56}}{\mathrm{9}}\:\:\:\:\bigstar \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{25}}{\mathrm{3}}\:−{k}<\frac{{k}+\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:\mathrm{50}−\mathrm{6}{k}<\mathrm{3}{k}+\mathrm{3} \\ $$$$\:\:\:\:\Rightarrow\:\:\:\:\:\frac{\mathrm{47}}{\mathrm{9}}\:<{x}\:\:\bigstar\bigstar \\…
Question Number 104235 by bemath last updated on 20/Jul/20 $${If}\:{you}\:{are}\:{given}\:{a}\:{triangle} \\ $$$${with}\:{side}\:{length}\:\mathrm{15}\:,\:\mathrm{20}\:{and} \\ $$$$\mathrm{25}.\:{what}\:{is}\:{the}\:{triangle}'{s} \\ $$$${shortest}\:{altitude}? \\ $$ Answered by nimnim last updated on 20/Jul/20…
Question Number 38696 by Sr@2004 last updated on 28/Jun/18 Answered by tanmay.chaudhury50@gmail.com last updated on 28/Jun/18 $$\frac{\mathrm{1}}{{b}+{c}}+\frac{\mathrm{1}}{{c}+{a}}=\frac{\mathrm{2}}{{a}+{b}} \\ $$$$\frac{\mathrm{1}}{{b}+{c}}−\frac{\mathrm{1}}{{a}+{b}}=\frac{\mathrm{1}}{{a}+{b}}−\frac{\mathrm{1}}{{c}+{a}} \\ $$$$\frac{{a}+{b}−{b}−{c}}{\left({a}+{b}\right)\left({b}+{c}\right)}=\frac{{c}+{a}−{a}−{b}}{\left({a}+{b}\right)\left({c}+{a}\right)} \\ $$$$\frac{{a}−{c}}{{b}+{c}}=\frac{{c}−{b}}{{c}+{a}} \\ $$$${a}^{\mathrm{2}}…
Question Number 169760 by Shrinava last updated on 07/May/22 $$\mathrm{Find}\:\:\boldsymbol{\mathrm{x}} \\ $$$$\left(\mathrm{5}\:-\:\mathrm{2x}\right)\left(\mathrm{5}\:+\:\mathrm{2}\:\sqrt{\mathrm{4}\:-\:\mathrm{2x}^{\mathrm{2}} }\right)\:=\:\mathrm{25} \\ $$ Answered by MJS_new last updated on 08/May/22 $$\mathrm{no}\:“\mathrm{nice}''\:\mathrm{solution},\:\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$$$\mathrm{I}\:\mathrm{found}…
Question Number 104201 by I want to learn more last updated on 20/Jul/20 $$\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{1}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{b}\:\:+\:\:\mathrm{ic}\:\:=\:\:\left(\mathrm{1}\:\:+\:\:\mathrm{a}\right)\mathrm{z}, \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\:\frac{\mathrm{a}\:\:+\:\:\mathrm{ib}}{\mathrm{i}\:\:+\:\:\mathrm{c}}\:\:\:=\:\:\:\frac{\mathrm{1}\:\:+\:\:\mathrm{iz}}{\mathrm{1}\:\:−\:\:\mathrm{iz}} \\ $$ Terms of Service Privacy…