Question Number 55482 by pooja24 last updated on 25/Feb/19 $${A}\:{group}\:{of}\:{n}\:{students}\:{are}\:{numbered} \\ $$$${continously}\:{from}\:{first}\:{sdtudent}\:{as}\:\mathrm{1},\mathrm{2},\mathrm{3},…… \\ $$$${If}\:\mathrm{1101}\:{digits}\:{had}\:{to}\:{be}\:{used}\:{in}\:{all},{what}\:{is}\:{the}\: \\ $$$${number}\:{of}\:{students}\:{in}\:{the}\:{group} \\ $$ Answered by mr W last updated on…
Question Number 186544 by ajfour last updated on 05/Feb/23 Commented by ajfour last updated on 05/Feb/23 $${If}\:{the}\:{cubic}\:{curve}\:{is}\:\:{y}={x}^{\mathrm{3}} −{x}−{c} \\ $$$${with},\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\:\:;\:{and}\: \\ $$$${the}\:{parabola}\:{be}\:\:{y}=\left({x}−{h}\right)^{\mathrm{2}} \\ $$$${Then}\:{find}\:{h}. \\…
Question Number 186540 by akuba last updated on 05/Feb/23 $${Complex}\:{Numbers} \\ $$$${Prove}\:{that} \\ $$$$\:\mathrm{1}.\:\mid{Z}_{\mathrm{1}} +{Z}_{\mathrm{2}} \mid\leq\mid{Z}_{\mathrm{1}} \mid+\mid{Z}_{\mathrm{2}} \mid \\ $$$$\mathrm{2}.\:\mid{Z}_{\mathrm{1}} −{Z}_{\mathrm{2}} \mid\geq\mid{Z}_{\mathrm{1}} \mid−\mid{Z}_{\mathrm{2}} \mid \\…
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Question Number 120984 by pooooop last updated on 04/Nov/20 $$\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{4}\centerdot\mathrm{7}}\:+\:\frac{\mathrm{1}}{\mathrm{4}\centerdot\mathrm{7}\centerdot\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{7}\centerdot\mathrm{10}\centerdot\mathrm{13}}+…+\frac{\mathrm{1}}{\mathrm{25}\centerdot\mathrm{28}\centerdot\mathrm{31}}=\:? \\ $$ Answered by Dwaipayan Shikari last updated on 04/Nov/20 $${T}_{{n}} =\frac{\mathrm{1}}{\left(\mathrm{3}{n}−\mathrm{2}\right)\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{4}\right)} \\ $$$$\overset{{n}} {\sum}{T}_{{n}}…
Question Number 186503 by mnjuly1970 last updated on 05/Feb/23 $$ \\ $$$$\:\:\:{function}\:{of}\:,\:{f}\:\left({x}\right)\:=\:{ax}\:\:+\:\mid\:{x}\:\mid\:{is}\:\:{one}\:{to}\:{one} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:.{find}\:\:\:\:''\:\:\:\:{a}\:\:\:\:''\:\:. \\ $$$$\:\: \\ $$ Commented by Frix last updated…
Question Number 120960 by Jamshidbek2311 last updated on 04/Nov/20 $${If}\:{x},{y},{z}>\mathrm{0}\:\:{then}\:{prove}\:{following} \\ $$$${inequality} \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({y}^{\mathrm{2}} +\mathrm{2}\right)\left({z}^{\mathrm{2}} +\mathrm{2}\right)\geqslant\mathrm{9}\left({xy}+{yz}+{xz}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 186489 by Mingma last updated on 05/Feb/23 Answered by Frix last updated on 06/Feb/23 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{1981}^{\mathrm{2}} =\mathrm{7}^{\mathrm{2}} ×\mathrm{283}^{\mathrm{2}} \\ $$$$\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}}…
Question Number 120953 by bemath last updated on 04/Nov/20 $$\mathrm{solve}\:\mathrm{in}\:\mathrm{x}\in\mathbb{R} \\ $$$$\mid\:\mathrm{3x}−\mathrm{4}\:\mid\:=\:\mathrm{x}−\mathrm{5}\: \\ $$ Answered by TANMAY PANACEA last updated on 04/Nov/20 $${when}\:\left(\mathrm{3}{x}−\mathrm{4}\right)>\mathrm{0}\rightarrow\:\:\:\:{x}>\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\left(\mathrm{3}{x}−\mathrm{4}\right)={x}−\mathrm{5}…
Question Number 186486 by a.lgnaoui last updated on 05/Feb/23 $${Question}\:{propose}\:{par} \\ $$$${Migma} \\ $$$$−−−−−−−−−−− \\ $$$${calcul}\:{de}\:{X} \\ $$$$ \\ $$$$\bigtriangleup{ABC}\:\:\:\:\:\:\measuredangle{ACB}=\mathrm{40}^{°} \\ $$$$\mathrm{AB}^{\mathrm{2}} =\mathrm{AC}^{\mathrm{2}} +\mathrm{BC}^{\mathrm{2}} −\mathrm{2AC}×\mathrm{BCcos}\:\mathrm{40}\:\:\:\:…