Question Number 150313 by dany last updated on 11/Aug/21 Answered by ajfour last updated on 11/Aug/21 $${f}\left({x}−{y}\right)={f}\left({x}\right){f}\left({y}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−{f}\left({a}−{x}\right){f}\left({a}+{y}\right) \\ $$$${y}=\mathrm{0} \\ $$$$\cancel{{f}\left({x}\right)}=\cancel{{f}\left({x}\right)}−{f}\left({a}−{x}\right){f}\left({a}\right) \\ $$$$\Rightarrow\:\:{f}\left({a}−{x}\right)=\mathrm{0}\:\:{and}/{or}\:{f}\left({a}\right)=\mathrm{0}…
Question Number 84778 by abdomathmax last updated on 16/Mar/20 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}+{sinx}} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 19243 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}\:{a},\:{b},\:{c}\:\mathrm{be}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{opposite}\:\mathrm{the} \\ $$$$\mathrm{angles}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{respectively}\:\mathrm{of}\:\mathrm{a} \\ $$$$\Delta\mathrm{ABC}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:{a}\:+\:{b}\:=\:{kc} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{cot}\:\frac{{A}}{\mathrm{2}}\:+\:\mathrm{cot}\:\frac{{B}}{\mathrm{2}}\:=\:{k}\:\mathrm{cot}\:\frac{{C}}{\mathrm{2}}. \\ $$ Commented by Tinkutara last updated…
Question Number 150312 by naka3546 last updated on 11/Aug/21 $${Find}\:\:{n}\:\:{lowest}\:\:{integers}\:\:{that}\:\:{divide}\:\:\left(\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\ldots+\:{n}^{\mathrm{2}} \right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 19239 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Assume}\:\mathrm{that}\:{a},\:{b},\:{c}\:\mathrm{and}\:{d}\:\mathrm{are}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:{a}^{\mathrm{5}} \:=\:{b}^{\mathrm{4}} ,\:{c}^{\mathrm{3}} \:=\:{d}^{\mathrm{2}} \:\mathrm{and} \\ $$$${c}\:−\:{a}\:=\:\mathrm{19}.\:\mathrm{Determine}\:{d}\:−\:{b}. \\ $$ Answered by ajfour last updated…
Question Number 150308 by ajfour last updated on 11/Aug/21 Commented by ajfour last updated on 11/Aug/21 $$\:\:{Q}.\mathrm{149894}\:\left({revisit}\right) \\ $$ Answered by ajfour last updated on…
Question Number 19238 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{parallelogram}.\:\mathrm{Two} \\ $$$$\mathrm{points}\:{E}\:\mathrm{and}\:{F}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sides} \\ $$$${BC}\:\mathrm{and}\:{CD},\:\mathrm{respectively},\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{{EB}}{{EC}}\:=\:{m},\:\mathrm{and}\:\frac{{FC}}{{FD}}\:=\:{n}.\:\mathrm{Lines}\:{AE}\:\mathrm{and}\:{BF} \\ $$$$\mathrm{intersect}\:\mathrm{at}\:{G}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\frac{{AG}}{{GE}}\:=\:\frac{\left({m}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{1}\right)}{{mn}}. \\ $$ Commented by ajfour…
Question Number 150311 by naka3546 last updated on 11/Aug/21 $${x},{y}\:\in\:\mathbb{R} \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right)\:\centerdot\:{f}\left({y}\right)\:−\:{f}\left({x}\:\centerdot\:{y}\right)\:+\:\mathrm{1} \\ $$$$ \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({f}\left({x}\right)\right)\:=\:{f}\left({x}\right)\:+\:{x} \\ $$ Answered by aleks041103…
Question Number 19236 by chernoaguero@gmail.com last updated on 07/Aug/17 Answered by ,25>( last updated on 07/Aug/17 $${x}\:=\:\mathrm{2}\:\mathrm{since}\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:=\:\mathrm{13}. \\ $$ Commented by chernoaguero@gmail.com last…
Question Number 150305 by Tawa11 last updated on 10/Aug/21 Commented by Tawa11 last updated on 10/Aug/21 $$\mathrm{Find}\:\:\:\:\frac{\mathrm{R}}{\mathrm{r}} \\ $$ Answered by nimnim last updated on…