Question Number 209131 by mahdipoor last updated on 02/Jul/24 $${prove}\:: \\ $$$${curve}\:\begin{cases}{{x}\left({t}\right)=\frac{{a}+{r}.{cos}\left({t}\right)}{{a}^{\mathrm{2}} +{r}^{\mathrm{2}} +\mathrm{2}{ar}.{cos}\left({t}\right)}}\\{{y}\left({t}\right)=\frac{{r}.{sin}\left({t}\right)}{{a}^{\mathrm{2}} +{r}^{\mathrm{2}} +\mathrm{2}{ar}.{cos}\left({t}\right)}}\end{cases}\:\:\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2}\pi \\ $$$${is}\:{circle}\:,\:{find}\:{center}\:\&\:{radius} \\ $$ Answered by Frix last updated…
Question Number 209072 by Tawa11 last updated on 01/Jul/24 Commented by A5T last updated on 01/Jul/24 $${What}\:{are}\:{the}\:{rules}\:{of}\:{the}\:“{game}''? \\ $$ Commented by Tawa11 last updated on…
Question Number 209065 by necx122 last updated on 01/Jul/24 $${The}\:{cost}\:{of}\:{maintaining}\:{a}\:{school}\:{is} \\ $$$${partly}\:{constant}\:{and}\:{partly}\:{varies}\:{as} \\ $$$${the}\:{number}\:{of}\:{students}.\:{With}\:\mathrm{50}\:{students} \\ $$$${the}\:{cost}\:{is}\:\$\mathrm{15705}\:{and}\:{with}\:\mathrm{40}\:{students} \\ $$$${the}\:{cost}\:{is}\:\$\mathrm{13305}.\:{If}\:{the}\:{fee}\:{per}\:{student} \\ $$$${is}\:\$\mathrm{360}.\mathrm{00},\:{what}\:{is}\:{the}\:{least}\:{number}\:{of} \\ $$$${students}\:{for}\:{which}\:{the}\:{school}\:{can}\:{be} \\ $$$${run}\:{without}\:{loss}? \\…
Question Number 209062 by hardmath last updated on 01/Jul/24 Answered by som(math1967) last updated on 01/Jul/24 $$\:{x}^{{y}^{{z}} } =\mathrm{1} \\ $$$$\:{x},{y},{z}\:\in{N}\:\Rightarrow\mathrm{1}^{{y}^{{z}} } =\mathrm{1}\:\Rightarrow{x}=\mathrm{1} \\ $$$$\:{y}^{{z}^{{x}}…
Question Number 209059 by hardmath last updated on 01/Jul/24 $$\mathrm{Compare}: \\ $$$$\mathrm{8}!\:\:\:\mathrm{and}\:\:\:\mathrm{8}!! \\ $$ Commented by mr W last updated on 01/Jul/24 $${if}\:\frac{{a}}{{b}}=\mathrm{1}\:\Rightarrow{a}={b} \\ $$$$\frac{\cancel{\mathrm{8}!}!}{\cancel{\mathrm{8}!}}=\mathrm{1}!=\mathrm{1}\:\Rightarrow\mathrm{8}!!=\mathrm{8}!\:\:\:\:\:\underset{\mid<>\mid}…
Question Number 209055 by hardmath last updated on 30/Jun/24 Commented by hardmath last updated on 30/Jun/24 $$\mathrm{dear}\:\mathrm{professor}\:\mathrm{mr}\:\mathrm{W} \\ $$ Commented by mr W last updated…
Question Number 209021 by hardmath last updated on 30/Jun/24 k part, that is, l > a1+a2+…+ak is given, that is, we have enough seats. ”…
Question Number 208959 by hardmath last updated on 28/Jun/24 $$\mathrm{If}\:\:\:\boldsymbol{\mathrm{z}}\:=\:−\:\frac{\mathrm{1}}{\mathrm{2}}\:\:+\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\boldsymbol{\mathrm{i}} \\ $$$$\mathrm{Find}\:\:\:\left(\mathrm{z}^{\mathrm{4}} \:+\:\mathrm{2z}\right)\centerdot\left(\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{z}\right)\:=\:? \\ $$ Answered by grigoriy last updated on 29/Jun/24 $$ \\…
Question Number 208951 by hardmath last updated on 28/Jun/24 $$\mathrm{2}^{\mathrm{2024}} \::\:\mathrm{2024}\:=\:…\:\left(\mathrm{Remainder}\:=\:?\right) \\ $$ Answered by A5T last updated on 28/Jun/24 $$\left(\mathrm{2}^{\mathrm{11}} \right)^{\mathrm{184}} \:\:\overset{\mathrm{2024}} {\equiv}\:\mathrm{24}^{\mathrm{184}} \\…
Question Number 208945 by hardmath last updated on 28/Jun/24 $$\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{x}\:−\:\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{3x}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{3x}\:=\:\mathrm{0} \\ $$$$\left[\:\mathrm{0}\:;\:\frac{\pi}{\mathrm{2}}\:\right] \\ $$$$\mathrm{Find}:\:\:\mathrm{x}\:=\:? \\ $$ Answered by Berbere last updated on…