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Author: Tinku Tara

prove-curve-x-t-a-r-cos-t-a-2-r-2-2ar-cos-t-y-t-r-sin-t-a-2-r-2-2ar-cos-t-0-t-2pi-is-circle-find-center-amp-radius-

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-209121

Question Number 209121 by Spillover last updated on 02/Jul/24 Answered by Spillover last updated on 04/Jul/24 $${r}={r}_{\mathrm{0}} {e}^{{k}\theta} \\ $$$${In}\:{central}\:{force}\:{field}, \\ $$$${the}\:{angular}\:{momentum}\:{L}\:{is}\:{conserved} \\ $$$${L}={mr}^{\mathrm{2}} \frac{{d}\theta}{{dt}}\:\:\:\:\:{where}\:{m}={mass}\:{of}\:{the}\:{particle}…

Question-209123

Question Number 209123 by Spillover last updated on 02/Jul/24 Answered by A5T last updated on 02/Jul/24 $${max}\left(\mathrm{1000}{x}+\mathrm{600}{c}\right)\:{given}\:{c}\geqslant\mathrm{4}{x}\:{and}\:{x}+{c}\leqslant\mathrm{200} \\ $$$$\mathrm{4}{x}−{c}\leqslant\mathrm{0}\:{and}\:{x}+{c}\leqslant\mathrm{200}\Rightarrow{x}\leqslant\mathrm{40} \\ $$$$\Rightarrow{max}\left(\mathrm{1000}{x}+\mathrm{600}{c}\right)=\mathrm{1000}×\mathrm{40}+\mathrm{600}×\mathrm{160} \\ $$$$=\mathrm{136000}. \\ $$…

The-cost-of-maintaining-a-school-is-partly-constant-and-partly-varies-as-the-number-of-students-With-50-students-the-cost-is-15705-and-with-40-students-the-cost-is-13305-If-the-fee-per-student-is-

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-209098

Question Number 209098 by Spillover last updated on 01/Jul/24 Answered by A5T last updated on 02/Jul/24 $$\mathrm{4}=\frac{{v}_{\mathrm{0}} ^{\mathrm{2}} {sin}^{\mathrm{2}} \theta}{\mathrm{2}{g}}\Rightarrow{sin}\theta=\frac{\sqrt{\mathrm{8}{g}}}{{v}_{\mathrm{0}} } \\ $$$${R}={v}_{\mathrm{0}} {cos}\theta×\mathrm{2}{t}={v}_{\mathrm{0}} \sqrt{\mathrm{1}−\frac{\mathrm{8}{g}}{{v}_{\mathrm{0}}…