Question Number 15284 by ajfour last updated on 09/Jun/17 Commented by ajfour last updated on 09/Jun/17 $${Q}.\mathrm{14940}\:\:\left({general}\:{proof}\::\:{sides}\:\right. \\ $$$$\left.\:{of}\:\Delta{ABC}\:{divided}\:{in}\:\boldsymbol{{n}}\:{equal}\:{parts}\right) \\ $$ Commented by RasheedSoomro last…
Question Number 146315 by mnjuly1970 last updated on 12/Jul/21 Answered by Olaf_Thorendsen last updated on 13/Jul/21 $$\sqrt{\frac{{x}\left({x}+\mathrm{5}\right)}{{x}+\mathrm{2}}}+\sqrt{{x}+\mathrm{3}}\:=\:\frac{\sqrt{\mathrm{16}{x}+\mathrm{32}}}{{x}+\mathrm{2}} \\ $$$$\sqrt{\frac{{x}\left({x}+\mathrm{5}\right)}{{x}+\mathrm{2}}}+\sqrt{{x}+\mathrm{3}}\:=\:\frac{\mathrm{4}}{\:\sqrt{{x}+\mathrm{2}}} \\ $$$$\sqrt{{x}\left({x}+\mathrm{5}\right)}+\sqrt{\left({x}+\mathrm{3}\right)\left({x}+\mathrm{2}\right)}\:=\:\mathrm{4} \\ $$$$\mathrm{Let}\:{u}\:=\:{x}+\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$\sqrt{\left({u}−\frac{\mathrm{5}}{\mathrm{2}}\right)\left({u}+\frac{\mathrm{5}}{\mathrm{2}}\right)}+\sqrt{\left({u}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left({u}−\frac{\mathrm{1}}{\mathrm{2}}\right)}\:=\:\mathrm{4}…
Question Number 15206 by tawa tawa last updated on 08/Jun/17 $$\mathrm{If}\:\:\:\mathrm{z}\:=\:\mathrm{x}\:+\:\mathrm{jy},\:\:\mathrm{detemine}\:\mathrm{the}\:\mathrm{cartesian}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\: \\ $$$$\mathrm{z}\:\mathrm{which}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{the}\:\mathrm{Argrand}\:\mathrm{diagram}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mid\mathrm{z}\:+\:\mathrm{j2}\mid^{\mathrm{2}} \:+\:\mid\mathrm{z}\:−\:\mathrm{j2}\mid^{\mathrm{2}\:} =\:\mathrm{40} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 15202 by tawa tawa last updated on 08/Jun/17 $$\mathrm{if}\:\mathrm{z}\:=\:\mathrm{x}\:+\:\mathrm{jy}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{loci}\:\mathrm{defined}\:\mathrm{by}: \\ $$$$\left(\mathrm{a}\right)\:\mid\mathrm{z}\:−\:\mathrm{4}\mid\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\left(\mathrm{b}\right)\:\mathrm{arg}\left(\mathrm{z}\:+\:\mathrm{2}\right)\:=\:\frac{\pi}{\mathrm{6}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 15172 by tawa tawa last updated on 07/Jun/17 $$\mathrm{If}\:\:\mathrm{z}\:=\:\mathrm{x}\:+\:\mathrm{jy},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{arg}\left\{\frac{\mathrm{z}\:−\:\mathrm{1}}{\mathrm{z}\:−\:\mathrm{j}}\right\}\:=\:\frac{\pi}{\mathrm{6}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:.\:\mathrm{Find}\:\mathrm{its}\:\mathrm{centre} \\ $$$$\mathrm{and}\:\mathrm{radius}.\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 80642 by naaz last updated on 05/Feb/20 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 14939 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{point}\:\mathrm{moves}\:\mathrm{in}\:{x}-{y}\:\mathrm{plane}\:\mathrm{according} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{law}\:{x}\:=\:\mathrm{4}\:\mathrm{sin}\:\mathrm{6}{t}\:\mathrm{and} \\ $$$${y}\:=\:\mathrm{4}\left(\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{6}{t}\right).\:\mathrm{Find}\:\mathrm{distance}\:\mathrm{traversed} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{in}\:\mathrm{5}\:\mathrm{seconds},\:\mathrm{when}\:{x}\:\mathrm{and} \\ $$$${y}\:\mathrm{are}\:\mathrm{in}\:\mathrm{metres}. \\ $$ Answered by ajfour last updated…
Question Number 14923 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{inclined}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}° \\ $$$$\mathrm{with}\:\mathrm{horizontal}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{force}\:\overset{\rightarrow} {{F}}\:=\:−\mathrm{10}\overset{\wedge} {{k}}\mathrm{N}\:\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{plane}.\:\mathrm{Given}\:\mathrm{that}\:{z}-\mathrm{direction}\:\mathrm{is} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}. \\ $$ Answered by ajfour…
Question Number 14921 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{car}\:\mathrm{travelling}\:\mathrm{at}\:\mathrm{36}\:\mathrm{km}/\mathrm{h}\:\mathrm{due}\:\mathrm{North} \\ $$$$\mathrm{turns}\:\mathrm{West}\:\mathrm{in}\:\mathrm{5}\:\mathrm{seconds}\:\mathrm{and}\:\mathrm{maintains} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{speed}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{car}? \\ $$ Commented by ajfour last updated on 05/Jun/17…
Question Number 14922 by Tinkutara last updated on 05/Jun/17 $$\mathrm{The}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{particle}\:{P}\:\mathrm{due}\:\mathrm{East}\:\mathrm{is} \\ $$$$\mathrm{4}\:\mathrm{m}/\mathrm{s},\:\mathrm{and}\:\mathrm{that}\:\mathrm{of}\:{Q}\:\mathrm{is}\:\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{due} \\ $$$$\mathrm{South}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:{P}\:\mathrm{w}.\mathrm{r}.\mathrm{t}. \\ $$$${Q}? \\ $$ Commented by ajfour last updated on 05/Jun/17…