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
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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…
Question Number 14920 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{swimmer}\:\mathrm{crosses}\:\mathrm{a}\:\mathrm{flowing}\:\mathrm{river}\:\mathrm{of} \\ $$$$\mathrm{width}\:{d}\:\mathrm{to}\:\mathrm{and}\:\mathrm{fro}\:\mathrm{in}\:\mathrm{time}\:{t}_{\mathrm{1}} .\:\mathrm{The}\:\mathrm{time} \\ $$$$\mathrm{taken}\:\mathrm{to}\:\mathrm{cover}\:\mathrm{the}\:\mathrm{same}\:\mathrm{distance}\:\mathrm{up} \\ $$$$\mathrm{and}\:\mathrm{down}\:\mathrm{the}\:\mathrm{stream}\:\mathrm{is}\:{t}_{\mathrm{2}} .\:\mathrm{If}\:{t}_{\mathrm{3}} \:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{time}\:\mathrm{the}\:\mathrm{swimmer}\:\mathrm{would}\:\mathrm{take}\:\mathrm{to}\:\mathrm{swim} \\ $$$$\mathrm{a}\:\mathrm{distance}\:\mathrm{2}{d}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{t}_{\mathrm{1}}…
Question Number 14882 by Tinkutara last updated on 05/Jun/17 $$\mathrm{Two}\:\mathrm{vectors}\:\overset{\rightarrow} {{a}}\:\mathrm{and}\:\overset{\rightarrow} {{b}}\:\mathrm{are}\:\mathrm{parallel}\:\mathrm{and} \\ $$$$\mathrm{have}\:\mathrm{same}\:\mathrm{magnitude}.\:\mathrm{Then}\:\mathrm{they} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{have}\:\mathrm{same}\:\mathrm{direction},\:\mathrm{but}\:\mathrm{they}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{equal} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{are}\:\mathrm{equal} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{are}\:\mathrm{not}\:\mathrm{equal} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{may}\:\mathrm{or}\:\mathrm{may}\:\mathrm{not}\:\mathrm{be}\:\mathrm{equal} \\…
Question Number 14876 by 1kanika# last updated on 05/Jun/17 Terms of Service Privacy Policy Contact: info@tinkutara.com