Question Number 113080 by bobhans last updated on 11/Sep/20 $$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{is} \\ $$$$\mathrm{84}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{it}'\mathrm{s}\:\mathrm{area}\:\mathrm{is}\:\mathrm{336}\:\mathrm{square}\:\mathrm{cm}.\:\mathrm{If}\:\mathrm{the}\: \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{one}\:\mathrm{side}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{30}\:\mathrm{cm},\:\mathrm{then} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{two} \\ $$$$\mathrm{sides}\:\mathrm{of}\:\mathrm{triangle}\:? \\ $$ Answered by bemath last updated…
Question Number 113059 by bemath last updated on 11/Sep/20 Answered by john santu last updated on 11/Sep/20 $$\:\frac{\mathrm{1}}{\mathrm{2}.\mathrm{3}.\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{3}.\mathrm{4}.\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{5}.\mathrm{6}.\mathrm{7}}\:= \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}\frac{\mathrm{1}}{\left({k}+\mathrm{1}\right).\left({k}+\mathrm{2}\right).\left({k}+\mathrm{3}\right)}\: \\ $$$$\frac{\mathrm{1}}{\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)\left({k}+\mathrm{3}\right)}=\frac{{p}}{{k}+\mathrm{1}}+\frac{{q}}{{k}+\mathrm{2}}+\frac{{r}}{{k}+\mathrm{3}} \\…
Question Number 47513 by ajfour last updated on 11/Nov/18 Commented by ajfour last updated on 11/Nov/18 $${Find}\:{coordinates}\:{of}\:{all}\:{points} \\ $$$${that}\:{have}\:{same}\:\bot\:{distance}\:{from} \\ $$$${from}\:{the}\:{three}\:{lines}. \\ $$$${For}\:{each}\:{such}\:{point}\:{this}\:\bot \\ $$$${distance}\:{may}\:{differ}.…
Question Number 47480 by ajfour last updated on 10/Nov/18 Answered by MrW3 last updated on 10/Nov/18 $${assume}\:{the}\:{major}\:{and}\:{minor}\:{axes} \\ $$$${are}\:{parallel}\:{to}\:{x}\:{axis}\:{and}\:{y}\:{axis}. \\ $$$${eqn}. \\ $$$$\frac{\left({x}−{h}\right)^{\mathrm{2}} }{{u}^{\mathrm{2}} }+\frac{\left({y}−{k}\right)^{\mathrm{2}}…
Question Number 47457 by rahul 19 last updated on 10/Nov/18 $${A}\:{straight}\:{line}\:{through}\:\left(\mathrm{2},\mathrm{2}\right)\:{intersects} \\ $$$${lines}\:\sqrt{\mathrm{3}}{x}+{y}=\mathrm{0}\:{and}\:\sqrt{\mathrm{3}}{x}−{y}=\mathrm{0}\:{at}\:{pts}. \\ $$$${A}\:\&\:{B}\:{respectively}.\:{Find}\:{equation} \\ $$$${of}\:{line}\:{AB}\:{so}\:{that}\:\Delta{OAB}\:{is}\:{equilateral}? \\ $$ Answered by rahul 19 last updated…
Question Number 47455 by ajfour last updated on 10/Nov/18 Commented by ajfour last updated on 10/Nov/18 $${Find}\:{maximum}\:{area}\:{of}\:{inscribed} \\ $$$${ellipse}\:{within}\:{AP},\:{BP},\:\&\:{x},{y}\:{axes}. \\ $$ Terms of Service Privacy…
Question Number 47438 by rahul 19 last updated on 10/Nov/18 $${Find}\:{locus}\:{of}\:{a}\:{point}\:{P}\:{which}\:{moves} \\ $$$${such}\:{that}\:{its}\:{distance}\:{from}\:{the}\:{line} \\ $$$${y}=\sqrt{\mathrm{3}}{x}−\mathrm{7}\:{is}\:{same}\:{as}\:{its}\:{distance}\:{from} \\ $$$$\left(\mathrm{2}\sqrt{\mathrm{3}},−\mathrm{1}\right)\:? \\ $$ Answered by ajfour last updated on…
Question Number 112746 by bemath last updated on 09/Sep/20 $$\mathrm{If}\:\mathrm{z}\:=\:−\mathrm{i}\:\mathrm{is}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{z}^{\mathrm{3}} +\mathrm{k}.\mathrm{z}^{\mathrm{2}} +\left(\mathrm{8}+\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{i}\right)\mathrm{z}+\mathrm{8i}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{other}\:\mathrm{roots} \\ $$ Commented by malwan last updated on 09/Sep/20…
Question Number 112751 by bemath last updated on 09/Sep/20 Answered by bobhans last updated on 09/Sep/20 $$\mathrm{let}\:\mathrm{w}\:=\:\mathrm{a}+\mathrm{bi}\:\mathrm{and}\:\mathrm{z}\:=\:\mathrm{p}+\mathrm{qi}\: \\ $$$$\mathrm{where}\:\overset{−} {\mathrm{z}}=\mathrm{p}−\mathrm{qi}\: \\ $$$$\Rightarrow\mathrm{w}−\mathrm{2z}\:=\:\mathrm{a}+\mathrm{bi}−\mathrm{2p}−\mathrm{2qi}\:=\:\mathrm{9} \\ $$$$\Rightarrow\left(\mathrm{a}−\mathrm{2p}\right)+\left(\mathrm{b}−\mathrm{2q}\right)\mathrm{i}\:=\:\mathrm{9}+\mathrm{0}.\mathrm{i} \\…
Question Number 112737 by bemath last updated on 09/Sep/20 $$\mathrm{Given}\:\mathrm{z}=−\mathrm{6}+\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{i} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{z}^{\mathrm{n}} .\overset{−} {\mathrm{z}}\:\mathrm{purelly}\:\mathrm{imaginary}. \\ $$ Commented by bemath last updated on 09/Sep/20…