Question Number 179567 by Acem last updated on 30/Oct/22 Answered by mr W last updated on 30/Oct/22 $${x}^{\mathrm{2}} =\left(\mathrm{3}+\mathrm{5}\right)^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} =\mathrm{71} \\ $$$$\Rightarrow{x}=\sqrt{\mathrm{71}} \\…
Question Number 179566 by Acem last updated on 30/Oct/22 Answered by a.lgnaoui last updated on 30/Oct/22 $$\mathrm{AC}\mid\mid\mathrm{FD}\:\:\measuredangle\mathrm{BAC}=\mathrm{120}−\mathrm{90}=\mathrm{30} \\ $$$$\mathrm{sin}\:\mathrm{30}=\frac{\mathrm{BH}}{\mathrm{3}}\:\:\mathrm{BH}=\frac{\mathrm{3}}{\mathrm{2}}\:\:\Rightarrow\mathrm{BE}=\frac{\mathrm{3}}{\mathrm{2}}+\mathrm{5}=\frac{\mathrm{13}}{\mathrm{2}}\:\:\:\left(\mathrm{1}\right) \\ $$$$\measuredangle\mathrm{ABD}=\mathrm{360}−\mathrm{240}=\mathrm{120}\:\:\Rightarrow\measuredangle\mathrm{BHC}=\measuredangle\mathrm{BED}=\mathrm{90}−\mathrm{30}=\mathrm{60} \\ $$$$\:\mathrm{cos}\:\mathrm{60}=\frac{\mathrm{BE}}{\mathrm{BD}}\:\:\:\mathrm{BD}=\frac{\mathrm{BE}}{\mathrm{cos}\:\mathrm{60}}=\frac{\mathrm{13}}{\mathrm{2cos}\:\mathrm{60}} \\ $$$$\:\:\:\mathrm{BD}=\mathrm{13}…
Question Number 48466 by Tawa1 last updated on 24/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 24/Nov/18 $${A}\left(\mathrm{1},\mathrm{3}\right)\:\:{B}\left(\mathrm{7},\mathrm{9}\right)\:\:\:{D}\left(\mathrm{4},\mathrm{6}\right) \\ $$$${eqn}\:{AB}\:\:\left({y}−\mathrm{3}\right)=\frac{\mathrm{9}−\mathrm{3}}{\mathrm{7}−\mathrm{1}}\left({x}−\mathrm{1}\right) \\ $$$${y}−\mathrm{3}−{x}+\mathrm{1}=\mathrm{0} \\ $$$${y}−{x}−\mathrm{2}=\mathrm{0} \\ $$$${point}\:{C}\left(−\mathrm{2},\mathrm{0}\right)…
Question Number 48460 by mr W last updated on 24/Nov/18 $${A}\:{point}\:{source}\:{has}\:{a}\:{distance}\:{d} \\ $$$${to}\:{the}\:{center}\:{of}\:{a}\:{big}\:{sphere}\:{with}\:{radius} \\ $$$${R}.\:\:{An}\:{other}\:{smaller}\:{sphere}\:{with}\:{radius} \\ $$$${r}\:{is}\:{placed}\:{between}\:{the}\:{point}\:{source} \\ $$$${and}\:{the}\:{big}\:{sphere}.\:{If}\:{the}\:{distance} \\ $$$${between}\:{the}\:{two}\:{spheres}\:{is}\:{constant}, \\ $$$${say}\:{it}'{s}\:{c}.\: \\ $$$${Find}\:{the}\:{maximal}\:{shadow}\:{area}\:{of}\:{the}…
Question Number 48388 by Tawa1 last updated on 23/Nov/18 Commented by Tawa1 last updated on 23/Nov/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{Area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle} \\ $$ Answered by mr W last updated…
Question Number 48384 by Tawa1 last updated on 23/Nov/18 Commented by Tawa1 last updated on 23/Nov/18 $$\left(\mathrm{1}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{scale}\:\mathrm{factor}.\: \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Find}\:\:\:\boldsymbol{\mathrm{OM}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 179440 by mr W last updated on 29/Oct/22 Commented by mr W last updated on 29/Oct/22 $${find}\:{the}\:{largest}\:{equilateral}\:{triangle} \\ $$$${which}\:{can}\:{be}\:{placed}\:{inside}\:{a}\:{square} \\ $$$${with}\:{side}\:{length}\:\mathrm{1}. \\ $$…
Question Number 179407 by Acem last updated on 29/Oct/22 $${Study}\:{the}\:{relative}\:{position}\:{of}\:{the}\:{curve}\:{C}_{{f}} \:{with} \\ $$$$\:{it}\:{asymptote};\:{f}\left({x}\right)=\:{x}+\:\frac{\mathrm{sin}\:{x}}{{x}} \\ $$ Commented by Acem last updated on 01/Nov/22 $${Is}\:{the}\:{question}\:{unclear}? \\ $$…
Question Number 48324 by mr W last updated on 22/Nov/18 Commented by ajfour last updated on 22/Nov/18 Commented by ajfour last updated on 22/Nov/18 $${let}\:{OB}\:=\:\mathrm{2}{a}\:…
Question Number 179386 by cherokeesay last updated on 29/Oct/22 Answered by DvMc last updated on 29/Oct/22 $$\frac{{y}}{{r}}=\frac{\mathrm{3}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:{y}=\frac{\mathrm{3}}{\mathrm{4}}{r} \\ $$$$\frac{{x}}{{r}}=\frac{\mathrm{4}}{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{4}}{\mathrm{3}}{r} \\ $$$${Sum}\:{of}\:{areas} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{yr}+{r}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}{rx}=\frac{\mathrm{3}×\mathrm{4}}{\mathrm{2}} \\…