Question Number 74712 by aliesam last updated on 29/Nov/19 Commented by MJS last updated on 29/Nov/19 $$\mathrm{easy}\:\mathrm{solutions} \\ $$$${x}={y}=\mathrm{1} \\ $$$${x}={y}=−\mathrm{2} \\ $$$$\mathrm{no}\:\mathrm{other}\:\mathrm{real}\:\mathrm{solutions} \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right)\:\mathrm{and}\:\mathrm{dividing}\:\mathrm{by}\:{x}^{\mathrm{2}}…
Question Number 74713 by ajfour last updated on 29/Nov/19 Commented by ajfour last updated on 29/Nov/19 $${If}\:{perimeter}\:{of}\:\bigtriangleup{ABC}\:=\:\mathrm{18}\:, \\ $$$${and}\:{area}\:{is}\:{maximum},\:{find} \\ $$$${coordinates}\:{of}\:{points}\:{A},\:{B},\:{C}. \\ $$ Answered by…
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Question Number 74703 by Mr. K last updated on 29/Nov/19 $${let}\:\boldsymbol{{b}}\:{and}\:\boldsymbol{{r}}\:{be}\:{two}\:{positive}\:{prime}\: \\ $$$${numbers}\:{such}\:{that}\:{b}\neq{r}\:{and}\:{b}×{r}\:{is} \\ $$$${a}\:{divisor}\:{of}\:\mathrm{138}.\:{Consider}\:{an}\: \\ $$$${arithmetic}\:{progression}\:{in}\:{which} \\ $$$${the}\:{first}\:{term}\:{is}\:\boldsymbol{{b}},\:{the}\:{ratio}\:{is}\:\boldsymbol{{r}} \\ $$$${and}\:{the}\:{fourth}\:{term}\:{is}\:\mathrm{71}.\:{What}\:{is}\:{the} \\ $$$${value}\:{of}\:\boldsymbol{{b}}+\boldsymbol{{r}}? \\ $$…
Question Number 74698 by ajfour last updated on 29/Nov/19 Commented by ajfour last updated on 29/Nov/19 $${If}\:\overset{\frown} {{AB}}\:=\overset{\frown} {{AE}}\:=\:\overset{\frown} {{DE}}\:. \\ $$$${Find}\:{equation}\:{of}\:{circle}. \\ $$ Answered…
show-that-the-ellipse-with-e-5-3-focus-0-2-and-directrix-x-4-5-3-has-the-equation-x-5-2-9-y-2-2-4-1-
Question Number 9163 by tawakalitu last updated on 21/Nov/16 $$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{ellipse}\:\mathrm{with}\:\mathrm{e}\:=\:\frac{\sqrt{\mathrm{5}}}{\mathrm{3}},\: \\ $$$$\mathrm{focus}\:\left(\mathrm{0},\:\mathrm{2}\right)\:\mathrm{and}\:\mathrm{directrix}\:\mathrm{x}\:=\:−\frac{\mathrm{4}\sqrt{\mathrm{5}}}{\mathrm{3}} \\ $$$$\mathrm{has}\:\mathrm{the}\:\mathrm{equation}\::\:\frac{\left(\mathrm{x}\:−\:\sqrt{\mathrm{5}}\right)^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\left(\mathrm{y}\:−\:\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{4}}\:=\:\mathrm{1} \\ $$ Commented by sandy_suhendra last updated on 22/Nov/16…
Question Number 9161 by tawakalitu last updated on 21/Nov/16 $$\mathrm{Consider}\:\mathrm{a}\:\mathrm{rectangular}\:\mathrm{plate}\:\mathrm{of}\:\mathrm{lamina}\: \\ $$$$\mathrm{density}\:\rho\:=\:\mathrm{0}.\mathrm{025}\:\mathrm{whose}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{5kg}\:\mathrm{about} \\ $$$$\mathrm{an}\:\mathrm{axis}\:\mathrm{3cm}\:\mathrm{from}\:\mathrm{one}\:\mathrm{of}\:\mathrm{its}\:\mathrm{sides}\:\mathrm{as}\:\mathrm{shown} \\ $$$$\mathrm{below}.\:\mathrm{using}\:\mathrm{parallel}\:\mathrm{axis}\:\mathrm{theorem}\:,\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{moment}\:\mathrm{of}\:\mathrm{inertia}\:\mathrm{about}\:\mathrm{the}\:\mathrm{xx}\:\mathrm{axis}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{gyration}. \\ $$ Commented by tawakalitu…
Question Number 74697 by chess1 last updated on 29/Nov/19 Answered by mr W last updated on 29/Nov/19 $${let}\:{BC}=\mathrm{1} \\ $$$${DC}=\frac{\mathrm{sin}\:\mathrm{6}}{\mathrm{sin}\:\mathrm{24}} \\ $$$${AC}=\frac{\mathrm{sin}\:\mathrm{24}}{\mathrm{sin}\:\mathrm{54}} \\ $$$$\frac{\mathrm{sin}\:\left(\mathrm{12}+{x}\right)}{\mathrm{sin}\:{x}}=\frac{\mathrm{sin}\:\mathrm{24}×\mathrm{sin}\:\mathrm{24}}{\mathrm{sin}\:\mathrm{54}×\mathrm{sin}\:\mathrm{6}} \\…