Question Number 151496 by puissant last updated on 21/Aug/21 $$\forall{x},{y}\in\mathbb{R}_{+} ^{\ast} ,\:{show}\:{that}\:\frac{{x}}{{x}^{\mathrm{4}} +{y}^{\mathrm{2}} }+\frac{{y}}{{y}^{\mathrm{4}} +{x}^{\mathrm{2}} }\leqslant\frac{\mathrm{1}}{{xy}} \\ $$ Answered by dumitrel last updated on 21/Aug/21…
Question Number 151444 by liberty last updated on 21/Aug/21 Answered by mr W last updated on 21/Aug/21 $${say}\:{BE}={diameter}=\mathrm{2}×{AB} \\ $$$$\frac{{BC}}{{BO}}=\frac{{BO}}{{BE}} \\ $$$$\Rightarrow{BC}×{BE}={BO}^{\mathrm{2}} \\ $$$$\Rightarrow{BC}×\mathrm{2}×{AB}={BO}^{\mathrm{2}} \\…
Question Number 20149 by ajfour last updated on 22/Aug/17 Commented by ajfour last updated on 22/Aug/17 $${The}\:{roof}\:{is}\:{even}\:{a}\:{flat}\:{plane}.{Lengths} \\ $$$$\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}},\:\boldsymbol{{y}}\:{are}\:{perpendicular}\:{to}\:{the} \\ $$$${bottom}\:{rectangular}\:{face}\:{with}\:{sides} \\ $$$$\boldsymbol{{h}}\:{and}\:\boldsymbol{{l}}\:.\:{Find}\:{height}\:\boldsymbol{{y}}\:{and}\:{the}\:\:{volume} \\ $$$${enclosed}\:{by}\:{the}\:{surfaces}.…
Question Number 151036 by text last updated on 17/Aug/21 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 19964 by ajfour last updated on 19/Aug/17 Commented by ajfour last updated on 19/Aug/17 $${Inscribed}\:{in}\:{a}\:{right}\:{circular}\:{cone} \\ $$$${is}\:{a}\:{sphere}\:{whose}\:{surface}\:{area}\:{is} \\ $$$${equal}\:{to}\:{the}\:{area}\:{of}\:{the}\:{base}\:{if}\:{the} \\ $$$${cone}.\:{In}\:{what}\:{ratio}\:{is}\:{the}\:{lateral} \\ $$$${side}\:{of}\:{the}\:{cone}\:{divided}\:{by}\:{the}\:{line}…
Question Number 19955 by ajfour last updated on 19/Aug/17 Commented by ajfour last updated on 19/Aug/17 $${Find}\:{the}\:{volume}\:{of}\:{the}\:{regular} \\ $$$${tetrahedron}\:{in}\:{terms}\:{of}\:\boldsymbol{{r}}\:. \\ $$ Commented by ajfour last…
Question Number 19940 by ajfour last updated on 18/Aug/17 $${A}\:{circle}\:{is}\:{inscribed}\:{in}\:{an} \\ $$$${isosceles}\:{trapezium}.\:{Prove}\:{that} \\ $$$${the}\:{ratio}\:{of}\:{the}\:{area}\:{of}\:{the}\:{circle} \\ $$$${to}\:{the}\:{area}\:{of}\:{the}\:{trapezium}\:{is} \\ $$$${equal}\:{to}\:{the}\:{ratio}\:{of}\:{the}\:{circum}- \\ $$$${ference}\:{of}\:{the}\:{circle}\:{to}\:{the}\: \\ $$$${perimeter}\:{of}\:{the}\:{trapezium}. \\ $$ Commented…
Question Number 19915 by ajfour last updated on 18/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Four}\:{equal}\:{spheres}\:{of}\:{radius}\:{r} \\ $$$${are}\:{externally}\:{tangent}\:{to}\:{the}\:{three} \\ $$$${others}.\:{Find}\:{the}\:{radius}\:{of}\:{a}\:{sphere} \\ $$$${tangent}\:{to}\:{all}\:{four}\:{spheres}\:{and} \\ $$$${containing}\:{them}\:{within}\:{it}.…
Question Number 19912 by ajfour last updated on 17/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Find}\:{tangent}\:{of}\:{the}\:{acute}\:{angle} \\ $$$${between}\:{AB}\:{and}\:{SC}\:{and}\:{the} \\ $$$${shortest}\:{distance}\:{between}\:{them}. \\ $$$${The}\:{side}\:{of}\:{the}\:{equilateral}\:{triangle} \\ $$$${is}\:{even}\:\boldsymbol{{a}}.\:{SA}\:{is}\:{perpendicular}\:{to}…
Question Number 19796 by ajfour last updated on 15/Aug/17 Commented by ajfour last updated on 15/Aug/17 $$\mathrm{Q}.\mathrm{19794}\:\:\:\left(\mathrm{solution}\right) \\ $$ Answered by ajfour last updated on…