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Category: Mensuration

1-Determine-the-following-if-it-is-convergent-or-divergent-n-1-sin-n-n-2-n-1-sin-n-p-n-p-p-R-find-the-range-of-p-when-it-is-convergent-

Question Number 86113 by Tony Lin last updated on 27/Mar/20 $$\left(\mathrm{1}\right){Determine}\:{the}\:{following} \\ $$$${if}\:{it}\:{is}\:{convergent}\:{or}\:{divergent} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}} \\ $$$$\left(\mathrm{2}\right)\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}^{{p}} \right)}{{n}^{{p}} },\:{p}\epsilon\mathbb{R},{find}\:{the}\:{range}\: \\ $$$${of}\:{p}\:{when}\:{it}\:{is}\:{convergent}…

Given-that-x-iy-a-b-sin-icos-show-that-b-2-1-x-2-y-2-a-2-2abx-

Question Number 151561 by peter frank last updated on 21/Aug/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{x}+\mathrm{iy}=\frac{\mathrm{a}}{\mathrm{b}+\mathrm{sin}\:\theta+\mathrm{icos}\:\theta} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{b}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)+\mathrm{a}^{\mathrm{2}} =\mathrm{2abx} \\ $$ Answered by peter frank…

Question-151444

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-20149

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-19964

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}…

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-perimete

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-19915

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}.…