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Category: Geometry

Question-59620

Question Number 59620 by ajfour last updated on 12/May/19 Commented by ajfour last updated on 12/May/19 $$\mathrm{Find}\:\mathrm{dimensions}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{volume} \\ $$$$\mathrm{cylinder}\:\mathrm{inscribed}\:\mathrm{within}\:\mathrm{a}\:\mathrm{hemi}- \\ $$$$\mathrm{sphere}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{R}\:\left(\mathrm{in}\:\mathrm{shown}\:\mathrm{orientation}\right). \\ $$ Commented by…

Question-190644

Question Number 190644 by cherokeesay last updated on 08/Apr/23 Answered by a.lgnaoui last updated on 09/Apr/23 $$\mathrm{Algebrique}\:\mathrm{solution} \\ $$$$\mathrm{CercleC}_{\mathrm{1}} \:\:\mathrm{B}:\mathrm{origine}\:\mathrm{du}\:\mathrm{Ref}\:\mathrm{B}\left(\mathrm{0},\mathrm{0}\right) \\ $$$$\mathrm{et}\:\mathrm{de}\:\mathrm{rayon}\:\mathrm{1}\:\:\:\mathrm{C}_{\mathrm{1}} \left(\mathrm{B},\mathrm{1}\right)\:\left(\:\mathrm{B},\mathrm{E}\right):\mathrm{C}_{\mathrm{1}} \cap\mathrm{C}_{\mathrm{2}} \\…

Question-190615

Question Number 190615 by mr W last updated on 07/Apr/23 Commented by mr W last updated on 08/Apr/23 $$\mathrm{1}.\:{find}\:{ratio}\:\frac{{a}_{\mathrm{1}} }{{a}}=?\:{such}\:{that}\:{the}\:{right} \\ $$$${circular}\:{cone}\:{is}\:{cut}\:{into}\:{two}\:{parts}\: \\ $$$${with}\:{equal}\:{volume}\:{as}\:{shown}. \\…

Question-125070

Question Number 125070 by Algoritm last updated on 08/Dec/20 Commented by mr W last updated on 08/Dec/20 $${x}\bot{y}\bot{z}\:{is}\:{not}\:{possible}. \\ $$$${do}\:{you}\:{mean}\:{x}\bot{a},\:{y}\bot{b},\:{z}\bot{c}? \\ $$$${but}\:{any}\:{way},\:{you}\:{can}\:{not}\:{determine} \\ $$$${the}\:{area}\:{of}\:{triangle}\:{with}\:{given} \\…

Question-190565

Question Number 190565 by cherokeesay last updated on 06/Apr/23 Answered by mr W last updated on 06/Apr/23 $$\frac{{CB}}{\mathrm{sin}\:{x}}=\frac{{AC}}{\mathrm{sin}\:\mathrm{30}°}\:\:\:…\left({i}\right) \\ $$$$\frac{\mathrm{sin}\:\left({x}+\mathrm{30}°\right)}{{CB}}=\frac{\mathrm{sin}\:\left({x}+\mathrm{60}°\right)}{{DB}}\:\:\:…\left({ii}\right) \\ $$$$\left({i}\right)×\left({ii}\right): \\ $$$$\frac{\mathrm{sin}\:\left({x}+\mathrm{30}°\right)}{\mathrm{sin}\:{x}}=\frac{\mathrm{sin}\:\left({x}+\mathrm{60}°\right)}{\mathrm{sin}\:\mathrm{30}°} \\…

Question-124953

Question Number 124953 by Algoritm last updated on 07/Dec/20 Answered by mr W last updated on 07/Dec/20 $${say}\:{AC}=\mathrm{1} \\ $$$$\frac{{BC}}{\mathrm{sin}\:\mathrm{30}}=\frac{{AC}}{\mathrm{sin}\:\mathrm{50}} \\ $$$$\Rightarrow{BC}=\frac{\mathrm{sin}\:\mathrm{30}}{\mathrm{sin}\:\mathrm{50}} \\ $$$${similarly} \\…

What-are-the-exact-values-of-k-for-which-the-line-y-kx-3-is-tangent-to-the-circle-with-centre-6-3-and-radius-2-

Question Number 124928 by bemath last updated on 07/Dec/20 $$\:{What}\:{are}\:{the}\:{exact}\:{values}\:{of}\:{k} \\ $$$${for}\:{which}\:{the}\:{line}\:{y}={kx}+\mathrm{3} \\ $$$${is}\:{tangent}\:{to}\:{the}\:{circle}\:{with} \\ $$$${centre}\:\left(\mathrm{6},\mathrm{3}\right)\:{and}\:{radius}\:\mathrm{2}? \\ $$ Answered by mr W last updated on…