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The-volume-of-a-right-circular-cone-is-5litres-Calculate-the-volume-of-the-part-into-which-the-cone-is-divided-by-a-plane-parallel-to-the-base-one-third-of-the-way-down-from-the-vertex-to-the-base-gi

Question Number 190634 by Mastermind last updated on 07/Apr/23 $$\mathrm{The}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{circular}\:\mathrm{cone} \\ $$$$\mathrm{is}\:\mathrm{5litres}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{part}\:\mathrm{into}\:\mathrm{which}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{base}\:\mathrm{one}−\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{way}\:\mathrm{down} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{to}\:\mathrm{the}\:\mathrm{base}\:\mathrm{giving} \\ $$$$\mathrm{your}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\: \\ $$$$\mathrm{millimetres}. \\…

Two-particles-P-and-Q-move-towards-each-other-along-a-straight-line-MN-51-meters-long-P-starts-fromM-with-velocity-5-ms-1-and-constant-acceleration-of-1-ms-2-Q-starts-from-N-at-the-same-tim

Question Number 59505 by pete last updated on 11/May/19 $$\mathrm{Two}\:\mathrm{particles}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:{MN},\:\mathrm{51}\:\mathrm{meters} \\ $$$$\mathrm{long}.\:\mathrm{P}\:\mathrm{starts}\:\mathrm{from}{M}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{5}\:\mathrm{ms}^{−\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{constant}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{1}\:\mathrm{ms}^{−\mathrm{2}} .\:\mathrm{Q}\:\mathrm{starts} \\ $$$$\mathrm{from}\:\mathrm{N}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{6}\:\mathrm{ms}^{−\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{3}\:\mathrm{ms}^{−\mathrm{2}} . \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{time}\:\mathrm{when}\:\mathrm{the}: \\…

Solve-the-system-xy-3x-2y-6-i-yx-y-3z-3-ii-zx-2z-x-2-iii-

Question Number 59442 by Tawa1 last updated on 10/May/19 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{xy}\:+\:\mathrm{3x}\:+\:\mathrm{2y}\:\:=\:−\:\mathrm{6}\:\:\:\:\:\:\:…..\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{yx}\:+\:\mathrm{y}\:+\:\mathrm{3z}\:\:\:=\:−\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:…..\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{zx}\:+\:\mathrm{2z}\:+\:\mathrm{x}\:\:\:=\:\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:…..\:\left(\mathrm{iii}\right) \\ $$ Commented by mr W last updated on…

6-4-6-3-

Question Number 59397 by hhghg last updated on 09/May/19 $$\mathrm{6}^{\mathrm{4}} ×\mathrm{6}^{\mathrm{3}} \\ $$ Commented by Mikael_Marshall last updated on 09/May/19 $$\mathrm{6}^{\mathrm{4}+\mathrm{3}} =\mathrm{6}^{\mathrm{7}} \\ $$$${use}\:{calculatr} \\…

1-1-3-3-1-5-5-1-7-7-

Question Number 124892 by Dwaipayan Shikari last updated on 06/Dec/20 $$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}.\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{5}.\mathrm{5}!}−\frac{\mathrm{1}}{\mathrm{7}.\mathrm{7}!}+… \\ $$ Commented by Dwaipayan Shikari last updated on 06/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sinx}}{{x}}{dx}=\int_{\mathrm{0}} ^{\mathrm{1}}…