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Question-59655

Question Number 59655 by aliesam last updated on 13/May/19 Commented by Mr X pcx last updated on 13/May/19 $${r}=\xi\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:}\:\Rightarrow\frac{\partial{r}}{\partial{x}}\:=\frac{\xi{x}}{\:\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}\:=\frac{\xi{x}}{{r}} \\ $$$$\frac{\partial\theta}{\partial{y}}\:=\xi\frac{{y}}{\:\sqrt{{x}^{\mathrm{2}}…

Question-59639

Question Number 59639 by Tawa1 last updated on 12/May/19 Commented by Tawa1 last updated on 12/May/19 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{continue}.\:\:\mathrm{My}\:\mathrm{final}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{wrong}. \\ $$$$\:\:\:\mathrm{I}\:\mathrm{got}:\:\:\:\mathrm{S}\:\:=\:\:\frac{\mathrm{2n}^{\mathrm{3}} \:+\:\mathrm{3n}^{\mathrm{2}} \:+\:\mathrm{n}}{\mathrm{6}}\:\:\:\:\:\:\mathrm{but}\:\:\mathrm{answer}\:\mathrm{is}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{S}\:\:=\:\:\frac{\mathrm{n}}{\mathrm{6}}\:\left(\mathrm{14n}^{\mathrm{2}} \:−\:\mathrm{9n}\:+\:\mathrm{1}\right) \\ $$ Commented…

f-x-cos-sinx-cos-2-x-1-sinxsin-sinx-dx-Find-f-1-

Question Number 125167 by Dwaipayan Shikari last updated on 08/Dec/20 $${f}\left({x}\right)=\int\frac{{cos}\left({sinx}\right)+{cos}^{\mathrm{2}} {x}}{\mathrm{1}+{sinxsin}\left({sinx}\right)}{dx} \\ $$$${Find}\:{f}\left(\mathrm{1}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 08/Dec/20 This is a problem from brilliant let's try this https://brilliant.org/problems/integration-grandmaster-p1…

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}: \\…