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what-is-the-average-area-of-a-triangle-formed-by-3-random-points-in-a-1-1-square-

Question Number 93203 by MAB last updated on 11/May/20 $${what}\:{is}\:{the}\:{average}\:{area}\:{of}\:{a}\:{triangle} \\ $$$${formed}\:{by}\:\mathrm{3}\:{random}\:{points}\:{in}\:{a}\:\mathrm{1}×\mathrm{1} \\ $$$${square}? \\ $$ Commented by prakash jain last updated on 11/May/20 https://math.stackexchange.com/questions/1236958/the-expected-area-of-a-triangle-formed-by-three-points-randomly-chosen-from-the…

log-3-3-3x-log-x-3-3x-log-3-x-3-log-3-3-x-3-log-x-3-x-3-log-3-x-3-2-please-i-need-help-Ive-been-trying-but-still-not-getting-answer-

Question Number 158699 by MathsFan last updated on 07/Nov/21 $$\sqrt{\left(\mathrm{log}_{\mathrm{3}} \mathrm{3}\sqrt{\mathrm{3x}}+\mathrm{log}_{\mathrm{x}} \mathrm{3}\sqrt{\mathrm{3x}}\right)\mathrm{log}_{\mathrm{3}} \mathrm{x}^{\mathrm{3}} }+\sqrt{\left(\frac{\mathrm{log}_{\mathrm{3}} \mathrm{3}\sqrt{\mathrm{x}}}{\mathrm{3}}+\frac{\mathrm{log}_{\mathrm{x}} \mathrm{3}\sqrt{\mathrm{x}}}{\mathrm{3}}\right)\mathrm{log}_{\mathrm{3}} \mathrm{x}^{\mathrm{3}} }=\mathrm{2} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{help}. \\ $$$$\mathrm{Ive}\:\mathrm{been}\:\mathrm{trying}\:\mathrm{but}\:\mathrm{still}\:\mathrm{not}\:\mathrm{getting}\: \\ $$$$\mathrm{answer}. \\…

If-f-x-4x-x-2-dx-f-3-22-find-f-x-

Question Number 27581 by Mcfaithal last updated on 10/Jan/18 $$\mathrm{If}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\int\left(\mathrm{4}\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{dx}} \\ $$$$\mathrm{f}\left(\mathrm{3}\right)=\mathrm{22},\:\mathrm{find}\:{f}\left(\mathrm{x}\right) \\ $$ Answered by Joel578 last updated on 10/Jan/18 $${f}\left({x}\right)\:=\:\int\:\mathrm{4}{x}\:−\:{x}^{\mathrm{2}} \:{dx}\:=\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}}…

A-circle-with-center-3-1-passes-through-the-point-3-1-Find-it-s-equation-

Question Number 27579 by Mcfaithal last updated on 10/Jan/18 $$\mathrm{A}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{center}\:\left(−\mathrm{3},\mathrm{1}\right) \\ $$$$\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right).\:\mathrm{Find}\:\mathrm{it}'\mathrm{s}\:\mathrm{equation} \\ $$ Answered by Joel578 last updated on 10/Jan/18 $${r}\:=\:\mathrm{distance}\:\mathrm{between}\:\left(−\mathrm{3},\mathrm{1}\right)\:\mathrm{and}\:\left(\mathrm{3},\mathrm{1}\right) \\…

Simplify-1-1-cos-a-1-1-cos-a-and-leave-the-answer-in-the-form-sin-a-

Question Number 27580 by Mcfaithal last updated on 10/Jan/18 $$\mathrm{Simplify}\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{a}} \\ $$$$\mathrm{and}\:\mathrm{leave}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{form}\Rightarrow\:\:\:\mathrm{sin}\:\mathrm{a} \\ $$ Answered by Joel578 last updated on 10/Jan/18 $$\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{cos}\:{a}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{cos}\:{a}}\:=\:\frac{\left(\mathrm{1}\:+\:\mathrm{cos}\:{a}\right)\:+\:\left(\mathrm{1}\:−\:\mathrm{cos}\:{a}\right)}{\left(\mathrm{1}\:−\:\mathrm{cos}\:{a}\right)\left(\mathrm{1}\:+\:\mathrm{cos}\:{a}\right)} \\…