Question Number 19683 by 786786AM last updated on 14/Aug/17 $$\mathrm{In}\:\mathrm{an}\:\mathrm{A}.\mathrm{P};\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{is}\:−\mathrm{2}\:\mathrm{and}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{term}\:\:\mathrm{exceeds}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{by}\:\mathrm{58}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}. \\ $$ Answered by Rasheed.Sindhi last updated on 15/Aug/17 $$\mathrm{Let}\:\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{middle}\:\mathrm{term} \\ $$$$\mathrm{m}+\mathrm{58}\:\mathrm{is}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{term}. \\…
Question Number 150752 by Jamshidbek last updated on 15/Aug/21 $$\mathrm{x}^{\mathrm{3}} +\mathrm{3x}+\mathrm{12}=\mathrm{0}\:\:\mathrm{solve}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\mathrm{help} \\ $$ Commented by liberty last updated on 15/Aug/21 x = root(3, - root(2, 37) - 6) - (1/root(3, - root(2, 37) - 6)) Commented by…
Question Number 150749 by mnjuly1970 last updated on 15/Aug/21 $$ \\ $$$$\:\:\mathrm{Prove}\:\:\:\mathrm{That}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathcal{I}\::=\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left(\:{sin}\:\left({x}\:\right).{cos}\:\left({x}\:\right)\right)^{\:\mathrm{4}} }{{x}\:.\:\sqrt{{x}}\:}{dx}=\frac{\mathrm{1}}{\mathrm{32}}\:\left(\mathrm{2}\:\sqrt{\mathrm{2}}\:−\mathrm{1}\:\right)\sqrt{\:\pi}\:….\blacksquare\:\: \\ $$$$\:\:\:..{m}.{n}..\:\: \\ $$ Terms of…
Question Number 19679 by myintkhaing last updated on 14/Aug/17 Commented by myintkhaing last updated on 14/Aug/17 $$\left(\mathrm{a}\right)\:\mathrm{A}\:\mathrm{will}\:\mathrm{win}\:\mathrm{both}\:\mathrm{races} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{A}\:\mathrm{will}\:\mathrm{win}\:\mathrm{either}\:\mathrm{race} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{A}\:\mathrm{will}\:\mathrm{win}\:\mathrm{only}\:\mathrm{one}\:\mathrm{race} \\ $$ Terms of…
Question Number 19675 by ajfour last updated on 14/Aug/17 Commented by ajfour last updated on 14/Aug/17 $$\mathrm{Q}.\mathrm{19668}\:\mathrm{Find}\:\mathrm{r}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{side}\:\boldsymbol{\mathrm{d}} \\ $$$$\mathrm{of}\:\mathrm{equilareral}\:\bigtriangleup\mathrm{ABC}\:. \\ $$ Answered by ajfour last…
Question Number 150747 by mnjuly1970 last updated on 15/Aug/21 $$ \\ $$$${prove}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\infty} {e}^{−\sqrt{{x}}} .{ln}\:\left(\sqrt[{\mathrm{4}}]{\:{x}}\:\right)\overset{?} {=}\:\mathrm{1}−\gamma \\ $$$$\:{m}.{n}.. \\ $$ Answered by Olaf_Thorendsen…
Question Number 150746 by naka3546 last updated on 15/Aug/21 $${Find}\:\:{the}\:\:{smallest}\:\:{positive}\:\:{integer}\:\:{n}\:\:{so}\:\:{that}\:\:\left(\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\ldots\:+\:{n}^{\mathrm{2}} \right)\:\:{is}\:\:{divided}\:\:{by}\:\:{n}\:. \\ $$ Answered by mr W last updated on 15/Aug/21 $${assume}\:{n}>\mathrm{1}.…
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Question Number 19668 by Joel577 last updated on 14/Aug/17 Commented by Joel577 last updated on 15/Aug/17 $$\mathrm{An}\:\mathrm{equateral}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{side}\:\mathrm{lenght} \\ $$$${d}.\:\mathrm{Circle}\:{L}_{\mathrm{1}} \:\mathrm{touching}\:\Delta{ABC}\:\mathrm{at}\:{A}\:\mathrm{and}\:{B}. \\ $$$$\mathrm{Circle}\:{L}_{\mathrm{2}} \:\mathrm{touching}\:{AC},\:{BC},\:\mathrm{and}\:{L}_{\mathrm{1}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{circle}\:{L}_{\mathrm{2}}…
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