Menu Close

Author: Tinku Tara

if-6-3-10-1-3-6-3-10-1-3-x-find-x-3-10-3x-

Question Number 147882 by mathdanisur last updated on 24/Jul/21 $${if}\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:+\:\mathrm{10}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:−\:\mathrm{10}}\:=\:\boldsymbol{{x}} \\ $$$${find}\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{10}−\mathrm{3}{x}}\:=\:? \\ $$ Answered by mr W last updated on 24/Jul/21 $${a}=\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:+\:\mathrm{10}}\:,{b}=\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:−\:\mathrm{10}} \\…

Find-the-sum-to-close-form-1-1-2-3-1-4-5-6-1-7-8-9-

Question Number 147877 by Tawa11 last updated on 24/Jul/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{close}\:\mathrm{form}. \\ $$$$\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:\:\:+\:\:\:…\:\:\: \\ $$ Commented by Tinku Tara last updated on 24/Jul/21 $$\mathrm{Welcome}\:\mathrm{back}.\:\mathrm{Tawa}. \\ $$🙂🙂…

a-2-sin-2a-1-cos-2a-1-then-tan-

Question Number 16807 by sushmitak last updated on 26/Jun/17 $$\left({a}+\mathrm{2}\right)\mathrm{sin}\:\alpha+\left(\mathrm{2}{a}−\mathrm{1}\right)\mathrm{cos}\:\alpha=\left(\mathrm{2}{a}+\mathrm{1}\right) \\ $$$$\mathrm{then}\:\mathrm{tan}\:\alpha=? \\ $$ Commented by prakash jain last updated on 26/Jun/17 $$\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}={u},\mathrm{sin}\:\alpha=\frac{\mathrm{2}{u}}{\mathrm{1}+{u}^{\mathrm{2}} },\mathrm{cos}\:\alpha=\frac{\mathrm{1}−{u}^{\mathrm{2}} }{\mathrm{1}+{u}^{\mathrm{2}}…

Question-147876

Question Number 147876 by puissant last updated on 24/Jul/21 Answered by Olaf_Thorendsen last updated on 24/Jul/21 $$\mathrm{On}\:\mathrm{raisonne}\:\mathrm{par}\:\mathrm{recurrence}. \\ $$$$ \\ $$$$\mathrm{On}\:\mathrm{considere}\:\mathrm{la}\:\mathrm{propriete}\:\mathrm{suivante}\:: \\ $$$$ \\ $$$$“\mathrm{Si}\:\mathrm{on}\:\mathrm{retire}\:\mathrm{une}\:\mathrm{case}\:\mathrm{quelconque}…

Question-147879

Question Number 147879 by 0731619 last updated on 24/Jul/21 Answered by puissant last updated on 24/Jul/21 $$\mathrm{I}=\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{5}} +\mathrm{1}}\mathrm{dx} \\ $$$$=\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)} \\ $$$$=\int\frac{\frac{\mathrm{1}}{\mathrm{5}}}{\mathrm{x}+\mathrm{1}}\mathrm{dx}+\int\frac{−\frac{\mathrm{1}}{\mathrm{5}}\mathrm{x}^{\mathrm{3}}…

Find-the-sum-to-n-term-1-2-3-4-5-6-7-8-9-

Question Number 147878 by Tawa11 last updated on 24/Jul/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\:\mathrm{n}\:\:\mathrm{term}:\:\:\:\:\:\mathrm{1}.\mathrm{2}.\mathrm{3}\:\:+\:\:\mathrm{4}.\mathrm{5}.\mathrm{6}\:\:+\:\:\mathrm{7}.\mathrm{8}.\mathrm{9}\:\:+\:\:… \\ $$ Answered by Olaf_Thorendsen last updated on 24/Jul/21 $$\mathrm{S}\:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{3}{k}−\mathrm{2}\right)\left(\mathrm{3}{k}−\mathrm{1}\right)\left(\mathrm{3}{k}\right) \\ $$$$\mathrm{S}\:=\:\mathrm{3}\underset{{k}=\mathrm{1}} {\overset{{n}}…

Question-147873

Question Number 147873 by 0731619 last updated on 24/Jul/21 Answered by Olaf_Thorendsen last updated on 24/Jul/21 $$\mathrm{S}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{4}}\right) \\ $$$$\mathrm{S}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}}{\left(\mathrm{3}{n}+\mathrm{2}\right)\left(\mathrm{3}{n}+\mathrm{4}\right)} \\ $$$$\mathrm{S}\:=\:\frac{\mathrm{2}}{\mathrm{9}}\underset{{n}=\mathrm{0}}…

Question-16803

Question Number 16803 by ajfour last updated on 26/Jun/17 Commented by ajfour last updated on 26/Jun/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{an}\:\mathrm{equilateral}\: \\ $$$$\mathrm{triangle}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{distances} \\ $$$$\mathrm{from}\:\mathrm{any}\:\mathrm{point}\:\mathrm{to}\:\mathrm{the}\:\mathrm{three}\:\mathrm{sides} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{constant}. \\ $$…