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Category: Algebra

Question-212470

Question Number 212470 by Spillover last updated on 14/Oct/24 Answered by Ar Brandon last updated on 14/Oct/24 $$\Omega=\int_{\mathrm{0}} ^{\infty} \frac{\left(\mathrm{1}−{x}\right)\mathrm{ln}{x}}{\mathrm{1}−{x}^{\mathrm{6}} }{dx} \\ $$$$\:\:\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}}{\mathrm{1}−{x}^{\mathrm{6}}…

9-2-4-9-4-6-9-4n-n-1-15-8-Find-n-

Question Number 212432 by hardmath last updated on 13/Oct/24 $$\frac{\mathrm{9}}{\mathrm{2}\centerdot\mathrm{4}}\:+\:\frac{\mathrm{9}}{\mathrm{4}\centerdot\mathrm{6}}\:+…+\:\frac{\mathrm{9}}{\mathrm{4n}\centerdot\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:=\:\frac{\mathrm{15}}{\mathrm{8}} \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{n}}\:=\:? \\ $$ Answered by Ar Brandon last updated on 13/Oct/24 $$\mathrm{9}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{4}{n}\left({n}+\mathrm{1}\right)}=\frac{\mathrm{15}}{\mathrm{8}}…

Question-212428

Question Number 212428 by Spillover last updated on 13/Oct/24 Answered by Yassine84 last updated on 13/Oct/24 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)\:{then} \\ $$$${li}\underset{\mathrm{1}} {{m}}\:\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}}…

x-2y-3z-1-2x-y-z-4-3x-y-2z-7-find-x-y-z-

Question Number 212424 by hardmath last updated on 13/Oct/24 $$\begin{cases}{\mathrm{x}\:+\:\mathrm{2y}\:−\:\mathrm{3z}\:=\:\mathrm{1}}\\{\mathrm{2x}\:−\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{4}}\\{\mathrm{3x}\:+\:\mathrm{y}\:+\:\mathrm{2z}\:=\:\mathrm{7}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\mathrm{x},\mathrm{y},\mathrm{z}\:=\:? \\ $$ Answered by A5T last updated on 13/Oct/24 $$\left({ii}\right)+\left({iii}\right)\Rightarrow\mathrm{5}{x}+\mathrm{3}{z}=\mathrm{11}…\left({iv}\right) \\ $$$$\mathrm{2}\left({iii}\right)−\left({i}\right)\Rightarrow\mathrm{5}{x}+\mathrm{7}{z}=\mathrm{13}…\left({v}\right) \\ $$$$\left({v}\right)−\left({iv}\right)\Rightarrow\mathrm{4}{z}=\mathrm{2}\Rightarrow{z}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}=\frac{\mathrm{19}}{\mathrm{10}}\Rightarrow{y}=\frac{\mathrm{3}}{\mathrm{10}} \\…

If-x-2-x-3-0-Find-x-9-x-2-

Question Number 212448 by hardmath last updated on 13/Oct/24 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\:\mathrm{x}\:+\:\frac{\mathrm{9}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$ Answered by A5T last updated on 13/Oct/24 $${x}^{\mathrm{2}} −{x}+\mathrm{3}=\mathrm{0}\Rightarrow{x}^{\mathrm{3}}…

ax-2-bx-c-0-a-b-c-and-two-roots-of-the-eqn-are-5-consecutive-integers-in-some-order-Find-their-values-

Question Number 212354 by RojaTaniya last updated on 11/Oct/24 $$\:\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\:{a},{b},{c}\:{and}\:{two}\:{roots}\:{of}\:{the}\:{eqn}. \\ $$$$\:{are}\:\mathrm{5}\:{consecutive}\:{integers}\:{in}\: \\ $$$$\:{some}\:{order}.\:{Find}\:{their}\:{values}. \\ $$ Answered by Rasheed.Sindhi last updated on…

Question-212341

Question Number 212341 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{5}}\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\right] \\ $$$$=−\frac{\mathrm{1}}{\mathrm{20}}\underset{\mathrm{0}} {\overset{\mathrm{4}/\mathrm{5}} {\int}}\frac{{dt}}{{t}^{\mathrm{2}}…