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Author: Tinku Tara

Question-193522

Question Number 193522 by Mingma last updated on 16/Jun/23 Answered by Subhi last updated on 16/Jun/23 $$\frac{{x}+{z}}{{sin}\left(\mathrm{100}\right)}=\frac{{x}}{{sin}\left(\mathrm{40}\right)} \\ $$$${sin}\left(\mathrm{100}\right){x}={sin}\left(\mathrm{40}\right){x}+{sin}\left(\mathrm{40}\right){z}\:\Rrightarrow\:{x}=\frac{{sin}\left(\mathrm{40}\right){z}}{{sin}\left(\mathrm{10}\right)−{sin}\left(\mathrm{40}\right)}\:\left({i}\right) \\ $$$$\frac{{z}}{{sin}\left({y}−\mathrm{40}\right)}=\frac{{x}+{z}}{{sin}\left({u}\right)} \\ $$$${u}+{y}−\mathrm{40}=\mathrm{180}−\mathrm{140}=\mathrm{40}\:\Rrightarrow\:{y}=\mathrm{80}−{u}\:\left({ii}\right) \\ $$$$\frac{{z}}{{sin}\left(\mathrm{40}−{u}\right)}=\frac{{x}+{z}}{{sin}\left({u}\right)}…

Question-193581

Question Number 193581 by Rupesh123 last updated on 16/Jun/23 Answered by Subhi last updated on 16/Jun/23 $${a}^{\mathrm{2}} =\left({c}+{d}\right)^{\mathrm{2}} +\left({c}+{e}\right)^{\mathrm{2}} =\mathrm{2}{c}^{\mathrm{2}} +\mathrm{2}{cd}+\mathrm{2}{ec}+{d}^{\mathrm{2}} +{e}^{\mathrm{2}} \\ $$$${b}^{\mathrm{2}} ={e}^{\mathrm{2}}…

dx-x-6-1-

Question Number 193538 by cortano12 last updated on 16/Jun/23 $$\:\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{6}} +\mathrm{1}}\:=? \\ $$ Answered by Subhi last updated on 16/Jun/23 $$\int\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}\right)}\:\Rrightarrow\:\int\frac{{a}}{{x}^{\mathrm{2}} +\mathrm{1}}+\frac{{bx}^{\mathrm{2}}…