Question Number 9920 by Tawakalitu ayo mi last updated on 15/Jan/17 Answered by mrW1 last updated on 16/Jan/17 $${x}=\mathrm{360}−\left(\mathrm{360}−\mathrm{290}\right)−\left(\mathrm{360}−\mathrm{320}\right) \\ $$$$=\mathrm{360}−\mathrm{70}−\mathrm{40} \\ $$$$=\mathrm{250} \\ $$$${or}…
Question Number 140988 by mohammad17 last updated on 14/May/21 $$\int\frac{−{csc}^{\mathrm{2}} {x}}{\left({cscx}+{cotx}\right)^{\mathrm{3}} }{dx} \\ $$ Answered by MJS_new last updated on 14/May/21 $$\int\frac{−\mathrm{csc}^{\mathrm{2}} \:{x}}{\left(\mathrm{csc}\:{x}\:+\mathrm{cot}\:{x}\right)}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{cos}\:{x}\:\rightarrow\:{dx}=−\frac{{dt}}{\mathrm{sin}\:{x}}\right]…
Question Number 75453 by Master last updated on 11/Dec/19 Commented by MJS last updated on 11/Dec/19 $$\mathrm{impossible}\:\mathrm{to}\:\mathrm{solve} \\ $$ Commented by Master last updated on…
Question Number 9914 by Tawakalitu ayo mi last updated on 15/Jan/17 Answered by mrW1 last updated on 15/Jan/17 $$\frac{{QA}}{{PQ}}=\frac{{RA}}{{PR}} \\ $$$$\frac{{QA}}{\mathrm{15}}=\frac{{RA}}{\mathrm{9}} \\ $$$${QA}=\frac{\mathrm{15}}{\mathrm{9}}{RA}=\frac{\mathrm{5}}{\mathrm{3}}{RA}=\frac{\mathrm{5}}{\mathrm{3}}\left({QR}−{QA}\right) \\ $$$$\mathrm{3}{QA}=\mathrm{5}{QR}−\mathrm{5}{QA}…
Question Number 9912 by ridwan balatif last updated on 15/Jan/17 Answered by mrW1 last updated on 15/Jan/17 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{cos}\:{x}}{\left({x}−\pi\right)^{\mathrm{2}} } \\ $$$${t}={x}−\pi \\ $$$${x}={t}+\pi \\…
Question Number 140981 by EnterUsername last updated on 14/May/21 $$\mathrm{Let}\:\alpha\neq\mathrm{1}\:\mathrm{and}\:\alpha^{\mathrm{13}} =\mathrm{1}.\:\mathrm{If}\:{a}=\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} + \\ $$$$\alpha^{−\mathrm{1}} \:\mathrm{and}\:{b}=\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{2}} \:\mathrm{then}\:\mathrm{the} \\…
Question Number 75446 by Crabby89p13 last updated on 11/Dec/19 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{5}} −\mathrm{1}}{dx} \\ $$ Answered by MJS last updated on 11/Dec/19 $$\mathrm{decomposing} \\ $$$$\int\frac{{dx}}{{x}^{\mathrm{5}} −\mathrm{1}}={I}_{\mathrm{1}} +{I}_{\mathrm{2}}…
Question Number 75444 by vishalbhardwaj last updated on 11/Dec/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{b}/\mathrm{w}\:\mathrm{the}\:\mathrm{lines} \\ $$$$\mathrm{whose}\:\mathrm{direction}\:\mathrm{cosines}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{equations}\:{l}\:+\:{m}\:+\:{n}\:=\:\mathrm{0} \\ $$$$,\:{l}^{\mathrm{2}} \:+\:{m}^{\mathrm{2}} \:−\:{n}^{\mathrm{2}} \:=\:\mathrm{0}\:?? \\ $$$$ \\ $$ Commented by…
Question Number 140982 by Mathspace last updated on 14/May/21 $${convergence}\:{and}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{n}^{{n}} }{\left({n}!\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$ Commented by mohammad17…
Question Number 75445 by vishalbhardwaj last updated on 11/Dec/19 $$\mathrm{If}\:\mathrm{a}\:\mathrm{variable}\:\mathrm{line}\:\mathrm{in}\:\mathrm{two}\:\mathrm{adjacent} \\ $$$$\mathrm{positions}\:\mathrm{has}\:\mathrm{direction}\:\mathrm{cosines} \\ $$$${l},{m},\:{n}\:\mathrm{and}\:{l}+\delta{l},\:{m}+\delta{m},\:{n}+\delta{n} \\ $$$$,\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{small}\:\mathrm{angle}\:\delta\theta\: \\ $$$$\mathrm{b}/\mathrm{w}\:\mathrm{the}\:\mathrm{two}\:\mathrm{positions}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\delta\theta^{\mathrm{2}} \:=\:\delta{l}^{\mathrm{2}} \:+\:\delta{m}^{\mathrm{2}} \:+\:\delta{n}^{\mathrm{2}} \:\:?? \\…