Question Number 140998 by mohammad17 last updated on 14/May/21 Answered by Ar Brandon last updated on 14/May/21 $$\mathcal{I}=\int\frac{\mathrm{sin4x}}{\mathrm{cos}^{\mathrm{4}} \mathrm{x}+\mathrm{4}}\mathrm{dx}=\int\frac{\mathrm{2sin2xcos2x}}{\left(\frac{\mathrm{1}+\mathrm{cos2x}}{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{4}}\mathrm{dx},\:\mathrm{c}=\mathrm{cos2x} \\ $$$$\:\:\:=−\int\frac{\mathrm{c}}{\frac{\left(\mathrm{c}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{4}}+\mathrm{4}}\mathrm{dc}=−\mathrm{4}\int\frac{\mathrm{cdc}}{\mathrm{c}^{\mathrm{2}} +\mathrm{2c}+\mathrm{17}}\mathrm{dc} \\…
Question Number 9923 by konen last updated on 16/Jan/17 $$\mathrm{i}=\sqrt{−\mathrm{1}} \\ $$$$\mathrm{z}=\:\left(\mathrm{1}−\mathrm{i}\right)^{\mathrm{17}} −\left(\mathrm{1}+\mathrm{i}\right)^{\mathrm{17}} \:\Rightarrow\:\mathrm{z}=?\: \\ $$ Commented by RasheedSoomro last updated on 16/Jan/17 $$\mathrm{z}=\:\left(\mathrm{1}−\mathrm{i}\right)^{\mathrm{17}} −\left(\mathrm{1}+\mathrm{i}\right)^{\mathrm{17}}…
Question Number 75456 by peter frank last updated on 11/Dec/19 $${Find}\:{the}\:{domain}\:{and}\: \\ $$$${range}\:{of}\:{relation} \\ $$$$\left({a}\right){R}=\left\{\left({x},{y}\right):{y}=\sqrt{{x}^{\mathrm{2}} −\mathrm{6}}\:\right\} \\ $$$$\left({b}\right){R}=\left\{\left({x},{y}\right):{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{1}\:\right\} \\ $$ Answered by Kunal12588…
Question Number 9921 by Tawakalitu ayo mi last updated on 15/Jan/17 Answered by mrW1 last updated on 16/Jan/17 $$\mathrm{2}{x}=\mathrm{180}−\mathrm{50}−\mathrm{70}=\mathrm{60} \\ $$$$\Rightarrow{x}=\mathrm{30} \\ $$$${y}=\mathrm{180}−\mathrm{50}−{x}=\mathrm{100} \\ $$$${z}=\mathrm{180}−{x}−\left(\mathrm{70}+\mathrm{50}\right)=\mathrm{180}−\mathrm{30}−\mathrm{120}=\mathrm{30}…
Question Number 75457 by Master last updated on 11/Dec/19 Commented by MJS last updated on 11/Dec/19 $$\mathrm{no}\:\mathrm{exact}\:\mathrm{solution}\:\mathrm{possible} \\ $$$$\mathrm{try}\:\mathrm{to}\:\mathrm{approximate},\:\mathrm{there}\:\mathrm{are}\:\mathrm{3}\:\mathrm{solutions}, \\ $$$$\mathrm{one}\:\mathrm{real}\:\mathrm{and}\:\mathrm{two}\:\mathrm{conjugated}\:\mathrm{complex} \\ $$ Commented by…
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 \\…