Question Number 74139 by MASANJAJ last updated on 19/Nov/19 Commented by TawaTawa last updated on 19/Nov/19 $$\mathrm{a}\::\:\mathrm{b}\:\:=\:\:\frac{\mathrm{21}}{\mathrm{4}}\:,\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\:\:\mathrm{b}\::\:\mathrm{c}\:\:=\:\:\frac{\mathrm{7}}{\mathrm{3}} \\ $$$$\therefore\:\:\:\:\:\:\:\frac{\mathrm{a}}{\mathrm{b}}\:\:=\:\:\frac{\mathrm{21}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\:\frac{\mathrm{b}}{\mathrm{c}}\:\:=\:\:\frac{\mathrm{7}}{\mathrm{3}} \\ $$$$\therefore\:\:\:\:\:\:\mathrm{a}\:\:=\:\:\frac{\mathrm{21b}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}\:\:\:=\:\:\frac{\mathrm{3b}}{\mathrm{7}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}\::\:\mathrm{b}\::\:\mathrm{c}\:\:\:=\:\:\:\frac{\mathrm{21b}}{\mathrm{4}}\::\:\mathrm{b}\::\:\frac{\mathrm{3b}}{\mathrm{7}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}\::\:\mathrm{b}\::\:\mathrm{c}\:\:\:=\:\:\:\frac{\mathrm{21b}}{\mathrm{4}}\:×\:\mathrm{28}\::\:\mathrm{b}\:×\:\mathrm{28}\::\:\frac{\mathrm{3b}}{\mathrm{7}}\:×\:\mathrm{28}…
Question Number 8602 by tawakalitu last updated on 17/Oct/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{that}\:\mathrm{will}\:\mathrm{make} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{13x}^{\mathrm{3}} \:+\:\mathrm{6x}^{\mathrm{2}} \:+\:\mathrm{px}\:+\:\mathrm{q}\:\: \\ $$$$\mathrm{a}\:\mathrm{perfect}\:\mathrm{square} \\ $$ Answered by sandy_suhendra last updated on…
Question Number 74137 by MASANJAJ last updated on 19/Nov/19 Commented by TawaTawa last updated on 19/Nov/19 $$\left(\mathrm{16a}\right) \\ $$$$\:\:\:\:\:\:\mathrm{5}\:\mathrm{painters}\:\mathrm{will}\:\mathrm{spend}\:\mathrm{less}\:\mathrm{hours} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\mathrm{1}\:\mathrm{painter}\:\:\:=\:\:\mathrm{2}\:×\:\mathrm{6}\:\:=\:\:\mathrm{12}\:\mathrm{hrs} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{painters}\:\:\:\:=\:\:\:\frac{\mathrm{12}}{\mathrm{5}}\:\mathrm{hrs} \\ $$…
Question Number 8600 by Chantria last updated on 17/Oct/16 $$\:\boldsymbol{{Test}}\: \\ $$$$\:\mathrm{1}=\sqrt{\mathrm{1}}=\sqrt{\left(−\mathrm{1}\right)\left(−\mathrm{1}\right)}=\sqrt{−\mathrm{1}}\centerdot\sqrt{−\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={i}\centerdot{i}={i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\:\:{so}\:\mathrm{1}=−\mathrm{1} \\ $$$$\:{Find}\:{the}\:{error}. \\ $$ Commented by prakash jain…
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Question Number 139668 by aupo14 last updated on 30/Apr/21 Commented by mr W last updated on 30/Apr/21 $${x}^{\mathrm{2}} \:{can}\:{only}\:{be}\:{formed}\:{from}\:{two}\:{times}\: \\ $$$$\left(\mathrm{1}+{x}+{x}^{\mathrm{3}} \right).\:{therefore}\:{the}\:{coefficient} \\ $$$${of}\:{x}^{\mathrm{2}} \:{is}\:{C}_{\mathrm{2}}…
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Question Number 74130 by mathocean1 last updated on 19/Nov/19 $$\left.\mathrm{h}\left.\mathrm{e}\left.\mathrm{l}\left.\mathrm{l}\left.\mathrm{o}\right]\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\right]−\Pi;\Pi\right]×\right]−\Pi;\Pi\right]\:\mathrm{please} \\ $$$$\begin{cases}{\mathrm{x}−\mathrm{y}=\frac{\Pi}{\mathrm{6}}}\\{\mathrm{cosx}−\sqrt{\mathrm{3}}\mathrm{cosy}=−\frac{\mathrm{1}}{\mathrm{2}}}\end{cases} \\ $$ Answered by Tanmay chaudhury last updated on 19/Nov/19 $${cos}\left(\frac{\pi}{\mathrm{6}}+{y}\right)−\sqrt{\mathrm{3}}\:{cosy}=\frac{−\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{cosy}−\frac{\mathrm{1}}{\mathrm{2}}{siny}−\sqrt{\mathrm{3}}\:{cosy}=\frac{−\mathrm{1}}{\mathrm{2}}…
Question Number 8595 by diofanto last updated on 17/Oct/16 $${Let}\:{N}\:\in\:\mathbb{Z}.\:{Show}\:{that} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{N}−\mathrm{1}} {\sum}}\frac{{N}−{k}}{{sin}\left({k}\pi/{N}\right)}\:>\:\mathrm{2}{N}−\mathrm{2}+\underset{{k}=\mathrm{2}} {\overset{{N}−\mathrm{1}} {\sum}}\frac{{N}−{k}}{{sin}\left(\left({k}−\mathrm{1}\right)\pi/\left({N}−\mathrm{1}\right)\right)} \\ $$$${if},\:{and}\:{only}\:{if},\:{N}\:\geqslant\:\mathrm{12} \\ $$ Commented by prakash jain last…
Question Number 74131 by Learner-123 last updated on 19/Nov/19 $${Can}\:{anyone}\:{share}\:{the}\:{solutions}\:\left({pdf}\right) \\ $$$${of}\:{the}\:{book}\:{Advanced}\:{engineering} \\ $$$${Mathematics}\:{by}\:{Erwin}\:{kreyzig}\:\mathrm{8}{th} \\ $$$${edition}\:? \\ $$$$ \\ $$ Commented by ajfour last updated…