Question Number 55587 by byaw last updated on 27/Feb/19 $$\mathrm{If}\:\mathrm{12\%}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:{s}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:{e\%}\:\mathrm{of}\:{s}? \\ $$$$\mathrm{A}.\:\frac{{es}}{\mathrm{12}} \\ $$$$\mathrm{B}.\:\frac{{es}}{\mathrm{88}} \\ $$$$\mathrm{C}.\:\frac{\mathrm{12}{s}}{{e}} \\ $$$$\mathrm{D}.\:\frac{\mathrm{12}{e}}{{s}} \\ $$ Answered by peter…
Question Number 55576 by pieroo last updated on 27/Feb/19 $$\mathrm{An}\:\mathrm{aeroplane}\:\mathrm{has}\:\mathrm{an}\:\mathrm{air}\:\mathrm{speed}\:\mathrm{of}\: \\ $$$$\mathrm{120kmh}^{−\mathrm{1}} \:\mathrm{and}\:\mathrm{flies}\:\mathrm{on}\:\mathrm{a}\:\mathrm{course}\:\mathrm{of} \\ $$$$\mathrm{bearing}\:\mathrm{S60}°\mathrm{E}.\:\mathrm{A}\:\mathrm{wind}\:\mathrm{is}\:\mathrm{blowing}\:\mathrm{steadily} \\ $$$$\mathrm{at}\:\mathrm{30kmh}^{−\mathrm{1}} \:\mathrm{from}\:\mathrm{a}\:\mathrm{bearing}\:\mathrm{of}\:\mathrm{N60}°\mathrm{E}. \\ $$$$\mathrm{Find}; \\ $$$$\mathrm{i}.\:\mathrm{the}\:\mathrm{ground}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{aeroplane} \\ $$$$\mathrm{ii}.\:\mathrm{the}\:\mathrm{path}\:\mathrm{of}\:\mathrm{the}\:\mathrm{aeroplane} \\…
Question Number 121099 by Anuragkar last updated on 05/Nov/20 $${Let}\:\alpha\:{be}\:{a}\:{root}\:{of}\:\:{x}^{\mathrm{5}} −{x}^{\mathrm{3}} +{x}−\mathrm{2}=\mathrm{0} \\ $$$${Then}\:{prove}\:{that}\:\:\:\left[\alpha^{\mathrm{6}} \right]=\mathrm{3}\:\:\:\:\:\:\:{where}\left[\lambda\right]\:\:{denotes}\:{greatest}\:{integer} \\ $$$${less}\:{than}\:{or}\:\:{equal}\:\lambda \\ $$ Answered by TANMAY PANACEA last updated…
Question Number 186627 by Mingma last updated on 07/Feb/23 Commented by Frix last updated on 07/Feb/23 $$\mathrm{As}\:\mathrm{always}:\:\mathrm{The}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{42} \\ $$$$\bullet\:\mathrm{We}\:\mathrm{have}\:\mathrm{2}\:\mathrm{equations}\:\mathrm{for}\:\mathrm{6}\:\mathrm{unknowns}\:\Rightarrow \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{choose}\:\mathrm{4}\:\mathrm{of}\:\mathrm{them}\:\mathrm{and}\:\mathrm{solve}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{2}. \\ $$$$\bullet\:\mathrm{We}\:\mathrm{can}\:\mathrm{set}\:\frac{{a}+{b}+{c}}{{x}+{y}+{z}}=\mathrm{42}\:\Rightarrow\:\mathrm{We}\:\mathrm{now}\:\mathrm{have}…
Question Number 186616 by ajfour last updated on 07/Feb/23 Answered by ajfour last updated on 07/Feb/23 $${say}\:{m}=\mathrm{1}\:\&\:{forget}\:{the}\:{tangent}. \\ $$$${C}\left({h},{k}\right)\equiv\left(\mathrm{1}+{p},\:{r}\right) \\ $$$${let}\:{circle}\:{touches}\:{cubic}\:{curve}\:{at} \\ $$$${Q}\left({q},\:{q}^{\mathrm{3}} −{q}−{c}\right) \\…
Question Number 186582 by ajfour last updated on 06/Feb/23 $$\left(\frac{\mathrm{10}{x}^{\mathrm{3}} −{c}}{\mathrm{4}{x}^{\mathrm{4}} −{x}+\mathrm{1}}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} ={x}\left({x}^{\mathrm{3}} +\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 121041 by bramlexs22 last updated on 05/Nov/20 $$\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\left(−\mathrm{1}\right)^{\mathrm{k}} .\mathrm{k}\:=?\: \\ $$ Answered by Dwaipayan Shikari last updated on 05/Nov/20 $$−\mathrm{1}+\mathrm{2}−\mathrm{3}+\mathrm{4}−\mathrm{5}+\mathrm{6}−\mathrm{7}+\mathrm{8}−…=\frac{{n}}{\mathrm{2}} \\…
Question Number 186572 by mustafazaheen last updated on 06/Feb/23 $${f}=\left\{\left(\mathrm{1},\mathrm{2}\right),\left(\mathrm{4},\mathrm{6}\right),\left(\mathrm{5},\mathrm{8}\right)\right\}\:\:{and}\:\:\:{g}=\left\{\left(\mathrm{1},\mathrm{7}\right),\left(\mathrm{2},\mathrm{4}\right),\left(\mathrm{5},\mathrm{8}\right)\right\} \\ $$$${the}\:{domain}\:{of}\:\:\:{f}\left({g}\left({x}\right)\right)\:\:\:{which}\:{number}\:{is}\:{not}\:{include}? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{1}\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right){all}\:{corect} \\ $$$${how}\:{is}\:{the}\:{solution}? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 06/Feb/23…
Question Number 186571 by ajfour last updated on 06/Feb/23 $${If}\:\:\:{x}=−\frac{\mathrm{1}}{\left(\mathrm{1}+{m}\right)}\left(\frac{\mathrm{2}}{\mathrm{3}}\pm\sqrt{\frac{\mathrm{4}}{\mathrm{9}}\pm\frac{{ia}\sqrt{{m}}}{\mathrm{12}}}\right) \\ $$$${where}\:\:\:\left(\mathrm{1}+{m}\right)^{\mathrm{2}} ={am} \\ $$$$\:\:\:\:{and}\:{that}\:\:\mathrm{9}{a}\left({a}+\mathrm{16}\right)^{\mathrm{2}} =\left(\mathrm{16}\right)^{\mathrm{3}} \\ $$$${Find}\:{real}\:{x}. \\ $$ Answered by ajfour last updated…
Question Number 55501 by ajfour last updated on 25/Feb/19 $${Roots}\:{of}\:{x}^{\mathrm{3}} +{px}+{q}=\mathrm{0} \\ $$$${are}\:\:{x}\:=\:{u}+{v} \\ $$$${u}^{\mathrm{3}} ,\:{v}^{\mathrm{3}} \:{are}\:{roots}\:{of} \\ $$$$\:\:\:\:\:\:\:{z}^{\mathrm{2}} −\alpha^{\mathrm{3}} {z}+\beta^{\mathrm{6}} =\mathrm{0} \\ $$$$\:\:\:\frac{{d}^{\mathrm{2}} \left({y}/{x}\right)}{{dx}^{\mathrm{2}}…