Question Number 48745 by peter frank last updated on 28/Nov/18 Answered by Kunal12588 last updated on 28/Nov/18 $$\left({i}\right){unique}\:{solution}\:\:\frac{{a}_{\mathrm{1}} }{{a}_{\mathrm{2}} }\neq\frac{{b}_{\mathrm{1}} }{{b}_{\mathrm{2}} } \\ $$$$\frac{\mathrm{2}}{\mathrm{4}}\neq\frac{\mathrm{3}}{{a}} \\…
Question Number 48742 by peter frank last updated on 28/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 28/Nov/18 $${xy}−\mathrm{4}{x}+\mathrm{3}{y}−\mathrm{1}=\mathrm{0} \\ $$$${x}\left({y}−\mathrm{4}\right)+\mathrm{3}\left({y}−\mathrm{4}+\mathrm{4}\right)−\mathrm{1}=\mathrm{0} \\ $$$${x}\left({y}−\mathrm{4}\right)+\mathrm{3}\left({y}−\mathrm{4}\right)+\mathrm{11}=\mathrm{0} \\ $$$$\left({x}+\mathrm{3}\right)\left({y}−\mathrm{4}\right)=\left(\sqrt{\mathrm{11}}\:\:\right)^{\mathrm{2}} {i}^{\mathrm{2}}…
Question Number 48744 by peter frank last updated on 28/Nov/18 Answered by Abdulhafeez Abu qatada last updated on 28/Nov/18 $$ \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{{x}\:+\:{iy}}\:=\:{a}\:+\:{ib} \\…
Question Number 48740 by peter frank last updated on 28/Nov/18 Commented by Abdo msup. last updated on 28/Nov/18 $${z}_{\mathrm{1}} {z}_{\mathrm{2}} =\left(\mathrm{1}−{i}\right)^{\mathrm{6}} \:\:{but}\:\mathrm{1}−{i}\:=\sqrt{\mathrm{2}}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:−\frac{{i}}{\:\sqrt{\mathrm{2}}}\right)\:=\sqrt{\mathrm{2}}{e}^{−{i}\frac{\pi}{\mathrm{4}}} \:\Rightarrow \\ $$$$\left(\mathrm{1}−{i}\right)^{\mathrm{6}}…
Question Number 48741 by peter frank last updated on 28/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 28/Nov/18 $${g}\left({x}\right)=\frac{{x}^{\mathrm{2}} −\mathrm{16}}{{x}−\mathrm{4}}\:{x}\neq\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={x}+\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:={t}\:\:\:\:{x}=−\mathrm{4}\:\left({that}\:{is}\:{x}+\mathrm{4}=\mathrm{0}\right) \\ $$$${now}\:{to}\:{find}\:{t}\:{such}\:{that}\:{f}\left({x}\right)={g}\left({x}\right)\:\:{for}\:{all}\:…
Question Number 48664 by ajfour last updated on 26/Nov/18 $${A}\:{travels}\:{in}\:{a}\:{desert},\:{reaches}\:{an} \\ $$$${oasis}\:{and}\:{rests}.\:{Then}\:{B}\:{comes}\:{in}, \\ $$$${followed}\:{by}\:{C}.\:{After}\:{a}\:{while}\:{they} \\ $$$${discuss},\:{what}\:{to}\:{lunch}\:{on};\: \\ $$$${B}\:{opens}\:{a}\:{lunch}\:{box}\:{with}\:\mathrm{5}\:{chapatis}, \\ $$$${C}\:{had}\:{got}\:\mathrm{3}\:{chapatis}.\:{A}\:{had}\:{got} \\ $$$${nothing}.\:{They}\:{lunched}\:{together} \\ $$$${sharing}\:{equally}.\:{Then}\:{A}\:{says}\:{he} \\…
Question Number 48659 by Cheyboy last updated on 26/Nov/18 $$\mathrm{Find}\:\mathrm{x} \\ $$$$\mathrm{3sec}\left[\mathrm{2}\left(\mathrm{x}+\frac{\pi}{\mathrm{6}}\right)\right]=\:\mathrm{4} \\ $$ Answered by ajfour last updated on 26/Nov/18 $${let}\:\:\theta={x}+\frac{\pi}{\mathrm{6}} \\ $$$$\Rightarrow\:\:\mathrm{cos}\:\mathrm{2}\theta\:=\:\mathrm{3}/\mathrm{4} \\…
Question Number 179574 by Ar Brandon last updated on 30/Oct/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{numbers} \\ $$$$\:\mathrm{less}\:\mathrm{than}\:\mathrm{400}\:\mathrm{and}\:\mathrm{not}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{6}. \\ $$ Commented by Ar Brandon last updated on 30/Oct/22 #include <stdio.h> int main(void) { int sum = 0; for (short i = 1; i < 400; i++) if (i % 6 != 0) sum += i; printf("%d", sum); return 0; } Commented…
Question Number 48500 by peter frank last updated on 24/Nov/18 Commented by Abdo msup. last updated on 24/Nov/18 $${y}\left({x}\right)={e}^{{arctan}\left({x}\right)} \:\Rightarrow{y}^{'} \left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:{y}\left({x}\right)\:\Rightarrow \\ $$$${y}^{''} \left({x}\right)\:=−\frac{\mathrm{2}{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 179571 by Ar Brandon last updated on 30/Oct/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{even} \\ $$$$\:\mathrm{3}-\mathrm{digits}\:\mathrm{numbers}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{17}. \\ $$ Commented by Ar Brandon last updated on 30/Oct/22 #include <stdio.h> int main(void) { short sum = 0; for (short i = 102; i < 1000; i += 17) if (i % 2 == 0) sum += i; printf("%hd", sum); return 0; } Commented…