Question Number 18758 by 786786AM last updated on 29/Jul/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:{r}^{\mathrm{th}} \:\mathrm{and}\:\left({r}+\mathrm{1}\right)^{\mathrm{th}} \:\mathrm{terms} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{3}+\mathrm{7}{x}\right)^{\mathrm{29}} \:\mathrm{are}\:\mathrm{equal}, \\ $$$$\mathrm{then}\:\:{r}\:\mathrm{equals} \\ $$ Answered by Tinkutara last updated on…
Question Number 18755 by ram1234 last updated on 29/Jul/17 $$\mathrm{In}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{if}\:{c}\:=\:\mathrm{2},\:{A}\:=\:\mathrm{120}°,\:{a}\:=\:\sqrt{\mathrm{6}}\:, \\ $$$$\mathrm{then}\:\:{C}\:= \\ $$ Answered by Tinkutara last updated on 29/Jul/17 $$\frac{\mathrm{sin}\:{C}}{\mathrm{2}}\:=\:\frac{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}{\:\sqrt{\mathrm{6}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$$$\mathrm{sin}\:{C}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\…
Question Number 18731 by juniorjoseph679@gmail.com last updated on 29/Jul/17 $$\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{5}}\:−\:\:\mathrm{tan}\:\frac{\pi}{\mathrm{15}}\:−\:\sqrt{\mathrm{3}}\:\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{5}}\:\mathrm{tan}\:\frac{\pi}{\mathrm{15}}\:= \\ $$ Answered by 32 last updated on 29/Jul/17 $$ \\ $$ Answered by Tinkutara…
Question Number 18730 by chernoaguero@gmail.com last updated on 29/Jul/17 $$\mathrm{If}\:\:\left[\sqrt[{\mathrm{9}}]{\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{5}} }\right]^{\sqrt{{x}−\mathrm{5}}} ={a}^{\mathrm{0}} ,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}. \\ $$ Commented by Tinkutara last updated on 29/Jul/17 $${x}\:=\:\mathrm{5}. \\ $$…
Question Number 18702 by Christo01 last updated on 28/Jul/17 $$\mathrm{If}\:\:\:{a}\:\mathrm{sin}^{\mathrm{2}} {x}+{b}\:\mathrm{cos}^{\mathrm{2}} {x}\:=\:{c},\: \\ $$$$\:\:\:\:\:\:\:{b}\:\mathrm{sin}^{\mathrm{2}} {y}+{a}\:\mathrm{cos}^{\mathrm{2}} {y}\:=\:{d}\:\:\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:{a}\:\mathrm{tan}^{\mathrm{2}} {x}\:=\:{b}\:\mathrm{tan}\:{y}\:\: \\ $$$$\mathrm{then}\:\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$…
Question Number 18701 by Christo01 last updated on 28/Jul/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\mathrm{tan}\:\mathrm{6}°\:\mathrm{tan}\:\mathrm{42}°\:\mathrm{tan}\:\mathrm{66}°\:\mathrm{tan}\:\mathrm{78}°\:\:\mathrm{is} \\ $$ Commented by eonni_hachi last updated on 28/Jul/17 $$\mathrm{1} \\ $$ Answered…
Question Number 18667 by chernoaguero@gmail.com last updated on 27/Jul/17 $$\mathrm{If}\:{x}=\mathrm{2}^{\mathrm{1}/\mathrm{3}} −\:\mathrm{2}^{−\mathrm{1}/\mathrm{3}} ,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\mathrm{2}{x}^{\mathrm{3}} +\mathrm{6}{x}. \\ $$ Answered by ajfour last updated on 27/Jul/17 $$\mathrm{2x}^{\mathrm{3}}…
Question Number 18466 by chernoaguero@gmail.com last updated on 22/Jul/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit} \\ $$$$\mathrm{number}\:\mathrm{is}\:\mathrm{5}\:\mathrm{and}\:\mathrm{their}\:\mathrm{difference}\:\mathrm{is}\:\mathrm{3}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}. \\ $$ Answered by Tinkutara last updated on 22/Jul/17 $$\mathrm{Let}\:\mathrm{number}\:=\:\mathrm{10}{x}\:+\:{y} \\…
Question Number 18465 by chernoaguero@gmail.com last updated on 22/Jul/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit} \\ $$$$\mathrm{number}\:\mathrm{is}\:\mathrm{5}\:\mathrm{and}\:\mathrm{their}\:\mathrm{difference}\:\mathrm{is}\:\mathrm{3}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}. \\ $$ Answered by ajfour last updated on 22/Jul/17 $$\mathrm{let}\:\mathrm{smaller}\:\mathrm{digit}=\mathrm{x} \\…
Question Number 18464 by chernoaguero@gmail.com last updated on 22/Jul/17 $$\mathrm{3}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{30}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{not}\:\mathrm{consecutive} \\ $$$$\mathrm{is} \\ $$ Answered by Tinkutara last updated on 22/Jul/17 $$\mathrm{Total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{a}\:\mathrm{triplet} \\…