Question Number 18133 by Tinkutara last updated on 15/Jul/17 $$\mathrm{A}\:\mathrm{4}×\mathrm{4}×\mathrm{4}\:\mathrm{wooden}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{painted}\:\mathrm{so} \\ $$$$\mathrm{that}\:\mathrm{one}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{opposite}\:\mathrm{faces}\:\mathrm{is}\:\mathrm{blue}, \\ $$$$\mathrm{one}\:\mathrm{pair}\:\mathrm{green}\:\mathrm{and}\:\mathrm{one}\:\mathrm{pair}\:\mathrm{red}.\:\mathrm{The} \\ $$$$\mathrm{cube}\:\mathrm{is}\:\mathrm{now}\:\mathrm{sliced}\:\mathrm{into}\:\mathrm{64}\:\mathrm{cubes}\:\mathrm{of}\:\mathrm{side} \\ $$$$\mathrm{1}\:\mathrm{unit}\:\mathrm{each}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{smaller}\:\mathrm{cubes}\:\mathrm{have} \\ $$$$\mathrm{no}\:\mathrm{painted}\:\mathrm{face}? \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{smaller}\:\mathrm{cubes}\:\mathrm{have} \\…
Question Number 18131 by Tinkutara last updated on 15/Jul/17 $$\mathrm{A}\:\mathrm{stone}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{direction}\:\mathrm{so}\:\mathrm{as}\:\mathrm{to}\:\mathrm{hit}\:\mathrm{a} \\ $$$$\mathrm{bird}\:\mathrm{on}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{telegraph}\:\mathrm{post}\:\mathrm{of} \\ $$$$\mathrm{height}\:{h},\:\mathrm{and}\:\mathrm{then}\:\mathrm{attain}\:\mathrm{a}\:\mathrm{height}\:\mathrm{2}{h} \\ $$$$\mathrm{above}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{If},\:\mathrm{at}\:\mathrm{an}\:\mathrm{instant}\:\mathrm{of} \\ $$$$\mathrm{projection},\:\mathrm{the}\:\mathrm{bird}\:\mathrm{were}\:\mathrm{to}\:\mathrm{fly}\:\mathrm{away} \\ $$$$\mathrm{horizontal}\:\mathrm{with}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{speed},\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{velocities}\:\mathrm{of} \\…
Question Number 83662 by jagoll last updated on 05/Mar/20 $$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{3}}} \\ $$$$\mathrm{find}\:\mathrm{domain}\:\mathrm{function}\: \\ $$$$\left(\mathrm{g}\:\bullet\:\mathrm{f}\right)\left(\mathrm{x}\right) \\ $$ Commented by MJS last updated on 05/Mar/20…
Question Number 18123 by mondodotto@gmail.com last updated on 15/Jul/17 Commented by prakash jain last updated on 15/Jul/17 $$\mathrm{log}\:\left({x}−\mathrm{3}\right)^{\mathrm{1}/\mathrm{3}} +\mathrm{log}\:\mathrm{5}−\mathrm{log}\:\left({x}−\mathrm{2}\right)^{\mathrm{2}} = \\ $$$$\mathrm{log}\:\mathrm{5}=\mathrm{log}\:\left({x}−\mathrm{2}\right)^{\mathrm{2}} −\mathrm{log}\:\left({x}−\mathrm{3}\right)^{\mathrm{1}/\mathrm{3}} \\ $$$$\mathrm{5}=\frac{\left({x}−\mathrm{2}\right)^{\mathrm{2}}…
Question Number 149192 by Samimsultani last updated on 03/Aug/21 Answered by prakash jain last updated on 03/Aug/21 $$\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}\right)^{{x}} ={u} \\ $$$$\left(\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}\right)^{{x}} =\frac{\mathrm{1}}{{u}} \\ $$$${u}−\frac{\mathrm{1}}{{u}}=\mathrm{40}\sqrt{\mathrm{6}} \\…
Question Number 149189 by Naser last updated on 03/Aug/21 Commented by Tawa11 last updated on 03/Aug/21 $$\mathrm{great} \\ $$ Answered by Ar Brandon last updated…
Question Number 83654 by jagoll last updated on 05/Mar/20 $$\mathrm{solve}\:\mathrm{this}\:\mathrm{equation}\: \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{4}} {x}=\mathrm{cos}\:^{\mathrm{2}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x} \\ $$ Commented by jagoll last updated on 05/Mar/20…
Question Number 149188 by mathdanisur last updated on 03/Aug/21 $${f}\left({x}\right)\:=\:{ax}^{\mathrm{99}} \:+\:{bx}^{\mathrm{77}} \:+\:{cx}^{\mathrm{55}} \:+\:\mathrm{975} \\ $$$${f}\left(−\mathrm{975}\right)\:=\:\mathrm{1000} \\ $$$${find}\:\:\:{f}\left(\mathrm{975}\right)\:=\:? \\ $$ Answered by mr W last updated…
Question Number 149191 by mnjuly1970 last updated on 03/Aug/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:……{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sech}\left(\pi{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\:\mathrm{2}} }\:{dx}=? \\ $$$$\:………{m}.{n}… \\ $$ Answered by mindispower last…
Question Number 83653 by jagoll last updated on 05/Mar/20 $$\mathrm{find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{y}=\:\frac{\mathrm{4}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)} \\ $$ Answered by MJS last updated on 05/Mar/20 $${x}=\pm\mathrm{2}\sqrt{\frac{{y}+\mathrm{1}}{{y}}} \\ $$$$\Rightarrow\:{y}\leqslant−\mathrm{1}\vee{y}>\mathrm{0}…