Question Number 210719 by lmcp1203 last updated on 17/Aug/24 $${find}\:\mathrm{63}!^{\mathrm{36}!} {mod}\mathrm{97}\:\:\:{thanks} \\ $$ Answered by A5T last updated on 19/Aug/24 $$\phi\left(\mathrm{97}\right)=\mathrm{96} \\ $$$$\mathrm{36}!\equiv\mathrm{0}\left({mod}\:\mathrm{96}\right)\Rightarrow\mathrm{36}!=\mathrm{96}{k} \\ $$$$\left(\mathrm{63}!,\mathrm{97}\right)=\mathrm{1}\Rightarrow\mathrm{63}!^{\mathrm{36}!}…
Question Number 210605 by peter frank last updated on 13/Aug/24 Answered by A5T last updated on 13/Aug/24 $${a}=\mathrm{2}^{{x}} ;{b}=\mathrm{2}^{{y}} \Rightarrow{a}+{b}=\mathrm{18};\frac{{a}}{{b}}=\mathrm{5}\Rightarrow{a}=\mathrm{5}{b} \\ $$$$\Rightarrow\mathrm{6}{b}=\mathrm{18}\Rightarrow{b}=\mathrm{3}\Rightarrow{a}=\mathrm{15} \\ $$$$\mathrm{2}^{{x}+{y}} ={ab}=\mathrm{15}×\mathrm{3}=\mathrm{45}…
Question Number 210607 by peter frank last updated on 13/Aug/24 Answered by A5T last updated on 14/Aug/24 $$\mathrm{75}\left(\mathrm{5}^{\mathrm{3}{log}_{\mathrm{2}} {x}} \right)=\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{5}} \right)^{{log}_{\mathrm{2}} {x}×\mathrm{3}} =\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} {x}}…
Question Number 210456 by peter frank last updated on 09/Aug/24 Commented by mr W last updated on 09/Aug/24 $${who}\:{knows}\:{what}\:{is}\:\mathrm{2}\:{and}\:{what}\:{is}\:{z} \\ $$$${when}\:{you}\:{write}\:{them}\:{identically}? \\ $$ Commented by…
Question Number 209892 by lmcp1203 last updated on 25/Jul/24 $${find}\:\:\mathrm{40}^{\mathrm{71}} {mod}\:\mathrm{437}.\:\:\:{thanks} \\ $$$${its}\:\mathrm{67}\:{but}\:{how}? \\ $$ Answered by Rasheed.Sindhi last updated on 25/Jul/24 $$\mathrm{40}^{\mathrm{25}} \equiv\mathrm{14}\:\left({mod}\:\mathrm{437}\right) \\…
Question Number 209860 by lmcp1203 last updated on 23/Jul/24 $$ \\ $$$$\mathrm{Magnitude}\:\mathrm{A}\:\mathrm{varies}\:\mathrm{proportionally}\:\mathrm{with}\:\left(\mathrm{B}\:\mathrm{squared}\:+\:\mathrm{4}\right)\:\mathrm{and}\:\mathrm{magnitude}\:\mathrm{B}\:\mathrm{varies}\:\mathrm{proportionally}\:\mathrm{with} \\ $$$$\left({t}\mathrm{he}\:\mathrm{root}\:\mathrm{of}\:\mathrm{C}\right)\:−\:\mathrm{5}.\:\mathrm{Also}\:\mathrm{when}\:\mathrm{A}\:\mathrm{is}\:\mathrm{16}\:,\:\mathrm{B}\:\mathrm{is}\:\mathrm{12}\:\mathrm{and}\:\mathrm{C}\:\mathrm{takes}\:\mathrm{the}\:\mathrm{value}\:\mathrm{81}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{that}\:\mathrm{A}\:\mathrm{takes} \\ $$$$\mathrm{wh}{e}\mathrm{n}\:\mathrm{C}\:\mathrm{is}\:\mathrm{49}.\:\:\:{help}\:\:{me}.\:{please}.\:{thanks} \\ $$ Answered by mr W last updated on…
Question Number 209744 by peter frank last updated on 20/Jul/24 Answered by mr W last updated on 20/Jul/24 $${X}={Y}=\frac{\mathrm{180}−\mathrm{40}}{\mathrm{2}}=\mathrm{70}° \\ $$ Answered by Spillover last…
Question Number 209598 by peter frank last updated on 16/Jul/24 Answered by Frix last updated on 16/Jul/24 $${a}:{b}=\mathrm{3}:\mathrm{5} \\ $$$${b}:{c}=\mathrm{2}:\mathrm{4}=\mathrm{5}:\mathrm{10} \\ $$$${a}:{b}:{c}=\mathrm{3}:\mathrm{5}:\mathrm{10} \\ $$ Answered…
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Question Number 209602 by peter frank last updated on 16/Jul/24 Answered by som(math1967) last updated on 16/Jul/24 $$\:{let}\:{number}={x} \\ $$$$\:\frac{\mathrm{120}{x}}{\mathrm{100}}\:−\frac{\mathrm{85}{x}}{\mathrm{100}}=\mathrm{14} \\ $$$$\:\frac{\mathrm{35}{x}}{\mathrm{100}}=\mathrm{14} \\ $$$$\Rightarrow{x}=\frac{\mathrm{14}×\mathrm{100}}{\mathrm{35}}=\mathrm{40} \\…