Question Number 211251 by hardmath last updated on 01/Sep/24 Commented by a.lgnaoui last updated on 04/Sep/24 Commented by a.lgnaoui last updated on 05/Sep/24 $$\frac{\mathrm{sin}\:\mathrm{C}}{\mathrm{MN}}=\frac{\mathrm{sin}\:\mathrm{M}}{\mathrm{BC}−\mathrm{AB}}=\frac{\mathrm{sin}\:\mathrm{N}}{\mathrm{CD}−\mathrm{AD}}\left(\mathrm{1}\right) \\…
Question Number 211207 by Etimbuk last updated on 31/Aug/24 Answered by mr W last updated on 03/Sep/24 $${e}_{\mathrm{1}} ={a}+{b}+{c}+{d} \\ $$$${e}_{\mathrm{2}} ={ab}+{bc}+{cd}+{da}+{ac}+{bd} \\ $$$${e}_{\mathrm{3}} ={abc}+{bcd}+{cda}+{dab}…
Question Number 211222 by RojaTaniya last updated on 31/Aug/24 $${How}\:{many}\:{integers}\:{are}\:{there} \\ $$$$\:\:\:{such}\:{that},\:\:\mathrm{0}\leqslant{n}\leqslant\mathrm{720}\:{and}\: \\ $$$$\:\:\:{n}^{\mathrm{2}} \equiv\mathrm{1}\left({mod}\right)\mathrm{720}? \\ $$ Answered by mahdipoor last updated on 31/Aug/24 $$\Rightarrow{n}^{\mathrm{2}}…
Question Number 211201 by efronzo1 last updated on 31/Aug/24 $$\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\:\mathrm{0} \\ $$$$\:\:\:\mathrm{x}=? \\ $$ Answered by Rasheed.Sindhi last updated on 31/Aug/24 $$\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\:\mathrm{0} \\ $$$$\because−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{2x}} \\…
Question Number 211191 by Tawa11 last updated on 30/Aug/24 Answered by mm1342 last updated on 30/Aug/24 $$\left(\left(\mathrm{2}^{{x}} \right)^{{y}} \right)^{{x}} =\left(\mathrm{3}^{{y}} \right)^{{z}} =\mathrm{7}^{{z}} =\mathrm{11}\:\checkmark \\ $$$$…
Question Number 211157 by RojaTaniya last updated on 30/Aug/24 Commented by Rasheed.Sindhi last updated on 30/Aug/24 $$\left({x},{y},{z}\right)=\left(\mathrm{1},\mathrm{0},\mathrm{0}\right),\left(\mathrm{0},\mathrm{1},\mathrm{0}\right),\left(\mathrm{0},\mathrm{0},\mathrm{1}\right) \\ $$ Answered by Rasheed.Sindhi last updated on…
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Question Number 211147 by hardmath last updated on 29/Aug/24 $$ \\ $$1414; 1515; 1616;…; From 5757 units How many of them are divided by 13…
Question Number 211143 by boblosh last updated on 29/Aug/24 Answered by A5T last updated on 29/Aug/24 $${Let}\:{width}\:{be}\:{w}\Rightarrow{w}={y}+\mathrm{12} \\ $$$${perimeter}=\mathrm{2}\left({w}+{y}\right) \\ $$$$\mathrm{2}\left({w}+\mathrm{30}+{y}+\mathrm{30}\right)=\mathrm{3}×\mathrm{2}\left({w}+{y}\right) \\ $$$$\Rightarrow{w}+{y}=\mathrm{30}\Rightarrow{y}+\mathrm{12}+{y}=\mathrm{30}\Rightarrow{y}=\mathrm{9} \\ $$$$\Rightarrow{length}=\mathrm{9}\:{and}\:{width}=\mathrm{21}…
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