Question Number 224989 by CrispyXYZ last updated on 15/Oct/25 $$\mathrm{Calculate} \\ $$$${D}_{{n}} =\begin{vmatrix}{{x}_{\mathrm{1}} +{a}_{\mathrm{1}} ^{\mathrm{2}} }&{{a}_{\mathrm{1}} {a}_{\mathrm{2}} }&{\ldots}&{{a}_{\mathrm{1}} {a}_{{n}} }\\{{a}_{\mathrm{2}} {a}_{\mathrm{1}} }&{{x}_{\mathrm{2}} +{a}_{\mathrm{2}} ^{\mathrm{2}} }&{\ldots}&{{a}_{\mathrm{2}}…
Question Number 225020 by Abdulazim last updated on 15/Oct/25 $$\:\:\:{tgx}+{tgy}+{tgz}={A} \\ $$$$\:\:\:{tg}^{\mathrm{3}} {x}+{tg}^{\mathrm{3}} {y}+{tg}^{\mathrm{3}} {z}=? \\ $$ Commented by mr W last updated on 16/Oct/25…
Question Number 224888 by Abdulazim last updated on 09/Oct/25 Commented by mr W last updated on 10/Oct/25 $${R}_{\Delta{PQR}} =\frac{{R}_{\Delta{ABC}} }{\mathrm{2}} \\ $$ Commented by mr…
Question Number 224886 by ajfour last updated on 09/Oct/25 $${Find}\:{for}\:{acute}\:\theta,\:\mathrm{sin}\:\theta\:{and}\:\mathrm{cos}\:\theta \\ $$$${in}\:{terms}\:{of}\:\mathrm{0}<{k}<\mathrm{1}, \\ $$$${if}\:\:\:\:\frac{\mathrm{sin}\:\theta\left(\mathrm{1}−\mathrm{cos}\:\theta\right)}{\mathrm{cos}\:\theta\left(\mathrm{1}−\mathrm{sin}\:\theta\right)}={k}. \\ $$ Commented by ajfour last updated on 09/Oct/25 https://youtu.be/0yTJet-ZrLw?si=eNV2L9JpjRiUepqX Commented…
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Question Number 224873 by ajfour last updated on 08/Oct/25 Commented by ajfour last updated on 08/Oct/25 $${If}\:\:{x}^{\mathrm{2}} +{bx}=−{c} \\ $$ Commented by ajfour last updated…
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Question Number 224819 by Abdulazim last updated on 05/Oct/25 Answered by fantastic last updated on 05/Oct/25 Answered by Ghisom_ last updated on 06/Oct/25 $$\left(\mathrm{2}{x}^{\mathrm{3}} +{x}−{a}\right)^{\mathrm{3}}…
Question Number 224770 by Abdulazim last updated on 03/Oct/25 $$\:\:\:\left(\mathrm{2}{x}^{\mathrm{3}} +{x}−\mathrm{3}\right)^{\mathrm{3}} =\mathrm{3}−{x}^{\mathrm{2}} \\ $$ Commented by Ghisom_ last updated on 04/Oct/25 $$\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$ Terms…
Question Number 224763 by behi834171 last updated on 02/Oct/25 Commented by Ghisom_ last updated on 03/Oct/25 $$\mathrm{min}\:{f}\left({x},\:{y}\right)\:\mathrm{is}\:\approx\mathrm{3}.\mathrm{67113410}\:\mathrm{at} \\ $$$$\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\begin{pmatrix}{\frac{\mathrm{5}\sqrt{\mathrm{6}}−\mathrm{3}\sqrt{\mathrm{5}}}{\mathrm{7}}}\\{\mathrm{3}\sqrt{\mathrm{10}}−\mathrm{5}\sqrt{\mathrm{3}}}\end{pmatrix} \\ $$ Commented by behi834171 last…