Question Number 162651 by Mathematification last updated on 31/Dec/21 Answered by tounghoungko last updated on 31/Dec/21 $$\:{y}=−{x}\left({x}+{a}\right)^{\mathrm{2}} \:=−{x}^{\mathrm{3}} −\mathrm{2}{ax}^{\mathrm{2}} −{a}^{\mathrm{2}} {x} \\ $$$$\:{y}'=−\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{ax}−{a}^{\mathrm{2}} \:=\:\mathrm{0}…
Question Number 162561 by Mathematification last updated on 30/Dec/21 Answered by MJS_new last updated on 30/Dec/21 $$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mid{AB}\mid \\ $$$$\mathrm{with}\:{A}=\begin{pmatrix}{{p}}\\{{p}^{\mathrm{2}} }\end{pmatrix}\:\mathrm{and}\:{B}=\begin{pmatrix}{{q}}\\{\mathrm{ln}\:{q}}\end{pmatrix}\:.\:\mathrm{this}\:\mathrm{can}\:\mathrm{only} \\ $$$$\mathrm{be}\:\mathrm{approximated}.\:\mathrm{I}\:\mathrm{get} \\ $$$${p}\approx.\mathrm{538167} \\…
Question Number 162496 by cortano last updated on 29/Dec/21 Answered by mr W last updated on 30/Dec/21 Commented by mr W last updated on 30/Dec/21…
Question Number 31406 by rahul 19 last updated on 08/Mar/18 Commented by mrW2 last updated on 08/Mar/18 $${OM}_{{r}} =\frac{{OA}_{{r}} +{OA}_{{r}+\mathrm{1}} }{\mathrm{2}}=\frac{\mathrm{1}+{q}}{\mathrm{2}}×{OA}_{{r}} \\ $$$$\Sigma{OM}_{{r}} =\frac{\mathrm{1}+{q}}{\mathrm{2}}×\Sigma{OA}_{{r}} =\frac{\mathrm{1}+{q}}{\mathrm{2}\left(\mathrm{1}−{q}\right)}×{OA}_{\mathrm{1}}…
Question Number 31383 by rahul 19 last updated on 07/Mar/18 Commented by rahul 19 last updated on 07/Mar/18 $${but}\:{this}\:{ans}.\:{i}\:{am}\:{getting}\:{by}\:{assuming} \\ $$$${isosceles}\:{triangle}.\:{for}\:{general}\:{triangle} \\ $$$${how}\:{can}\:{do}\:? \\ $$…
Question Number 96907 by bemath last updated on 05/Jun/20 $$\underset{\mathrm{z}\:=\:\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\:\mathrm{cos}\:^{\mathrm{3}} \left(\frac{\pi\mathrm{z}}{\mathrm{3}}\right)\:=\:? \\ $$ Commented by john santu last updated on 05/Jun/20 $$\mathrm{cos}\:\mathrm{3x}\:=\:\mathrm{4cos}\:^{\mathrm{3}} \mathrm{x}−\mathrm{3cos}\:\mathrm{x}…
Question Number 31371 by momo last updated on 07/Mar/18 $${A}\:{point}\:{moves}\:{in}\:{xy}\:{plane}\:{such}\: \\ $$$${that}\:{sum}\:{of}\:{its}\:{distance}\:{from}\:{two}\: \\ $$$${mutually}\:{perpendicular}\:{lines}\:{is} \\ $$$${always}\:\mathrm{3}.{The}\:{area}\:{encloded}\:{by} \\ $$$${the}\:{locus}\:{of}\:{the}\:{point}\:{is} \\ $$ Answered by ajfour last updated…
Question Number 162396 by Mathematification last updated on 29/Dec/21 Commented by Mathematification last updated on 29/Dec/21 $${Thank}\:{you}\:{so}\:{much}.\:{But}\:{how}\:{do}\:{we}\:{know}\: \\ $$$${when}\:{to}\:{apply}\:{the}\:{formula}? \\ $$ Answered by mr W…
Question Number 162309 by Mathematification last updated on 28/Dec/21 Commented by mr W last updated on 28/Dec/21 $${it}\:{seems}\:{that}\:{you}\:{and}\:{ms}.\:{tawa}\:{are} \\ $$$${visiting}\:{the}\:{same}\:{college},\:{since}\:{your} \\ $$$${questions}\:{seem}\:{to}\:{be}\:{from}\:{the}\:{same} \\ $$$${source}\:\left({or}\:{teacher}\right). \\…
Question Number 31147 by momo last updated on 03/Mar/18 $${if}\:{point}\:{of}\:{intersection}\:{of}\:{curves} \\ $$$${C}_{\mathrm{1}} =\lambda{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{9}{x}+\mathrm{3}\:{and} \\ $$$${C}_{\mathrm{2}} =\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} −\mathrm{4}{xy}+\mathrm{3}{x}−\mathrm{1}\: \\ $$$${subtends}\:{a}\:{right}\:{angle}\:{at}\:{origin}\:{the} \\ $$$${value}\:{of}\:\lambda\:{is}? \\…