Question Number 214199 by mr W last updated on 01/Dec/24 Commented by mr W last updated on 01/Dec/24 $$\left[{see}\:{Q}\mathrm{214176}\right] \\ $$$${find}\:{the}\:{radius}\:{of}\:{the}\:{maximal} \\ $$$${circle}\:{inscribed}\:{between}\:{the}\:{curves} \\ $$$${f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{as}\:{shown}.…
Question Number 214186 by hardmath last updated on 30/Nov/24 $$\mathrm{If}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{1}\:\:\:\mathrm{find}\:\:\:\mathrm{x}^{\mathrm{61}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{61}} }+\:\mathrm{4}\:\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 30/Nov/24 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{1};\:{x}^{\mathrm{61}} +\frac{\mathrm{1}}{{x}^{\mathrm{61}} }+\mathrm{4}=? \\…
Question Number 214181 by golsendro last updated on 30/Nov/24 $$\:\:\:\:\underbrace{\:} \\ $$ Answered by efronzo1 last updated on 30/Nov/24 $$\:\:\:\cancel{\nprec} \\ $$ Terms of Service…
Question Number 214183 by jlewis last updated on 30/Nov/24 $$\left.\mathrm{a}\right)\:\mathrm{The}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{elevation}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{A}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{top}\:\mathrm{of}\:\mathrm{building}\:\mathrm{5m}\:\mathrm{away}\:\mathrm{is}\:\mathrm{45}°.\:\mathrm{Another}\:\mathrm{point} \\ $$$$\mathrm{B}\:\mathrm{is}\:\mathrm{4m}\:\mathrm{from}\:\mathrm{A}.\:\mathrm{By}\:\mathrm{scale}\:\mathrm{drawing}\:\mathrm{determine}. \\ $$$$\left.\mathrm{i}\right)\:\mathrm{the}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{elevation}\:\mathrm{from}\:\mathrm{point}\:\mathrm{B} \\ $$$$\left.\mathrm{ii}\right)\mathrm{the}\:\mathrm{height}\:\mathrm{of}\:\mathrm{the}\:\mathrm{building} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{A}\:\mathrm{man}\:\mathrm{who}\:\mathrm{is}\:\mathrm{in}\:\mathrm{the}\:\mathrm{elevator}\:\mathrm{half}\:\mathrm{way}\:\mathrm{the} \\ $$$$\mathrm{building}\:\mathrm{notices}\:\mathrm{a}\:\mathrm{lorry}\:\mathrm{approaching}\:\mathrm{the} \\ $$$$\mathrm{building}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{20}°.\:\mathrm{How} \\…
Question Number 214176 by a.lgnaoui last updated on 30/Nov/24 $$\mathrm{find}\:\mathrm{the}\:\mathrm{vslue}\:\mathrm{of}\:\boldsymbol{\mathrm{R}}\left(\mathrm{radius}\:\boldsymbol{\mathrm{o}}\mathrm{f}\:\mathrm{circle}\:\mathrm{betwen}\:\mathrm{two}\:\right. \\ $$$$\:\mathrm{diagrame}\:\mathrm{curves}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\mathrm{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)\:\mathrm{as}\:\mathrm{showen}. \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{use}\:\mathrm{the}\:\mathrm{programer}\:\mathrm{calculator}. \\ $$ Commented by a.lgnaoui last updated on 30/Nov/24 Commented by…
Question Number 214178 by ajfour last updated on 30/Nov/24 Commented by ajfour last updated on 01/Dec/24 $${Q}.\:\mathrm{214132}\:\:{But}\:{with}\:{left}\:{roller}\:{fixed}. \\ $$ Answered by ajfour last updated on…
Question Number 214140 by issac last updated on 29/Nov/24 $$\mathrm{Let}\:{F}\:;\:\mathbb{R}^{{n}} \rightarrow\mathbb{R}^{{n}} \:\mathrm{be}\:\mathrm{continuously} \\ $$$$\mathrm{differentiable}\: \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\:\mathrm{assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Jacoboian}\:\mathrm{matrix}\: \\ $$$$\frac{\partial{f}_{{i}} }{\partial{x}_{{j}} }\:\mathrm{has}\:\mathrm{rank}\:{n}\:\mathrm{everywhere} \\ $$$$\mathrm{prove}\:\mathrm{that}\:{f}\left(\mathbb{R}^{{n}} \right)\mathrm{is}\:\mathrm{open} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\:\mathrm{suppose}\:\mathrm{that}\:{f}^{−\mathrm{1}}…
Question Number 214152 by Ismoiljon_008 last updated on 29/Nov/24 Commented by Ismoiljon_008 last updated on 29/Nov/24 $$ \\ $$$$\:\:\:{What}\:{is}\:{the}\:{number}\:{of}\:{points}\:{in}\:{the}\: \\ $$$$\:\:\:{interval}\:\left(−\mathrm{1};\mathrm{12}\right)\:{where}\:{the}\:{derivative} \\ $$$$\:\:\:{of}\:{the}\:{function}\:{y}\:=\:{f}\left({x}\right)\:{is}\:{equal}\:{to}\:{zero}\:? \\ $$…
Question Number 214138 by abdelsalam last updated on 29/Nov/24 Commented by abdelsalam last updated on 29/Nov/24 $${find}\:\:{x} \\ $$ Answered by issac last updated on…
Question Number 214132 by ajfour last updated on 29/Nov/24 Answered by MathematicalUser2357 last updated on 29/Nov/24 $${b}^{\mathrm{2}} ={a}^{\mathrm{2}} +{c}^{\mathrm{2}} −\mathrm{2}{ac}\:\mathrm{cos}\:\theta \\ $$$$\mathrm{cos}\:\theta=\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }{\mathrm{2}{ac}}…