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Category: Algebra

Question-145801

Question Number 145801 by mathdanisur last updated on 08/Jul/21 Answered by ajfour last updated on 08/Jul/21 $${xy}+{tz}={a} \\ $$$${solving}\:{for}\:{x},{y}\:{in}\:{terms}\:{of} \\ $$$${t},{z}\:{from}\:\mathrm{2}{nd}\:{and}\:\mathrm{3}{rd}\:{eqs}. \\ $$$${x}=\frac{{bz}−{ct}}{{z}^{\mathrm{2}} −{t}^{\mathrm{2}} }\:\:;\:\:{y}=\frac{{bt}−{cz}}{{t}^{\mathrm{2}}…

Question-80261

Question Number 80261 by Power last updated on 01/Feb/20 Commented by MJS last updated on 01/Feb/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{obvious}\:\mathrm{maximum}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{2}}\:\mathrm{with}\:{x}>\mathrm{0}?\:\mathrm{this}\:\mathrm{is}\:\mathrm{clear}\:\mathrm{as}\:\mathrm{anything} \\ $$$$\mathrm{might}\:\mathrm{be}. \\ $$ Terms…

find-the-area-bounded-by-y-2x-y-x-2-and-xy-2-

Question Number 145774 by Engr_Jidda last updated on 08/Jul/21 $${find}\:{the}\:{area}\:{bounded}\:{by}\:{y}=\mathrm{2}{x},\:{y}=\frac{{x}}{\mathrm{2}}\:{and}?{xy}=\mathrm{2} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $$\forall{x}\in\mathbb{R}\:\mathrm{2}{x}\geqslant\frac{{x}}{\mathrm{2}}\:\:{A}=\int\left(\mathrm{2}{x}−\frac{{x}}{\mathrm{2}}\right){dx}=\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} \\ $$$${A}={x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}{x}^{\mathrm{2}} =\frac{\mathrm{3}}{\mathrm{4}}{x}^{\mathrm{2}}…