Category: Algebra

Question Number 66743 by pete last updated on 19/Aug/19 $$\mathrm{Each}\mathrm{month}\mathrm{a}\mathrm{store}\mathrm{owner}\mathrm{can}\mathrm{spend}\mathrm{at}$$$$\mathrm{most}\mathrm{\$}100,000\mathrm{on}{\mathrm{PC}}^{\prime }\mathrm{s}\mathrm{and}\mathrm{laptops}.\mathrm{A}$$$$\mathrm{PC}\mathrm{costs}\mathrm{the}\mathrm{store}\mathrm{owner}\mathrm{\$}1000\mathrm{and}\mathrm{a}$$$$\mathrm{laptop}\mathrm{costs}\mathrm{him}\mathrm{\$}1500.\mathrm{Each}\mathrm{PC}\mathrm{is}\mathrm{sold}$$$$\mathrm{for}\mathrm{a}\mathrm{profit}\mathrm{of}\mathrm{\$}400\mathrm{while}\mathrm{a}\mathrm{laptop}\mathrm{is}\mathrm{sold}$$$$\mathrm{for}\mathrm{a}\mathrm{profit}\mathrm{of}\mathrm{\$}700.\mathrm{The}\mathrm{store}\mathrm{owner}\mathrm{estimates}$$$$\mathrm{that}\mathrm{at}\mathrm{least}15{\mathrm{PC}}^{\prime }\mathrm{s}\mathrm{but}\mathrm{no}\mathrm{more}\mathrm{than}$$$$\mathrm{80}\:\mathrm{are}\:\mathrm{sold}\:\mathrm{each}\:\mathrm{month}.\:\mathrm{He}\:\mathrm{also}\:\mathrm{estimates} \…

Question Number 132257 by Salman_Abir last updated on 12/Feb/21 Answered by bemath last updated on 12/Feb/21 $$\left(\mathrm{i}\right)\mathrm{E}(0,0,8),\mathrm{C}(3,3,0)\mathrm{vector}$$$$\mathrm{EC}=3\hat{\mathrm{i}}+3\hat{\mathrm{j}}-8\hat{\mathrm{k}};\mid \mathrm{EC}\mid =\sqrt{9+9+64}=\sqrt{82}$$$$\:\mathrm{H}\left(\mathrm{0},\mathrm{3},\mathrm{8}\right)\:,\mathrm{B}\left(\mathrm{3},\mathrm{0},\mathrm{0}\right)\:\mathrm{vector}\: \…

Question Number 1147 by prakash jain last updated on 04/Jul/15 $$f\left(f\left(x\right)\right)=x^2-x+1$$$$f\left(0\right)=?$$ Commented by prakash jain last updated on 04/Jul/15 $${f}\left({f}\left(\mathrm{0}\right)\right)=\mathrm{1}…

Question Number 132180 by bounhome last updated on 12/Feb/21 $$solve:$$$$2{sec}^{2}x+(2\sqrt{2}-3)secx-3\sqrt{2}=0;0⩽x⩽\frac{\pi }{4}$$ Answered by benjo_mathlover last updated on 12/Feb/21 $$\:\mathrm{3}\sqrt{\mathrm{2}}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\left(\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{3}\right)\mathrm{cos}\:\mathrm{x}−\mathrm{2}=\mathrm{0} \…

Question Number 1041 by tera last updated on 22/May/15 $$iftherootsoftheequation{ax}^2+5x-2=0is2andb.$$$$$$$$then4a^2-4ab+b^2=\dots$$ Answered by prakash jain last updated…