Category: Algebra

Question Number 185723 by mnjuly1970 last updated on 26/Jan/23 Answered by cortano1 last updated on 26/Jan/23 $$g^{\prime }\left(x\right)=\frac{\frac{1}{3\sqrt[3]{x^2}}.f(1+x)-\sqrt[3]{x}.f{}^{\prime }(1+x)}{{\left[f(1+x)\right]}^2}$$$$g{}^{\prime }\left(1\right)=\frac{\frac{1}{3}.(-4)-1.\left(\frac{1}{6}\right)}{16}$$$$=\frac{1}{16}.(-\frac{8}{6}-\frac{1}{6})=-\frac{9}{16.6}$$$$\:\:\:\:\:\:\:\:\:=−\frac{\mathrm{3}}{\mathrm{32}}…

Question Number 185706 by Shrinava last updated on 26/Jan/23 $$\mathrm{if}{\mathrm{x}}^2+\mathrm{x}+1=0$$$$\mathrm{find}:{\mathrm{x}}^{2011}+\frac{1}{{\mathrm{x}}^{2011}}=?$$ Answered by Rajpurohith last updated on 26/Jan/23 Answered…

Question Number 185695 by Spillover last updated on 25/Jan/23 $$If\overrightarrow{u}and\overrightarrow{v}arevectorsin{\mathbb{R}}^3$$$$thenprovethat$$$$\overrightarrow{u}.\overrightarrow{v}=\frac{1}{4}\parallel \overrightarrow{u}+\overrightarrow{v}{\parallel }^2-\frac{1}{4}\parallel \overrightarrow{u}-\overrightarrow{v}{\parallel }^2$$…

Question Number 185694 by Spillover last updated on 25/Jan/23 $$ShowthatthesetV={\mathbb{R}}^{3}with$$$$standardvectoradditionand$$$$multiplicationdefinedas$$$$c(u_1,u_2,u_3)=(0,0,{cu}_3)$$ Terms of…

Question Number 120154 by mathace last updated on 29/Oct/20 $$solveusingLambertWfunction$$$${\left(\frac{8}{7}\right)}^x+17=25x$$ Answered by mr W last updated on 29/Oct/20 $$\left(\frac{\mathrm{8}}{\mathrm{7}}\right)^{{x}} =\mathrm{25}\left({x}−\frac{\mathrm{17}}{\mathrm{25}}\right)…