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Author: Tinku Tara

A-1-2-2-3-3-4-10-11-B-3-8-6-12-9-16-30-44-A-B-

Question Number 10339 by konen last updated on 04/Feb/17 $$\mathrm{A}=\mathrm{1}×\mathrm{2}\:+\:\mathrm{2}×\mathrm{3}\:+\mathrm{3}×\mathrm{4}+…+\mathrm{10}×\mathrm{11} \\ $$$$\mathrm{B}=\mathrm{3}×\mathrm{8}\:+\mathrm{6}×\mathrm{12}\:+\mathrm{9}×\mathrm{16}+…+\mathrm{30}×\mathrm{44} \\ $$$$\Rightarrow\frac{\mathrm{A}}{\mathrm{B}}=? \\ $$ Answered by mrW1 last updated on 04/Feb/17 $${a}_{{n}} ={n}×\left({n}+\mathrm{1}\right)…

Find-the-minimum-value-of-k-such-that-for-arbitrary-a-b-gt-0-we-have-a-1-3-b-1-3-k-a-b-1-3-

Question Number 141405 by iloveisrael last updated on 18/May/21 $$\:\:\:\:\:{Find}\:{the}\:{minimum}\:{value}\:{of}\:{k} \\ $$$$\:\:\:\:\:{such}\:{that}\:{for}\:{arbitrary}\:{a},{b}\:>\mathrm{0} \\ $$$$\:\:\:\:\:{we}\:{have}\:\:\sqrt[{\mathrm{3}\:}]{{a}}\:+\:\sqrt[{\mathrm{3}\:}]{{b}}\:\leqslant\:{k}\:\sqrt[{\mathrm{3}\:}]{{a}+{b}}\: \\ $$ Answered by EDWIN88 last updated on 18/May/21 $$\:\mathrm{consider}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt[{\mathrm{3}\:}]{\mathrm{x}} \\…

fjnd-inverse-of-matrix-2-5-1-3-

Question Number 141400 by Raffaqet last updated on 18/May/21 $${fjnd}\:{inverse}\:{of}\:{matrix}\begin{bmatrix}{\mathrm{2}}&{−\mathrm{5}}\\{\mathrm{1}}&{\mathrm{3}}\end{bmatrix} \\ $$ Answered by iloveisrael last updated on 18/May/21 $$\:{A}^{−\mathrm{1}} \:=\:\frac{\mathrm{1}}{\mathrm{6}−\left(−\mathrm{5}\right)}\:\begin{bmatrix}{\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{5}}\\{−\mathrm{1}\:\:\:\:\:\mathrm{2}}\end{bmatrix} \\ $$$${A}^{−\mathrm{1}} \:=\:\begin{bmatrix}{\mathrm{3}/\mathrm{11}\:\:\:\:\:\:\:\:\:\mathrm{5}/\mathrm{11}}\\{−\mathrm{1}/\mathrm{11}\:\:\:\:\:\mathrm{2}/\mathrm{11}}\end{bmatrix} \\…

Question-10324

Question Number 10324 by amir last updated on 04/Feb/17 Answered by mrW1 last updated on 04/Feb/17 $${y}=\frac{\mathrm{1}}{{x}} \\ $$$${slope}\:{of}\:{tangent}\:{line}: \\ $$$${m}_{{t}} \left({x}\right)=\mathrm{tan}\:\theta={y}'\left({x}\right)=−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$${let}\:{B}\left({t},{s}\right)\:{be}\:{a}\:{point}\:{on}\:{the}\:{curve}\:…

Question-10323

Question Number 10323 by amir last updated on 04/Feb/17 Answered by mrW1 last updated on 04/Feb/17 $${there}\:{are}\:\mathrm{4}\:{circles}\:{which}\:{tangent} \\ $$$${the}\:{curve}\:{and}\:{the}\:{both}\:{coordinate}\:{axes}. \\ $$$${they}\:{tangent}\:{the}\:{curve}\:{at}\:{point}\:\left(\mathrm{1},\mathrm{1}\right) \\ $$$${as}\:{well}\:{as}\:{at}\:{point}\left(−\mathrm{1},−\mathrm{1}\right). \\ $$$$…