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For-this-problem-we-define-the-fractional-part-of-x-R-0-as-x-x-x-where-x-is-the-integer-part-of-x-i-e-the-greatest-integer-less-than-or-equal-to-x-a-Draw-the-function-x-in-a-cord

Question Number 180926 by Mastermind last updated on 19/Nov/22 $$\mathrm{For}\:\mathrm{this}\:\mathrm{problem},\:\mathrm{we}\:\mathrm{define}\:\mathrm{the}\: \\ $$$$\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:\mathrm{x}\in\mathbb{R}_{\geqslant\mathrm{0}} \:\mathrm{as} \\ $$$$\left\{\mathrm{x}\right\}\:=\:\mathrm{x}\:−\:\lfloor\mathrm{x}\rfloor \\ $$$$\mathrm{where}\:\lfloor\mathrm{x}\rfloor\:\mathrm{is}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{part}\:\mathrm{of}\:\mathrm{x},\:\mathrm{i}.\mathrm{e} \\ $$$$\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{less}\:\mathrm{than}\:\mathrm{or}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{x}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Draw}\:\mathrm{the}\:\mathrm{function}\:\left\{\mathrm{x}\right\}\:\mathrm{in}\:\mathrm{a}\:\mathrm{cordinate} \\ $$$$\mathrm{system}\:\mathrm{for}\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{3}…

Question-180867

Question Number 180867 by Noorzai last updated on 18/Nov/22 Answered by mr W last updated on 18/Nov/22 $${n}\mathrm{ln}\:{n}=\mathrm{ln}\:\mathrm{100} \\ $$$${e}^{\mathrm{ln}\:{n}} \mathrm{ln}\:{n}=\mathrm{ln}\:\mathrm{100} \\ $$$$\Rightarrow\mathrm{ln}\:{n}={W}\left(\mathrm{ln}\:\mathrm{100}\right) \\ $$$$\Rightarrow{n}={e}^{{W}\left(\mathrm{ln}\:\mathrm{100}\right)}…

Question-180866

Question Number 180866 by Mastermind last updated on 18/Nov/22 Answered by mr W last updated on 18/Nov/22 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}=\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +…+{n}^{\mathrm{2}} =\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{6}} \\…

Question-180858

Question Number 180858 by Mastermind last updated on 18/Nov/22 Answered by mr W last updated on 18/Nov/22 $${A}=\mathrm{2}×\frac{{a}×{a}×\mathrm{tan}\:\left[\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\pi}{\mathrm{2}}−\alpha\right)\right]}{\mathrm{2}} \\ $$$$\:\:\:={a}^{\mathrm{2}} \mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−\frac{\alpha}{\mathrm{2}}\right) \\ $$ Commented by…

Without-using-table-find-the-values-of-1-1-3-2-1-1-3-2-Mastermind-

Question Number 180837 by Mastermind last updated on 17/Nov/22 $$\mathrm{Without}\:\mathrm{using}\:\mathrm{table},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values} \\ $$$$\mathrm{of}: \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{1}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$ Answered by Rasheed.Sindhi…

Find-the-derivatives-f-x-of-the-following-function-with-respect-to-x-f-x-Sin-pi-Sinx-pi-Cosx-Mastermind-

Question Number 180839 by Mastermind last updated on 17/Nov/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{derivatives}\:\mathrm{f}^{'} \left(\mathrm{x}\right)\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{function}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{x}: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{Sin}\left(\pi^{\mathrm{Sinx}} +\pi^{\mathrm{Cosx}} \right). \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$ Answered by…

Determine-A-B-C-such-that-all-of-the-following-function-intersect-the-point-2-2-f-1-x-Ax-1-f-2-x-Bx-2-2-f-3-x-Cx-3-3-Mastermind-

Question Number 180836 by Mastermind last updated on 17/Nov/22 $$\mathrm{Determine}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{such}\:\mathrm{that}\:\mathrm{all}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{function}\:\mathrm{intersect}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left(\mathrm{2},\mathrm{2}\right)\:; \\ $$$$\mathrm{f}_{\mathrm{1}} \left(\mathrm{x}\right)=\mathrm{Ax}\:+\:\mathrm{1},\:\:\mathrm{f}_{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{Bx}^{\mathrm{2}} \:+\:\mathrm{2},\:\: \\ $$$$\mathrm{f}_{\mathrm{3}} \left(\mathrm{x}\right)=\mathrm{Cx}^{\mathrm{3}} \:+\:\mathrm{3} \\ $$$$…