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Author: Tinku Tara

for-what-value-of-k-the-system-of-equation-has-no-solution-x-2y-3z-1-2x-ky-5z-1-3x-4y-7z-1-

Question Number 5963 by Ashis last updated on 07/Jun/16 $$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{k}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{system}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{no}}\:\boldsymbol{\mathrm{solution}} \\ $$$$\boldsymbol{\mathrm{x}}+\mathrm{2}\boldsymbol{\mathrm{y}}+\mathrm{3}\boldsymbol{\mathrm{z}}=\mathrm{1} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{ky}}+\mathrm{5}\boldsymbol{\mathrm{z}}=\mathrm{1} \\ $$$$\mathrm{3}\boldsymbol{\mathrm{x}}+\mathrm{4}\boldsymbol{\mathrm{y}}+\mathrm{7}\boldsymbol{\mathrm{z}}=\mathrm{1} \\ $$ Commented by Yozzii last updated on 07/Jun/16…

Given-a-10-digit-number-X-1345789026-How-many-10-digit-number-that-can-be-made-using-every-digit-from-X-with-condition-If-a-number-n-is-located-in-k-th-position-of-X-then-the-new-created-numb

Question Number 137035 by mr W last updated on 29/Mar/21 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:{X}\:=\:\mathrm{1345789026} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{using}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{from}\:{X},\:\mathrm{with}\:\mathrm{condition}: \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:{n}\:\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{created}\:\mathrm{number}\:\mathrm{must}\:\mathrm{not}\:\mathrm{contain} \\ $$$$\mathrm{number}\:{n}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position} \\ $$$$…

Question-71490

Question Number 71490 by oyemi kemewari last updated on 16/Oct/19 Commented by mathmax by abdo last updated on 16/Oct/19 $${let}\:{A}=\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\left(^{\mathrm{4}} \sqrt{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{6}} }\right.}{dx}\:\Rightarrow{A}=\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)\int_{\mathrm{0}}…