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Use-mathematical-induction-to-prove-that-the-statement-a-a-d-a-2d-a-n-1-d-n-2-2a-n-1-d-is-true-for-all-natural-numbers-Any-help-please-

Question Number 199987 by Yakubu last updated on 11/Nov/23 $$\:\boldsymbol{{Use}}\:\boldsymbol{{mathematical}}\:\boldsymbol{{induction}} \\ $$$$\:\boldsymbol{{to}}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{statement}} \\ $$$$\:\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{d}}\right)+\left(\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{d}}\right)+…+\left(\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right)=\frac{\boldsymbol{\mathrm{n}}}{\mathrm{2}}\left[\mathrm{2}\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right] \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{true}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{natural}}\:\boldsymbol{\mathrm{numbers}} \\ $$$$\boldsymbol{\mathrm{A}{ny}}\:\boldsymbol{{help}}\:\boldsymbol{{please}} \\ $$ Answered by Rasheed.Sindhi last updated…

Question-199915

Question Number 199915 by lealiegalendez last updated on 11/Nov/23 Answered by Rasheed.Sindhi last updated on 11/Nov/23 $$\mathrm{5}{x}+\mathrm{30}−\mathrm{3}{x}−\mathrm{24}=\mathrm{0} \\ $$$$\mathrm{2}{x}=−\mathrm{6}\Rightarrow{x}=−\mathrm{6}/\mathrm{2}=−\mathrm{3} \\ $$ Terms of Service Privacy…

Question-199899

Question Number 199899 by sonukgindia last updated on 11/Nov/23 Answered by Rajpurohith last updated on 11/Nov/23 $${cos}\left({z}\right)+{sin}\left({z}\right)={k}\: \\ $$$$\Rightarrow\left(\frac{{e}^{{iz}} +{e}^{−{iz}} }{\mathrm{2}}\right)+\left(\frac{{e}^{{iz}} −{e}^{−{iz}} }{\mathrm{2}{i}}\right)={k} \\ $$$$\Rightarrow{e}^{{iz}}…

how-do-I-calculate-for-7-86-without-calculator-

Question Number 199959 by Yakubu last updated on 11/Nov/23 $$\:\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{I}}\:\boldsymbol{{calculate}}\:\boldsymbol{{for}} \\ $$$$\:\mathrm{7}.\mathrm{86}!\:\boldsymbol{{without}}\:\boldsymbol{{calculator}}? \\ $$ Commented by mr W last updated on 11/Nov/23 $$\mathrm{7}.\mathrm{86}!=\Gamma\left(\mathrm{8}.\mathrm{86}\right) \\ $$$${i}\:{think}\:{you}\:{can}'{t}\:{calculate}\:{it}\:{even}\:{with}…

Question-199854

Question Number 199854 by sonukgindia last updated on 10/Nov/23 Answered by aleks041103 last updated on 10/Nov/23 $${every}\:{fold}\:{is}\:{done}\:{at}\:{the}\:{angle}\:{bisector} \\ $$$$\Rightarrow{final}\:{accute}\:{angle}=\mathrm{90}°/\mathrm{4}=\mathrm{22}.\mathrm{5}° \\ $$$${S}=\mathrm{8}×\mathrm{6}−\mathrm{2}×\frac{\mathrm{3}×\left(\frac{\mathrm{3}}{{tan}\left(\mathrm{22}.\mathrm{5}°\right)}\right)}{\mathrm{2}}= \\ $$$$=\mathrm{48}−\mathrm{9}{cot}\left(\frac{\mathrm{45}°}{\mathrm{2}}\right)=\mathrm{48}−\mathrm{9}{cot}\left({x}\right)=\mathrm{48}−\mathrm{9}{z} \\ $$$$…