Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

For any positive integer n, let n~ be defined by n~ = 2n(n+1). What is the value of 8~/2~ ?

Sagot :

LammettHash

If [tex]\tilde n = 2n(n+1)[/tex], then

[tex]\tilde 8 = 2\times8\times9 = 144[/tex]

[tex]\tilde 2 = 2\times2\times3 = 12[/tex]

so that

[tex]\dfrac{\tilde8}{\tilde2} = \dfrac{144}{12} = \boxed{12}[/tex]

We are given that [tex]{\bf{\tilde{n}=2n(n+1)\:\: \forall \:\: n\in \mathbb{N}}}[/tex] and need to find the value of [tex]{\bf{\dfrac{\tilde{8}}{\tilde{2}}}}[/tex] . Now , let's find it ;

[tex]{:\implies \quad \sf \dfrac{\tilde{8}}{\tilde{2}}=\dfrac{2\times 8(8+1)}{2\times 2(2+1)}}[/tex]

[tex]{:\implies \quad \sf \dfrac{\tilde{8}}{\tilde{2}}=\dfrac{\cancel{2}\times 8(9)}{\cancel{2}\times 2(3)}}[/tex]

[tex]{:\implies \quad \sf \dfrac{\tilde{8}}{\tilde{2}}=\dfrac{8(9)}{2(3)}}[/tex]

[tex]{:\implies \quad \sf \dfrac{\tilde{8}}{\tilde{2}}=\dfrac{2\times 4\times 3\times 3}{2\times 3}}[/tex]

Cancelling 2 and 3 from denominator

[tex]{:\implies \quad \sf \dfrac{\tilde{8}}{\tilde{2}}=4\times 3}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\dfrac{\tilde{8}}{\tilde{2}}=12}}}[/tex]

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.