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Home » How Many Cups Are in a Quarter? The Simple Map Every Kitchen Wishlist Needs - Dyverse

How Many Cups Are in a Quarter? The Simple Map Every Kitchen Wishlist Needs - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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If the sum of the first \( n \) natural numbers is 210, find \( n \).
The formula for the sum is \( \frac{n(n+1)}{2} = 210 \).
Solving \( n(n+1) = 420 \).
\( n^2 + n - 420 = 0 \).
Using the quadratic formula, \( n = \frac{-1 \pm \sqrt{1 + 1680}}{2} \...
\( n = \frac{-1 \pm \sqrt{1681}}{2} \).
\( n = \frac{-1 \pm 41}{2} \).
A rectangular garden has a length 5 meters more than twice its width....
Let width be \( w \). Then length is \( 2w + 5 \).
Area: \( w(2w + 5) = 150 \).

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