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Home » Now sum until total ≥ 729? No — total filled up to that point. - Ready Digital AB

Now sum until total ≥ 729? No — total filled up to that point. - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 The polynomial \( f(x) = x^3 - 6x^2 + 11x - 6 \) can be analyzed using Vieta's formulas. For a cubic polynomial of the form \( ax^3 + bx^2 + cx + d \), the sum of the roots is given by \( -b/a \). Here, \( a = 1 \) and \( b = -6 \). Therefore, the sum of the roots is \( -(-6)/1 = 6 \).

📌 A glaciologist is using remote sensing data to model glacier melt over time. The rate of change in glacier volume is represented by \( g(t) = t^3 - 4t^2 + 4t \). Determine the critical points where the volume change rate is zero.

📌 To find the critical points, we compute the derivative \( g'(t) \) and set it to zero.

📌 g(t) = t^3 - 4t^2 + 4t

📌 g'(t) = 3t^2 - 8t + 4

📌 Setting \( g'(t) = 0 \) gives the equation \( 3t^2 - 8t + 4 = 0 \). Solving this quadratic equation using the quadratic formula \( t = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 3 \), \( b = -8 \), and \( c = 4 \), we find:

📌 t = rac{8 \pm \sqrt{(-8)^2 - 4 \cdot 3 \cdot 4}}{2 \cdot 3} = rac{8 \pm \sqrt{64 - 48}}{6} = rac{8 \pm \sqrt{16}}{6} = rac{8 \pm 4}{6}

📌 The solutions are \( t = 2 \) and \( t = rac{2}{3} \).

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