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Home » The final answer is \(\boxed-2\). - Databee Business Systems

The final answer is \(\boxed-2\). - Databee Business Systems

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 A city planner is analyzing a model where the traffic flow \( f(t) \) through an intersection is given by the polynomial \( f(t) = 4t^3 - 9t^2 + 6t - 1 \). Compute the sum of the roots of the equation \( f(t) = 0 \).

📌 To find the sum of the roots of the polynomial \( f(t) = 4t^3 - 9t^2 + 6t - 1 \), we use Vieta's formulas. For a cubic equation \( at^3 + bt^2 + ct + d = 0 \), the sum of the roots is given by \( -\frac{b}{a} \).

📌 Here, \( a = 4 \) and \( b = -9 \). Therefore, the sum of the roots is:

📌 -\frac{-9}{4} = \frac{9}{4}

📌 Thus, the sum of the roots is \(\boxed{\frac{9}{4}}\).

📌 A science communicator is explaining the exponential growth of bacteria in a petri dish. If the growth is modeled by the equation \( 5e^{kt} = 100 \), where \( k \) and \( t \) are positive, solve for \( t \) when \( k = 0.3 \).

📌 Start by isolating the exponential term:

🔥 Popular Posts

\[ \log_2(x) + \log_2(x - 2) = \log_2[x(x - 2)] \]
\[ \log_2[x(x - 2)] = 3 \]
\[ x(x - 2) = 2^3 = 8 \]
\[ x = \frac{2 \pm \sqrt{(-2)^2 - 4(1)(-8)}}{2(1)} = \frac{2 \pm \sqrt...
\[ x = \frac{8}{2} = 4 \quad \text{or} \quad x = \frac{-4}{2} = -2 \]
\(x > 2\)（対数の定義域より）なので、\(x = 4\)
一辺の長さ \(s = 6\) の正三角形の面積は：
\[ \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} \...
\[ 6 \times 9\sqrt{3} = 54\sqrt{3} \]
#### \(54\sqrt{3}\)

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