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Home » Calculate \( 2^8 = 256 \). - Abu Waleed Tea

Calculate \( 2^8 = 256 \). - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 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:

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Plug into (a):
7\left(rac{2}{3}
ight) + p = 6 \Rightarrow rac{14}{3} + p = 6 \Rightarrow p = 6 - rac...
Now from (1):
rac{2}{3} + rac{4}{3} + q = 4 \Rightarrow rac{6}{3} + q = 4 \Rightar...
Thus \( h(x) = rac{2}{3}x^3 + rac{4}{3}x + 2 \)
Now compute \( h(0) = 0 + 0 + 2 = 2 \)
Question: A historian of science analyzing Newtonâs early work consi...
Solution: We are given the equation:
v\sqrt{v} - 5v + 6\sqrt{v} = 0, \quad v > 0

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