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📅 May 14, 2026 👤 scraface

May 14, 2026

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So, \( v(t) = \frac{d}{dt}(t^3 - 6t^2 + 9t) = 3t^2 - 12t + 9 \).
At \( t = 4 \), \( v(4) = 3(4)^2 - 12(4) + 9 \).
Calculating gives \( v(4) = 48 - 48 + 9 = 9 \).
If \( \log_b(64) = 3 \), find the value of \( b \).
The equation \( \log_b(64) = 3 \) implies \( b^3 = 64 \).
Solving for \( b \) gives \( b = \sqrt[3]{64} = 4 \).
Solve for \( x \) in the equation \( 2x^2 - 3x - 5 = 0 \).
Here, \( a = 2 \), \( b = -3 \), and \( c = -5 \).
Calculate the discriminant: \( b^2 - 4ac = (-3)^2 - 4(2)(-5) = 9 + 40...
So, \( x = \frac{3 \pm \sqrt{49}}{4} = \frac{3 \pm 7}{4} \).

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