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\binom41 = 4 - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 A ball is thrown upward from a 45-meter tall building with initial velocity 20 m/s. Its height is modeled by \( h(t) = -5t^2 + 20t + 45 \). When does it hit the ground?

📌 Set \( h(t) = 0 \): \( -5t^2 + 20t + 45 = 0 \)

📌 Divide by -5: \( t^2 - 4t - 9 = 0 \)

📌 Use quadratic formula: \( t = \frac{4 \pm \sqrt{16 + 36}}{2} = \frac{4 \pm \sqrt{52}}{2} = \frac{4 \pm 2\sqrt{13}}{2} = 2 \pm \sqrt{13} \)

📌 Only positive root: \( t = 2 + \sqrt{13} \approx 5.605 \) seconds

📌 #### Time when ball hits ground: \( 2 + \sqrt{13} \) seconds

📌 Simplify \( \frac{3 + 2i}{4 - i} \) and express in rectangular form.

📌 Multiply numerator and denominator by conjugate \( 4 + i \):

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