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Home » Therefore, the horizontal asymptote is \(\boxedy = 3\). - Aurero

Therefore, the horizontal asymptote is \(\boxedy = 3\). - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 The maximum height is reached when the velocity becomes zero. Using \( v^2 = u^2 + 2as \):

📌 = (20)^2 + 2(-9.8)s \implies 0 = 400 - 19.6s \implies s = \frac{400}{19.6} \approx 20.41 \, \text{m}

📌 Adding the initial height: \( 20.41 + 5 = 25.41 \, \text{m} \).

📌 The maximum height reached is approximately 25.41 meters.

📌 #### 25.41

📌 A radioactive substance decays exponentially with a half-life of 10 years. If the initial mass is 50 grams, calculate the remaining mass after 25 years.

📌 The decay formula is \( M(t) = M_0 \left(\frac{1}{2}\right)^{t/T_{1/2}} \), where \( M_0 = 50 \), \( T_{1/2} = 10 \), and \( t = 25 \).

📌 M(25) = 50 \cdot \left(\frac{1}{2}\right)^{25/10} = 50 \cdot \left(\frac{1}{2}\right)^{2.5} = 50 \cdot \frac{1}{5.6569} \approx 8.84 \, \text{g}

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