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Home » Now substitute $ r = 9 $: - ToelettAPP

Now substitute $ r = 9 $: - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \( \ln(490.195) \approx 6.192 \), \( \frac{2}{5} \times 6.192 = 2.477 \), \( e^{2.477} \approx 11.94 \)

📌 So \( h \approx 11.94 \) cm.

📌 #### 11.94

📌 A satellite orbits Earth in an elliptical path where the Earth is at one focus. The semi-major axis is 15,000 km and the eccentricity is 0.2. What is the distance from the satellite to the Earth’s center at the closest approach (perigee)?

📌 Perigee distance = \( a(1 - e) = 15000 \times (1 - 0.2) = 15000 \times 0.8 = 12,000 \, \text{km} \).

📌 A factory produces widgets with a defect rate of 3%. A quality inspector selects a random sample of 150 widgets. What is the probability that exactly 5 are defective?

📌 Use binomial distribution: \( n = 150 \), \( p = 0.03 \), \( k = 5 \).

📌 \( P(X=5) = \binom{150}{5} (0.03)^5 (0.97)^{145} \).

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