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9) A skydiver jumps from a plane from 4000 meters and begins to fall at a velocity of v(t) = (2t + 40 + 1)² where v(t) is measured in meters per second. What is the skydiver's altitude after 15 seconds? -60, "

9) A skydiver jumps from a plane from 4000 meters and begins to fall at a velocity of v(t) = (2t + 40 + 1)² where v(t) is measured in meters per second. What is the skydiver's altitude after 15 seconds? -60, "

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Calculus Problem Set #### Problem 9: A skydiver jumps from a plane from 4000 meters and begins to fall at a velocity \( v(t) = \frac{40}{(2t + 1)^2} - 60 \) meters per second. What is the skydiver’s altitude after 15 seconds? *Note:* \( v(t) \) is measured in meters per second. **Answer:** ---- #### Problem 10: The rate of change in the volume of a tank is known to be \( \frac{dV}{dt} = 0.6t \cdot \cos(0.08t^2 - 1) \), where \( V(t) \) is in gallons per minute and \(0 \leq t \leq 10 \). If the tank has a volume of 14 gallons initially, what is its volume at 10 minutes? **Answer:** ---- This page provides detailed problems requiring the application of calculus concepts to determine the altitude of a skydiver and the volume of a tank over time. Each problem involves setting up and solving a differential equation based on given conditions.
Transcribed Image Text:### Calculus Problem Set #### Problem 9: A skydiver jumps from a plane from 4000 meters and begins to fall at a velocity \( v(t) = \frac{40}{(2t + 1)^2} - 60 \) meters per second. What is the skydiver’s altitude after 15 seconds? *Note:* \( v(t) \) is measured in meters per second. **Answer:** ---- #### Problem 10: The rate of change in the volume of a tank is known to be \( \frac{dV}{dt} = 0.6t \cdot \cos(0.08t^2 - 1) \), where \( V(t) \) is in gallons per minute and \(0 \leq t \leq 10 \). If the tank has a volume of 14 gallons initially, what is its volume at 10 minutes? **Answer:** ---- This page provides detailed problems requiring the application of calculus concepts to determine the altitude of a skydiver and the volume of a tank over time. Each problem involves setting up and solving a differential equation based on given conditions.
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