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A baseball diamond is a square of side 90 ft. A baseball player runs from a home plate toward the first base at 31 ft/s. How fast is the player's distance from the second base changing when the player is halfway to the first base? (Give your answer to two decimal places.)

A baseball diamond is a square of side 90 ft. A baseball player runs from a home plate toward the first base at 31 ft/s. How fast is the player's distance from the second base changing when the player is halfway to the first base? (Give your answer to two decimal places.)

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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A baseball diamond is a square of side 90 ft. A baseball player runs from a home plate toward the first base at 31 ft/s. How fast is the player's distance from the second base changing when the player is halfway to the first base? (Give your answer to two decimal places.)
Transcribed Image Text:A baseball diamond is a square of side 90 ft. A baseball player runs from a home plate toward the first base at 31 ft/s. How fast is the player's distance from the second base changing when the player is halfway to the first base? (Give your answer to two decimal places.)
The pressure \( P \) and volume \( V \) of an expanding gas are related by the formula \( PV^b = C \), where \( b \) and \( C \) are constants (this holds in adiabatic expansion, with or without loss). Find \( \frac{dP}{dt} \) if \( b = 1.3 \), \( P = 14 \text{ kPa} \), \( V = 70 \text{ cm}^3 \), and \( \frac{dV}{dt} = 20 \text{ cm}^3/\text{min} \). (Use symbolic notation and fractions where needed.)
Transcribed Image Text:The pressure \( P \) and volume \( V \) of an expanding gas are related by the formula \( PV^b = C \), where \( b \) and \( C \) are constants (this holds in adiabatic expansion, with or without loss). Find \( \frac{dP}{dt} \) if \( b = 1.3 \), \( P = 14 \text{ kPa} \), \( V = 70 \text{ cm}^3 \), and \( \frac{dV}{dt} = 20 \text{ cm}^3/\text{min} \). (Use symbolic notation and fractions where needed.)
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