1. Here the the volume of between 0 and z (in meters) is ㅠ - - V(z) = (12z – (z − 1)³ — 1) . 3 The barrel is being filled with liquid in such a way that at a certain moment in time (in seconds), the rate of change of the volume occupied by the liquid is 127 m³/s and the rate of increase of the level z is 3 m/s. (a) Find the level z at which this occurs. (b) Find the volume of liquid at that time.
1. Here the the volume of between 0 and z (in meters) is ㅠ - - V(z) = (12z – (z − 1)³ — 1) . 3 The barrel is being filled with liquid in such a way that at a certain moment in time (in seconds), the rate of change of the volume occupied by the liquid is 127 m³/s and the rate of increase of the level z is 3 m/s. (a) Find the level z at which this occurs. (b) Find the volume of liquid at that time.
Calculus: Early Transcendentals
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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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![1. Here the volume of between 0 and \( z \) (in meters) is
\[
V(z) = \frac{\pi}{3} \left( 12z - (z - 1)^3 - 1 \right).
\]
The barrel is being filled with liquid in such a way that at a certain moment in time (in seconds), the rate of change of the volume occupied by the liquid is 12π m\(^3\)/s and the rate of increase of the level \( z \) is 3 m/s.
(a) Find the level \( z \) at which this occurs.
(b) Find the volume of liquid at that time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F593e4a4c-a9fc-4231-bacd-fbc9affb1612%2Ff1a679e7-0bf9-4046-bf37-767e6c7d6481%2F3p42oxf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Here the volume of between 0 and \( z \) (in meters) is
\[
V(z) = \frac{\pi}{3} \left( 12z - (z - 1)^3 - 1 \right).
\]
The barrel is being filled with liquid in such a way that at a certain moment in time (in seconds), the rate of change of the volume occupied by the liquid is 12π m\(^3\)/s and the rate of increase of the level \( z \) is 3 m/s.
(a) Find the level \( z \) at which this occurs.
(b) Find the volume of liquid at that time.
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