38. When air expands adiabatically (without gaining or losing zi heat), its pressure P and volume V are related by the equa- tion PV1.4 C, where C is a constant. Suppose that at a certain instant the volume is 400 cm³ and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what hear rate is the volume increasing at this instant? =
38. When air expands adiabatically (without gaining or losing zi heat), its pressure P and volume V are related by the equa- tion PV1.4 C, where C is a constant. Suppose that at a certain instant the volume is 400 cm³ and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what hear rate is the volume increasing at this instant? =
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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question 38
![### Transcription of Educational Content
**Problem 36:**
A faucet is filling a hemispherical basin of diameter 60 cm with water at a rate of 2 L/min. Find the rate at which the water is rising in the basin when it is half full. [Use the following facts: 1 L is 1000 cm³. The volume of the portion of a sphere with radius \( r \) from the bottom to a height \( h \) is \( V = \pi (rh^2 - \frac{1}{3}h^3) \), as we will show in Chapter 5.]
**Problem 37:**
Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure \( P \) and volume \( V \) satisfy the equation \( PV = C \), where \( C \) is a constant. Suppose that at a certain instant the volume is 600 cm³, the pressure is 150 kPa, and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?
**Problem 38:**
When air expands adiabatically (without gaining or losing heat), its pressure \( P \) and volume \( V \) are related by the equation \( PV^{1.4} = C \), where \( C \) is a constant. Suppose that at a certain instant the volume is 400 cm³ and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what rate is the volume increasing at this instant?
**Problem 39:**
If two resistors with resistances \( R_1 \) and \( R_2 \) are connected in parallel, as in the figure, then the total resistance \( R \), measured in ohms (\( \Omega \)), is given by
\[
\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}
\]
If \( R_1 \) and \( R_2 \) are increasing at rates of 0.3 \( \Omega/s \) and 0.2 \( \Omega/s \), respectively, how fast is \( R \) changing when \( R_1 = 80 \, \Omega \) and \( R_2 = 100 \, \Omega \)?
**Diagram](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F613af2f8-f901-4d4b-81fe-790ed0ca6df6%2F137e8fbf-33b6-4b48-96a1-1b51f1bd4567%2Fln5ulpj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Transcription of Educational Content
**Problem 36:**
A faucet is filling a hemispherical basin of diameter 60 cm with water at a rate of 2 L/min. Find the rate at which the water is rising in the basin when it is half full. [Use the following facts: 1 L is 1000 cm³. The volume of the portion of a sphere with radius \( r \) from the bottom to a height \( h \) is \( V = \pi (rh^2 - \frac{1}{3}h^3) \), as we will show in Chapter 5.]
**Problem 37:**
Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure \( P \) and volume \( V \) satisfy the equation \( PV = C \), where \( C \) is a constant. Suppose that at a certain instant the volume is 600 cm³, the pressure is 150 kPa, and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?
**Problem 38:**
When air expands adiabatically (without gaining or losing heat), its pressure \( P \) and volume \( V \) are related by the equation \( PV^{1.4} = C \), where \( C \) is a constant. Suppose that at a certain instant the volume is 400 cm³ and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what rate is the volume increasing at this instant?
**Problem 39:**
If two resistors with resistances \( R_1 \) and \( R_2 \) are connected in parallel, as in the figure, then the total resistance \( R \), measured in ohms (\( \Omega \)), is given by
\[
\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}
\]
If \( R_1 \) and \( R_2 \) are increasing at rates of 0.3 \( \Omega/s \) and 0.2 \( \Omega/s \), respectively, how fast is \( R \) changing when \( R_1 = 80 \, \Omega \) and \( R_2 = 100 \, \Omega \)?
**Diagram
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