#18 ### Calculus and Physics Applications**Problem 17: Temperature Modeling**In a certain city, the temperature (in °F) *t* hours after 9 AM is modeled by the function:\[ T(t) = 50 + 14 \sin \frac{\pi t}{12} \]**Objective:** Find the average temperature during the period from 9 AM to 9 PM.---**Problem 18: Blood Flow Velocity**The velocity \( v \) of blood that flows in a blood vessel with radius \( R \) and length \( l \) at a distance \( r \) from the central axis is given by the equation:\[ v(r) = \frac{P}{4\eta l} (R^2 - r^2) \]where:- \( P \) is the pressure difference between the ends of the vessel.- \( \eta \) is the viscosity of the blood.**Objective:** Find the average velocity (with respect to \( r \)) over the interval \( 0 \leq r \leq R \) and compare the average velocity with the maximum velocity.---**Problem 19: Linear Density of a Rod**The linear density in a rod 8 meters long is:\[ \frac{12}{\sqrt{x}} + 1 \, \text{kg/m} \]where \( x \) is measured in meters from one end of the rod.**Objective:** Find the average density of the rod.---**Problem 20: Free Fall Displacement**If a freely falling body starts from rest, then its displacement is given by:\[ s = \frac{1}{2} gt^2 \]**Objective:** Examine the velocity after a time \( T \) being \( v_T \), and show that computing the average of the velocities with respect to \( t \) results in \( v_{\text{ave}} = \frac{1}{2} v_T \).

Name: #18 ### Calculus and Physics Applications**Problem 17: Temperature Mod
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #18 ### Calculus and Physics Applications**Problem 17: Temperature Modeling**In a certain city, the temperature (in °F) *t* hours after 9 AM is modeled by the function:\[ T(t) = 50 + 14 \sin \frac{\pi t}{12} \]**Objective:** Find the average temperat