A typical human heart pumps 70 milliliters(mL) of blood with each heartbeat. Assuming a heart rate of 60 beats per minute, a reasonable model for the outflow rate is V'(t) = 70(1 + sin(2πt), where V(t) is the amount of blood in mL pumped since time 0, and t is measured in seconds. 1. Use the FTC to verify that the amount of blood pumped in the first second is 70 mL. 2. Sketch a picture of V'(t) for 0 ≤ t ≤ 2 and explain your answer to 1. geometrically. 3. Find V(T), the amount of blood pumped up to time T.
A typical human heart pumps 70 milliliters(mL) of blood with each heartbeat. Assuming a heart rate of 60 beats per minute, a reasonable model for the outflow rate is V'(t) = 70(1 + sin(2πt), where V(t) is the amount of blood in mL pumped since time 0, and t is measured in seconds. 1. Use the FTC to verify that the amount of blood pumped in the first second is 70 mL. 2. Sketch a picture of V'(t) for 0 ≤ t ≤ 2 and explain your answer to 1. geometrically. 3. Find V(T), the amount of blood pumped up to time T.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Transcribed Image Text:A typical human heart pumps 70 milliliters (mL) of blood with each heartbeat. Assuming a heart
rate of 60 beats per minute, a reasonable model for the outflow rate is V'(t) = 70(1 + sin(2πt),
where V(t) is the amount of blood in mL pumped since time 0, and t is measured in seconds.
1. Use the FTC to verify that the amount of blood pumped in the first second is 70 mL.
2. Sketch a picture of V'(t) for 0 ≤ t ≤ 2 and explain your answer to 1. geometrically.
3. Find V(T), the amount of blood pumped up to time T.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
