On a given day, the flow rate F (in cars per hour) on a congested roadway is given by the equation below, where v is the speed of traffic in miles per hour. V 23 +0.04v² What speed will maximize the flow rate on the road? Step 1 F = To find the speed that maximizes the flow rate on the road, we differentiate F = Therefore, Step 2 dF dv 23 0.04 Now solve (23+0.04v2) 23 - 0.04v² (23 +0.04v²)2 230.04v² = 0 V = V 0.04 2 2 2 = 0. V 23 +0.04v² = 0 for v. (Round your answers to one decimal place.) X with respect to v, set it equal to zero and solve for v.
On a given day, the flow rate F (in cars per hour) on a congested roadway is given by the equation below, where v is the speed of traffic in miles per hour. V 23 +0.04v² What speed will maximize the flow rate on the road? Step 1 F = To find the speed that maximizes the flow rate on the road, we differentiate F = Therefore, Step 2 dF dv 23 0.04 Now solve (23+0.04v2) 23 - 0.04v² (23 +0.04v²)2 230.04v² = 0 V = V 0.04 2 2 2 = 0. V 23 +0.04v² = 0 for v. (Round your answers to one decimal place.) X with respect to v, set it equal to zero and solve for v.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.4: Solving Quadratic Equations By Factoring
Problem 59HP
Related questions
Question
100%
Transcribed Image Text:On a given day, the flow rate F (in cars per hour) on a congested roadway is given by the equation below, where v is the speed of traffic in miles per hour.
V
23 +0.04v²
What speed will maximize the flow rate on the road?
Step 1
F =
To find the speed that maximizes the flow rate on the road, we differentiate F =
Therefore,
Step 2
dF
dv
Now solve
23 0.04
(23 +0.04v²) 2
23 - 0.04v²
(23 +0.04v²)²
= 0
23 -0.04v²:
0.04 ²
V = V
= 0.
V
23 +0.04v²
= 0 for v. (Round your answers to one decimal place.)
with respect to v, set it equal to zero and solve for v.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
