For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the function d(v) = v + (v^2 / 25) where d is measured in feet. Kerry wants her stopping distance not to exceed 165 ft. At what range of speeds can she travel? (Assume v is positive. Round your values to one decimal place. Enter your answer using interval notation.)
in Algebra 2 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Given,

Distance should not exceed 165 ft.

So d(v) <= 165,

d(v) = v + (v^2 /25) <= 165

=> 25v + v^2 <= 165 * 25

=> v^2 +25v - 4125 <=0

On solving above quadratic equation we get,

1/2 (-25 - 5 sqrt(685))<=v<=1/2 (5 sqrt(685) - 25)

or

-77.93 <= v <= 52.93

but since velocity is assumed to be non-negative.

Therefore,

0 <= v <= 52.93
by Level 7 User (26.8k points)

Related questions

1 answer
1 answer
asked Oct 9, 2013 in Calculus Answers by ALISSA | 237 views
1 answer
asked Aug 25, 2013 in Other Math Topics by SuckmyNick71 Level 1 User (160 points) | 256 views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,022 questions
91,946 answers
2,238 comments
23,906 users