SOLUTION: 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 formula d = v + v2 20 where d is measured in feet. kerry wants h
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Question 1203691: 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 formula d = v + v2 20 where d is measured in feet. kerry wants her stopping distance not to exceed 40ft. at what range of speeds (in mi/h) can she travel? (enter your answer using interval notation
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
The formula d = v + v2 20 seems strangely formed. Please double-check to make sure you typed this correctly.
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After some online searching, I found a similar problem with the formula and the stopping distance was 240 feet (instead of 40 feet)
If this is the formula and stopping distance your teacher gave you, then read on. If not then let me know.
d = stopping distance or braking distance = the distance the car travels when the brakes are first applied to when the car comes to a complete stop
Let's complete the square
Use the rule sqrt(x^2) = |x|
we use the rule that |x| < k becomes -k < x < k, for some positive value k.
Another way to solve would be to factor to get
The roots are v = -80 and v = 60
The region between these roots will make the left hand side either 0 or negative.
Clearly we cannot have negative speeds.
Therefore we must revise to
To be more technical, since she is driving, her speed cannot be zero.
So we further would say
That converts to the interval notation (0, 60]
The parenthesis excludes the endpoint 0.
A square bracket is used to include the endpoint 60.
Answer: (0, 60]
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