Asked by Jennifer
two cars are approaching an intersection one is 3 miles south of the intersection and is moving at a constant speed of 20 miles per hour. at the same time the other car is 4 miles east of the intersection and is moving at the constant speed of 30 miles per hour.
a)express the distance d as a function of time t.
b)Use a graphing utility to graph d=d(t). For what value of t is d smallest?
a)express the distance d as a function of time t.
b)Use a graphing utility to graph d=d(t). For what value of t is d smallest?
Answers
Answered by
Reiny
At a time of t hours after the action started,
- distance remaining for the northbound car before reaching intersection is 3 - 20t
- distance remaining for the westbound car before reaching the intersection is 4 - 30t
let d be the distance between them
d^2= (3-20t)^2 + (4-30t)^2
= 9 - 120t + 400t^2 + 16 - 240t + 900t^2
= 1300t^2 - 360t + 25
I have no idea what "graphing utility " you are using.
for a min of d , dd/dt = 0
2d dd/dt = 2600t - 360
2600t = 360
t = .13846... hrs
- distance remaining for the northbound car before reaching intersection is 3 - 20t
- distance remaining for the westbound car before reaching the intersection is 4 - 30t
let d be the distance between them
d^2= (3-20t)^2 + (4-30t)^2
= 9 - 120t + 400t^2 + 16 - 240t + 900t^2
= 1300t^2 - 360t + 25
I have no idea what "graphing utility " you are using.
for a min of d , dd/dt = 0
2d dd/dt = 2600t - 360
2600t = 360
t = .13846... hrs
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.