How fast is the distance between the cars changing at this moment

In summary, the conversation discusses finding the value of dz/dt in a given equation and clarifies a potential issue with negative notation.
  • #1
paraboloid
17
0
[Solved]How fast is the distance between the cars changing at this moment

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I'm in need of help with the last part (finding dz/dt).

I'm sorry I don't know how to use latex.
Let D refer to partial derivatives.

This was my attempt best try:

Given dz/dt = Dz/Dt*dx/d+ Dz/Dt*dy/dt and z = (x^2+y^2)^(1/2),

2z*dz/dt = 2x*dx/dt + 2y*dy/dt
2(.36+.49)^(1/2)*dz/dt= 2(.6)(-55)+2(.7)(-60)
dz/dt = (2(.6)(-55)+2(.7)(-60)) / (2(.36+.49)^(1/2))
dz/dt = -81.3489

Any help would be great,
thanks
 
Last edited:
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  • #2
I don't see anything wrong with how you are working it out. The only thing that comes to mind is that you are saying the distance is "decreasing" at the rate of "-81.3489". Isn't that sort of double negative? I would say it's decreasing at the rate of +81.3489.
 
  • #3
Good call. Thanks Dick!
 

1. What is the meaning of "distance between the cars" in this context?

The "distance between the cars" refers to the physical space between two vehicles, typically measured in units such as meters or feet.

2. How is the speed of the cars related to the changing distance between them?

The speed of the cars directly affects the changing distance between them. If the cars are moving at a constant speed, the distance between them will remain the same. However, if one car is accelerating or decelerating, the distance between them will change.

3. What factors can affect the rate at which the distance between the cars is changing?

The rate at which the distance between the cars is changing can be affected by factors such as the speed of the cars, the acceleration or deceleration of the cars, and any external forces such as wind or road conditions.

4. How is the changing distance between the cars calculated?

The changing distance between the cars can be calculated by subtracting the initial distance between them from the current distance between them. This will give the change in distance over a specific time interval.

5. Can the changing distance between the cars be negative?

Yes, the changing distance between the cars can be negative if one car is moving in the opposite direction of the other car. This indicates that the distance between the cars is decreasing rather than increasing.

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