Thread: After many hours of trying, I am stuck.

Theres this one question I was doing for practice that I just cannot do. Even though I know the answer is -0.94, I cant figure out how.

The question goes as followed.

In a computer game, the motion of a car is enhanced by showing headlights on a building, when the car approaches the building. The headlights form a parabola on the road. As the car approaches the building, the beam narrows. The equation of the parabola is y = x^2 - 4x +c, where c < 0 and dc/dt = 14. The x-axis represents the wall, let length be measured in meteres and time in seconds.


Determine the rate at which the width of the beam is narrowing when c = -14.


The answer at the back is -0.94. But I really cant figure out how to get this, and how to approach this question.

help would be appreciated.

Originally Posted by Dave J

Theres this one question I was doing for practice that I just cannot do. Even though I know the answer is -0.94, I cant figure out how.

The question goes as followed.

In a computer game, the motion of a car is enhanced by showing headlights on a building, when the car approaches the building. The headlights form a parabola on the road. As the car approaches the building, the beam narrows. The equation of the parabola is y = x^2 - 4x +c, where c < 0 and dc/dt = 14. The x-axis represents the wall, let length be measured in meteres and time in seconds.


Determine the rate at which the width of the beam is narrowing when c = -14.


The answer at the back is -0.94. But I really cant figure out how to get this, and how to approach this question.

help would be appreciated.

This is poorly worded. I will assume "the width of the beam" is actually the
distance between the roots of the quadratic:



The roots of this are:

,

and the distance between the roots is:



Then:






Putting and , gives:



which does not agree with your book.

The possibilities are: that I have interpreted the problem incorrectly, I have
made a mistake in my algebra and derivatives, I have made a mistake in the
arithmetic, the book is wrong. No doubt my fellow helpers will comment on
the first three of these.

RonL

Hello, Dave!

In a computer game, the motion of a car is enhanced by showing headlights on a building
when the car approaches the building. .The headlights form a parabola on the road.
As the car approaches the building, the beam narrows.
The equation of the parabola is: where and
The x-axis represents the wall. Length is measured in meters and time in seconds.

Determine the rate at which the width of the beam is narrowing when

I agree completely with Captain Black.

Code:

              |
       *      |                        *
              |
        *     |                       *
      ---o----+----------------------o---
           *  |                    *
             c*                 *
              |   *         *
              |       ***
              |

The width of the beam is the distance between the two x-intecepts.

I have the same steps as the Captain . . . and the same answer.
I don't see how we could have misread the problem.