# The Rate of Change

Topics: Analytic geometry, Derivative, Slope Pages: 3 (648 words) Published: February 4, 2013
Integrating Project :The rate of change|
INTEGRATING PROJECT :THE RATE OF CHANGE|
Part:2|
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Pamela Villarreal A01192011Paulina Arizpe A01191939Adrian Covarrubias| 16/11/2012|

During this investigation we will achieve to discover how math can be applied to our everyday lives by using what we have learned in our math class to find out data. |

y=.0125x2
y=.0125x2

Finding the original equation:
y=ax2vertex= (0,0)point= (20,5)
35=a(55)2Domain= (-∞,∞)Range= [0, ∞)
35/25= a
a=.0125
1) Considering the map assigned to your team determine the position of the car when the headlights illuminate the sculpture.

Position= (-65,52.8)
By using the program graphmatica to be more accurate, we found out that in the parabola representing the road (y=.0125x2) the point where the car’s headlights illuminate the sculpture, which the sculpture is in the coordinate (-20,-20), is in the position of (-65, 52.8) because the car is moving to the right and this means that is going to the positive side of the graph.

2) Determine the equation of the line followed by the light of the car when the headlights hit the sculpture

Tangent line=
y=.0125x2
y’=.025x
y’=.025(-65)
y’= -1.625x
y=-1.625x-52.81

To find out the equation of the tangent line we first found the point where the car illuminated the sculpture which is (-65, 52.81), then we found the derivative of the original equation y=.0125x2 and the derivative is y'=.025x . After finding the derivative we needed to find the slope of the tangent line so we used the equation of the derivative and replaced the x with the x of the position and after solving it we got the slope of y’= -1.625x, and to finish the equation we added the y of the position to finally get y=-1.625x-52.81

3) Now determine the position of the car when the tail lights hit the sculpture.

Position (30,11.25)

By using the program graphmatica to get more accurate results, we found out that in...