The Rate of Change Essay Sample

During this probe we will accomplish to detect how math can be applied to our mundane lives by utilizing what we have learned in our math category to happen out informations.

y= . 0125?2
y= . 0125?2

Finding the original equation:
y=ax2vertex= ( 0. 0 ) point= ( 20. 5 )
35=a ( 55 ) 2Domain= ( -? . ? ) Range= [ 0. ? )
35/25= a
a= . 0125
1 ) Sing the map assigned to your squad find the place of the auto when the headlamps illuminate the sculpture.

Position= ( -65. 52. 8 )
By utilizing the plan graphmatica to be more accurate. we found out that in the parabola stand foring the route ( y= . 0125?2 ) the point where the car’s headlamps illuminate the sculpture. which the sculpture is in the co-ordinate ( -20. -20 ) . is in the place of ( -65. 52. 8 ) because the auto is traveling to the right and this means that is traveling to the positive side of the graph.

2 ) Determine the equation of the line followed by the visible radiation of the auto when the headlamps hit the sculpture

Tangent line=
y= . 0125?2
y’= . 025x
y’= . 025 ( -65 )
y’= -1. 625x
y=-1. 625x-52. 81

To happen out the equation of the tangent line we foremost found the point where the auto illuminated the sculpture which is ( -65. 52. 81 ) . so we found the derived function of the original equation y= . 0125?2 and the derivative is y’= . 025x. After happening the derived function we needed to happen the incline of the tangent line so we used the equation of the derivative and replaced the ten with the ten of the place and after work outing it we got the incline of y’= -1. 625x. and to complete the equation we added the Y of the place to eventually acquire y=-1. 625x-52. 81

3 ) Now determine the place of the auto when the tail visible radiations hit the sculpture.

Position ( 30. 11. 25 )

By utilizing the plan graphmatica to acquire more accurate consequences. we found out that in the parabola stand foring the route ( y= . 0125?2 ) . the point where the car’s tail visible radiations hit the sculpture. which is found in the co-ordinate ( -20. -20 ) . is in the place of ( 30. 11. 25 ) . The auto is traveling to the right and this means that is traveling to the positive side of the graph. 4 ) Determine the equation of the line followed by the visible radiation of the auto when the tail visible radiations hit the sculpture.

Tangent Line
y= . 0125?2 y= . 0125x^2 y-11. 25=0. 75 ( x-30 ) y= . 0125 ( 30 ) 2 y= 0. 025x y=0. 75x-22. 5+11. 25 y= 11. 25 y=0. 025 ( 30 ) y=0. 75x+33. 75 m=0. 75

To happen out the equation of the tangent line we foremost found the point where
the auto illuminated the sculpture which is ( 30. 11. 25 ) . so we found the derived function of the original equation y= . 0125?2 which is is y’= . 025x. After happening the derived function we needed to happen the incline of the tangent line so we used the equation of the derivative and replaced the ten of that equation with the x-coordinate of the place ( 30. 11. 25 ) and after work outing it we got the incline of m=0. 75. and to complete the equation of the line which is: y-y0=m ( x-x0 ) . we substitute the Y and ten values with the incline and we solve to acquire the concluding equation which is: y=0. 75x+33. 75

5 ) Find the point of intersection of the two lines. where do the two lines run into?

6 ) There is another sculpture located on the co-ordinate ( 20. 40 ) on the map assigned to your squad. when will the visible radiations ( caput or tail ) of the auto hit the sculpture?