We use cookies to give you the best experience possible. By continuing we’ll assume you’re on board with our cookie policy

The Rate of Change Essay Sample

essay
The whole doc is available only for registered users OPEN DOC
  • Pages:
  • Word count: 543
  • Category: change

Get Full Essay

Get access to this section to get all help you need with your essay and educational issues.

Get Access

The Rate of Change Essay Sample

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=.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) 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=.0125×2) 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=.0125×2
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=.0125×2 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 the parabola representing the road (y=.0125×2), the point where the car’s tail lights hit the sculpture, which is found in the coordinate (-20,-20), is in the position of (30, 11.25). The car is moving to the right and this means that is going to the positive side of the graph. 4) Determine the equation of the line followed by the light of the car when the tail lights 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 find out the equation of the tangent line we first found the point where
the car illuminated the sculpture which is (30,11.25), then we found the derivative of the original equation y=.0125×2 which is 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 of that equation with the x-coordinate of the position (30,11.25) and after solving it we got the slope of m=0.75, and to finish the equation of the line which is: y-y0=m(x-x0) , we substitute the y and x values with the slope and we solve to get the final equation which is: y=0.75x+33.75

5) Find the point of intersection of the two lines, where do the two lines meet?

6) There is another sculpture located on the coordinate (20, 40) on the map assigned to your team, when will the lights (head or tail) of the car hit the sculpture?

We can write a custom essay

According to Your Specific Requirements

Order an essay

You May Also Find These Documents Helpful

Virginia Commission on Climate Change

In December 2007, the Executive Order 5 was issued by the then Virginia Governor Timothy Kaine that created the Virginia Commission on Climate Change. Recognizing One of the most pressing problems facing the world today and Virginia regarding the use of energy fueled the need to convene the commission to fulfill the Virginia Energy Plan that aimed to return the states greenhouse gas emissions to...

Capability of Change

People are known for growing: growing in height, age, and in this case, as a person. In addition to growing, people can also change. Someone can go from being detestable to being admired, and so much more. A clear example of this kind of person would be Guy Montag from Fahrenheit 451, who goes from being a serious firefighter to someone who goes against the...

To changed my life

There are number of people who have prominently changed my life. I thank my little sister for introducing me to the world of siblinghood. My 4th grade teacher also had a huge impact on me because he motivated me to have a great passion for studying and working hard. But I must say, my mother has had the most significant influence on me because she...

Changes In Business

I. Introduction In our world today changes have been made not just in technology, how roads turn but also in our businesses. Due to these changes people adapt to it and so do organizations. For an organization to be able to survive in our competitive world, one must adapt to the changes gradually even better if they assimilate at once to avoid mishaps. II. The...

Mining Changes for Real-Life Applications

School of Computing National University of Singapore 3 Science Drive 2 Singapore 117543 {liub, whsu, xiayy}@comp.nus.edu.sg Abstract. Much of the data mining research has been focused on devising techniques to build accurate models and to discover rules from databases. Relatively little attention has been paid to mining changes in databases collected over time. For businesses, knowing what is changing and how it has changed is...

Get Access To The Full Essay
icon
300+
Materials Daily
icon
100,000+ Subjects
2000+ Topics
icon
Free Plagiarism
Checker
icon
All Materials
are Cataloged Well

Sorry, but copying text is forbidden on this website. If you need this or any other sample, we can send it to you via email.

By clicking "SEND", you agree to our terms of service and privacy policy. We'll occasionally send you account related and promo emails.
Sorry, but only registered users have full access

How about getting this access
immediately?

Become a member

Your Answer Is Very Helpful For Us
Thank You A Lot!

logo

Emma Taylor

online

Hi there!
Would you like to get such a paper?
How about getting a customized one?

Couldn't Find What You Looking For?

Get access to our huge knowledge base which is continuously updated

Next Update Will Be About:
14 : 59 : 59
Become a Member