anonymous one year ago The table below represents the distance of a car from its destination as a function of time: (I'll post the table right now, also person who helps gets a medal, fan, and testimony) Part A: What is the y-intercept of the function and what does this tell you about the car? Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 and what does the average rate represent? Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination?

1. anonymous

Time (Hour) x Distance (Miles) y 0 900 1 850 2 800 3 750

2. anonymous

I have absolutly no clear what I am doing but I have only 5 minutes to get the answer. :O

3. nincompoop

can you try to graph it first? this is an important skill to hone and then we can try to solve for other things analytically and graphically

4. anonymous

I would except I don't have graph paper or anything like it

5. nincompoop

oh this is a study site, not answer my homework site

6. anonymous

I understand that completely

7. nincompoop

try to solve for the slope from the start of the time and distance (initial) and end time and distance (final)

8. anonymous

Never mind I ran out of time, thanks anyway :). I'll still fan, medal, and write a testimony about you though.

9. nincompoop

time (x) distance (y) x initial (x1) y initial (y1) x.. y.. x.. y.. x.. y... x final (x2) y final (y2)

10. Teddyiswatshecallsme

Part A is just talking about what is it the Y-intercept of the function, in other words, which column which is the y and what does it say about the equation?

11. anonymous

ok

12. nincompoop

once you figure out the slope, then you can use the slope-intercept form $$(y-y_1) = m \times (x-x_1)$$ solve for y and whatever your constant is the y-intercept

13. anonymous

I am still confsued about part b though

14. nincompoop

average rate of change is just your slope :)

15. Teddyiswatshecallsme

Nin that's point slope form.

16. Teddyiswatshecallsme

Not Slope Intercept.

17. anonymous

Sorry guys I am just confused because I am a 7th grader and this is way beyand me.

18. Teddyiswatshecallsme

Slope Intercept: y = mx + b

19. Teddyiswatshecallsme

Hmm, then why do you have this homework?

20. nincompoop

point-slope form and slope-intercept form are related. you cannot arrive into the latter without solving the former in this scenario

21. anonymous

I have this homeowkr because I am taking this advanced course

22. Teddyiswatshecallsme

Ahhh alright.

23. nincompoop

try doing what I have been telling you and then we will go through them individually

24. anonymous

Ok umm, hang on

25. nincompoop

I will give you the graphical and analytical point of view of the words such as intercepts

26. nincompoop

teaching you the concepts will help you solve future problems compare to telling you how to solve this.

27. nincompoop

at no extra cost :)

28. nincompoop

just pay me with your attention (time)

29. anonymous

OK so what do I do for the first step? to solve part b?

30. nincompoop

so average rate of change or any rate of change pertains to the slope, m

31. anonymous

Is there a formula for that?

32. Teddyiswatshecallsme

Yes.

33. nincompoop

have you got an idea what slope is yet?

34. anonymous

m = y1- y2 / x1 - x2? is that right?

35. nincompoop

correct

36. anonymous

Yes!

37. nincompoop

now that is analytically looking at things, but what if you are not provided the x's and y's and you have to figure them yourself?

38. nincompoop

bear with me, I will draw some things for you to look at

39. anonymous

Yes, I was just about to say dosn't slope only work for points? (ex. (3, 5) or (-2, 7))

40. nincompoop

it does and then we can use that same knowledge to solve any related-rate problem

41. nincompoop

|dw:1435975261422:dw|

42. nincompoop

we can say that your average rate of change (how much you're traveling at every moment in time) or simply your speed is going to be $$\large s = \frac{final~distance - initial~distance}{final ~time - initial~ time}$$

43. anonymous

I understand this now thanks so much can you help with one more?

44. anonymous

45. nincompoop

let us not try to skip because it will expand and be more complicated from this

46. anonymous

Yes, I understood this and I wrote down my answer and got it right, I just need help with one more thing.

47. anonymous

Explain how the Quotient of Powers was used to simplify this expression: $2^{5}/8 = 22$ By finding the quotient of the bases to be 1/4 and cancelling common factors By finding the quotient of the bases to be 1/4 and simplifying the expression By simplifying 8 to 23 to make both powers base two and subtracting the exponents By simplifying 8 to 23 to make both powers base two and adding the exponents

48. nincompoop

now if we represent first drawing into graph, this is where the x's and y's appear |dw:1435975525773:dw|

49. nincompoop

thank you for your time. I do not like being rushed when I am trying to provide critical concepts.

50. nincompoop

|dw:1435975838805:dw|