## math456 3 years ago a) If P is the point (15,250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t=5,10,20,25 & 30; a) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines.

1. math456

|dw:1347078037836:dw|

2. Hero

Have you graphed the function yet?

3. math456

yea as the time increases the volume decreases!

4. Hero

Okay, so where are you stuck with this? You have two points P = (15,250) and Q = (20, 111). Use the slope formula and find the slope of PQ

5. math456

y did u picked the time 20?

6. Hero

Because it is the next point P = (15,250) Q = (20,111) R = (25,28) Get it?

7. math456

okay so i thought we hv to pick the closest point to 15

8. math456

so is the slope -27.8?

9. Hero

I will assume you have calculated it correctly

10. math456

okay so how do i find the other part of this question?

11. Hero

Find the slope of Point PR

12. math456

-22.2

13. Hero

Okay, now find the average of both both slopes

14. math456

how? by subtracting them?

15. Hero

then dividing by 2

16. math456

-2.8?

17. Hero

That's not what I got

18. math456

like: -27.8-(-22.2)/2

19. Hero

No, not like that

20. math456

is it -25?

21. Hero

Yes

22. math456

great so this the slope of the tangent line at P!

23. Hero

It's an "estimate"

24. math456

lastly how do i use a graph of the function to estimate the slope of the tangent line at P?

25. math456

(This slope represents the rate at which the water is flowing form the tank after 15 mins)

26. Hero

I would use rise over run to find the slope.

27. math456

u mean delta y/delta x?

28. Hero

I don't know what kind of answer they expect from you however. Yes, delta y/delta x if you want to say it that way.

29. math456

hmm in this case how can I find my delta y/x values?

30. Hero

By using points on the tangent line. You have to find them for yourself.

31. Hero

Actually, use the tangent line approxmation formula

32. math456

which is?

33. Hero

Well, that depends on how far along you are.

34. math456

like i can pick (15,250) ; (14.09, 249.99)

35. Hero

On second thought, you don't need tangent line approximation formula. You just need graph paper, really.

36. math456

|dw:1347079571561:dw|

37. Hero

Graph the points on graph paper, draw a smooth curve through them, then take a ruler and draw a tangent line through point P and through the x-axis

38. Hero

Then you will have two points on the tangent line. Use those two points to find the slope

39. math456

|dw:1347079627933:dw| something like this

40. Hero

Yeah, something like that. But use graph paper.

41. math456

okay

42. Hero

Use the good kind with the smaller squares.

43. math456

okay and after doing it lets say my values are 14.009 and 249.001

44. math456

i just divide them out?

45. Hero

I just told you what to do. Now you have just came up with random values that don't mean anything.

46. math456

alright well thanks for your help. I appreciate it..

47. Hero

Should I repeat the steps again?

48. math456

no its fine thank you once i come up with the accurate values i will ask u again.!

49. Hero

1. Get some graph paper 2. Plot the points you were given on an xy plane 3. Draw a smooth curve through them 4. Draw a tangent line through point P and the x-axis 5. Take those two points and find the slope of the tangent line.

50. math456

thanks ^^

51. Hero

When I say draw tangent line, I mean a straight line using a ruler

52. Hero

If your line goes through the y-axis, you can use that too. Try to set up your xy axes in a way where your points are convenient to calculate.

53. math456

okay, gotch ya..

54. math456

|dw:1347081039622:dw| so this is how it looks like on my graph paper

55. Hero

Well, you can't really draw the line without a curve. That's why you need the other points AND the curve drawn through them first.

56. math456

|dw:1347081239380:dw| a lil more like this!

57. Hero

Well, I'm sure you're getting the hang of it. All you have to do is find a point on the line that goes through one of the intersections on the graph paper and use that point as your second point for a more accurate measure of slope. It's a pretty intuitive thing if you know what you're doing.

58. math456

yea i am finding the values now. and i hope i found the precise one!

59. Hero

You already know what it should be close to.

60. math456

yea