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.

- anonymous

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- anonymous

|dw:1347078037836:dw|

- Hero

Have you graphed the function yet?

- anonymous

yea as the time increases the volume decreases!

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## More answers

- 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

- anonymous

y did u picked the time 20?

- Hero

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

- anonymous

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

- anonymous

so is the slope -27.8?

- Hero

I will assume you have calculated it correctly

- anonymous

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

- Hero

Find the slope of Point PR

- anonymous

-22.2

- Hero

Okay, now find the average of both both slopes

- anonymous

how? by subtracting them?

- Hero

then dividing by 2

- anonymous

-2.8?

- Hero

That's not what I got

- anonymous

like: -27.8-(-22.2)/2

- Hero

No, not like that

- anonymous

is it -25?

- Hero

Yes

- anonymous

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

- Hero

It's an "estimate"

- anonymous

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

- anonymous

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

- Hero

I would use rise over run to find the slope.

- anonymous

u mean delta y/delta x?

- 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.

- anonymous

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

- Hero

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

- Hero

Actually, use the tangent line approxmation formula

- anonymous

which is?

- Hero

Well, that depends on how far along you are.

- anonymous

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

- Hero

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

- anonymous

|dw:1347079571561:dw|

- 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

- Hero

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

- anonymous

|dw:1347079627933:dw| something like this

- Hero

Yeah, something like that. But use graph paper.

- anonymous

okay

- Hero

Use the good kind with the smaller squares.

- anonymous

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

- anonymous

i just divide them out?

- Hero

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

- anonymous

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

- Hero

Should I repeat the steps again?

- anonymous

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

- 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.

- anonymous

thanks ^^

- Hero

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

- 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.

- anonymous

okay, gotch ya..

- anonymous

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

- 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.

- anonymous

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

- 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.

- anonymous

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

- Hero

You already know what it should be close to.

- anonymous

yea

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