Have you graphed the function yet?
yea as the time increases the volume decreases!
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
y did u picked the time 20?
Because it is the next point P = (15,250) Q = (20,111) R = (25,28) Get it?
okay so i thought we hv to pick the closest point to 15
so is the slope -27.8?
I will assume you have calculated it correctly
okay so how do i find the other part of this question?
Find the slope of Point PR
Okay, now find the average of both both slopes
how? by subtracting them?
then dividing by 2
That's not what I got
No, not like that
is it -25?
great so this the slope of the tangent line at P!
It's an "estimate"
lastly how do i use a graph of the function to estimate the slope of the tangent line at P?
(This slope represents the rate at which the water is flowing form the tank after 15 mins)
I would use rise over run to find the slope.
u mean delta y/delta x?
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.
hmm in this case how can I find my delta y/x values?
By using points on the tangent line. You have to find them for yourself.
Actually, use the tangent line approxmation formula
Well, that depends on how far along you are.
like i can pick (15,250) ; (14.09, 249.99)
On second thought, you don't need tangent line approximation formula. You just need graph paper, really.
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
Then you will have two points on the tangent line. Use those two points to find the slope
|dw:1347079627933:dw| something like this
Yeah, something like that. But use graph paper.
Use the good kind with the smaller squares.
okay and after doing it lets say my values are 14.009 and 249.001
i just divide them out?
I just told you what to do. Now you have just came up with random values that don't mean anything.
alright well thanks for your help. I appreciate it..
Should I repeat the steps again?
no its fine thank you once i come up with the accurate values i will ask u again.!
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.
When I say draw tangent line, I mean a straight line using a ruler
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.
okay, gotch ya..
|dw:1347081039622:dw| so this is how it looks like on my graph paper
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.
|dw:1347081239380:dw| a lil more like this!
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.
yea i am finding the values now. and i hope i found the precise one!
You already know what it should be close to.