math456
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.
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math456
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|dw:1347078037836:dw|
Hero
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Have you graphed the function yet?
math456
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yea as the time increases the volume decreases!
Hero
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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
math456
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y did u picked the time 20?
Hero
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Because it is the next point
P = (15,250)
Q = (20,111)
R = (25,28)
Get it?
math456
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okay so i thought we hv to pick the closest point to 15
math456
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so is the slope -27.8?
Hero
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I will assume you have calculated it correctly
math456
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okay so how do i find the other part of this question?
Hero
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Find the slope of Point PR
math456
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-22.2
Hero
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Okay, now find the average of both both slopes
math456
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how? by subtracting them?
Hero
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then dividing by 2
math456
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-2.8?
Hero
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That's not what I got
math456
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like: -27.8-(-22.2)/2
Hero
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No, not like that
math456
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is it -25?
Hero
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Yes
math456
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great so this the slope of the tangent line at P!
Hero
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It's an "estimate"
math456
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lastly how do i use a graph of the function to estimate the slope of the tangent line at P?
math456
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(This slope represents the rate at which the water is flowing form the tank after 15 mins)
Hero
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I would use rise over run to find the slope.
math456
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u mean delta y/delta x?
Hero
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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.
math456
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hmm in this case how can I find my delta y/x values?
Hero
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By using points on the tangent line. You have to find them for yourself.
Hero
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Actually, use the tangent line approxmation formula
math456
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which is?
Hero
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Well, that depends on how far along you are.
math456
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like i can pick (15,250) ; (14.09, 249.99)
Hero
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On second thought, you don't need tangent line approximation formula. You just need graph paper, really.
math456
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|dw:1347079571561:dw|
Hero
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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
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Then you will have two points on the tangent line. Use those two points to find the slope
math456
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|dw:1347079627933:dw| something like this
Hero
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Yeah, something like that. But use graph paper.
math456
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okay
Hero
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Use the good kind with the smaller squares.
math456
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okay and after doing it lets say my values are 14.009 and 249.001
math456
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i just divide them out?
Hero
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I just told you what to do. Now you have just came up with random values that don't mean anything.
math456
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alright well thanks for your help. I appreciate it..
Hero
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Should I repeat the steps again?
math456
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no its fine thank you once i come up with the accurate values i will ask u again.!
Hero
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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.
math456
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thanks ^^
Hero
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When I say draw tangent line, I mean a straight line using a ruler
Hero
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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.
math456
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okay, gotch ya..
math456
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|dw:1347081039622:dw| so this is how it looks like on my graph paper
Hero
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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.
math456
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|dw:1347081239380:dw| a lil more like this!
Hero
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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.
math456
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yea i am finding the values now. and i hope i found the precise one!
Hero
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You already know what it should be close to.
math456
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yea