# Basic Graphing help

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• December 2nd 2009, 04:09 PM
agent2421
Basic Graphing help
Hey all, fisrt of all i'm not sure if this should go here or not but I didn't know where to post it... I'm having a bit of trouble with math and hoping someone can explain it to me.

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Water is being poured into a container as illustrated below at a constant rate. The height of the water level is then recorded every second. Draw the graph of the height of water level versus time for this container.

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Basically I'm not sure how to draw the graph, I'm not sure what values to use etc. Can anyone help me out? I just need to know what values to use and why I have to use those values..

Thanks :)
• December 2nd 2009, 04:16 PM
Bacterius
It depends on the shape of the container. If the container has no special features (basic cylinder), then it is just a straight line OR more likely a parabola. You need to know the surface of the bottom of the cylinder, and know the quantity of water poured each second into the cylinder. Then it is a basic multiplication/squaring.

If the container is some exotic shape, then the graph may take any possible shape.

Do you have any more information ? Maybe it might be a good idea to show us the illustration, I'm pretty sure it contains the information you need (Nod) And don't try to hide it, I know you have an illustration :p
• December 2nd 2009, 04:20 PM
agent2421
yes there is abit more info... I did'nt know if I needed to post it or not but here's the illustration.

http://hwdsb.elearningontario.ca/con...s/assign_4.gif

I'm not sure if you get the image or not.... if it doesn't work I"ll tyr something else.
• December 2nd 2009, 04:21 PM
Bacterius
• December 2nd 2009, 04:22 PM
agent2421
Is it okay if I do it like this... I put it as an attachment
• December 2nd 2009, 04:25 PM
Bacterius
That's fine. Where is the scale ? Can you measure the illustration for us and put some values on the illustration, such as the full height and the base length ?
Is it a 2D shape ? Don't we consider the water is poured in a 3-dimensional object ?
There is a lot of information missing, please give everything you know otherwise there might be infinitely many solutions (Lipssealed)
• December 2nd 2009, 04:27 PM
agent2421
That is actually all the information from this question... There is no measures on the illustartion and they give no other information. maybe this is why I'm so confused on how to do it.
• December 2nd 2009, 04:30 PM
Bacterius
Strange ... without a scale we cannot know exactly how much water has been poured. Is it a paper illustration ? Is the illustration annoted "not to scale", or is it allowed to take some measures on the image to get the scales ? :(
• December 2nd 2009, 04:31 PM
agent2421
nope the illustration says nothing like that... it just shows the picture of what I posted above.. other than that theres absolutley no other information.
• December 2nd 2009, 04:40 PM
Bacterius
Then I guess you are going to have to measure your values on the illustration.
Here is the way to do it in the general way :

You know that the formula to calculate the area of a trapezium is :

$A = \frac{h(a + b)}{2}$, where $h$ is the height of the trapezium, $a$ is the bottom length and $b$ is the top length.
You know the bottom and top lengths by measuring them on the illustration. Try to isolate $h$ :

$A = \frac{h(a + b)}{2}$

$2A = h(a + b)$

$h = \frac{2A}{a + b}$

Good. Your equation thus is $y = \frac{2A}{a + b}$.
But there is something missing : $A$. That would be our water quantity, I guess. Is there some relationship between the water poured into the container and the area taken by the water ? I guess so ... Can you work the rest from now ? :)
• December 2nd 2009, 04:43 PM
agent2421
Thanks for the help... I actually think we don't have to do that for this problem because we haven't been taught how to do it... Hold on there's another example, I"m going to post that and maybe it will help out a bit.. It's the same type of question but a different problem.
• December 2nd 2009, 04:47 PM
agent2421
Quote:

Originally Posted by agent2421
Thanks for the help... I actually think we don't have to do that for this problem because we haven't been taught how to do it... Hold on there's another example, I"m going to post that and maybe it will help out a bit.. It's the same type of question but a different problem.

Here's the other question which gave us an answer already... Maybe this will help me for the problem I'm trying to do... It looks almost the same, so maybe someone might be able to figure it out... Where i say Attachment #, just look at the attachment listed below and it's in the same order.

Water is being poured at a constant rate into a container as shown below. What would the graph of the Height of the Water level related to the time look like?

(Attachment 1)

Let us look at the rate of change at various water levels:
(Attachment 2)

A http://hwdsb.elearningontario.ca/con...images/rar.gif The rate of change of the water level is not constant and decreases as it approaches the red line.

B http://hwdsb.elearningontario.ca/con...images/rar.gif After the level passes the first red line the container becomes more narrow resulting in the rate of change of the water level to increase until the second red line

C http://hwdsb.elearningontario.ca/con...images/rar.gif As the level reaches and passes the second red line the rate of change remains constant for the rest of the fill up. This is a narrow section so the rate is faster than the other major sections.

(attachment 3)
• December 2nd 2009, 04:50 PM
Bacterius
Yep. Do you understand this problem and the answer ? The only thing you have to understand in this type of question is : how does the shape of the container (or more accurately the width of the container at one height) influence the rate of the fill and the shape of the graph ?
• December 2nd 2009, 04:52 PM
agent2421
I still dont understand how to do it for my problem. I'm not the greatest at math and really have trouble with some of this stuff... I still have no idea how to do this question:

Water is being poured into a container as illustrated below at a constant rate. The height of the water level is then recorded every second. Draw the graph of the height of water level versus time for this container.
• December 2nd 2009, 05:00 PM
Bacterius
I honestly think they don't want you to calculate anything. They just want you to think and investigate how the water height would evoluate.
It should give something like a square root graph (try plotting $y = \sqrt{x}$ on your computer). Because it is harder and harder for the water to gain in height because your container gets larger and larger.
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