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yorkmanz

Member

Registered: 2019-01-12

Posts: 13

Interpreting Graphs

A liquid is heated in lab using hot plate the graph temperature vs time is shown below

https://imgur.com/c6ehBn5

answer using letter A, B, C, D FROM THE ABOVE GRAPH

1) WHERE IS THE RATE OF CHANGE ZERO?

2) WHERE IS THE RATE OF CHANGE CHANGING?

3) WHERE IS THE RATE OF CHANGE POSITIVE?

4) WHERE IS THE RATE OF CHANGE GREATEST?

5) CALCULATE RATE OF CHANGE FOR SECTION A, INCLUDING UNITS?

MY ANSWER FOR

1)  C

2)  B

3)  A

4)  D

5) NOT SURE HOW TO SOLVE

PLEASE CHECK MY ANSWERS AND HELP ME

THANKS

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

Re: Interpreting Graphs

Hi yorkmanz,

I think you are correct for 1, 2, 3, and 4.

Regarding 5, I think it is 30 degrees per 20 minutes or 1.5 degrees per minute.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Interpreting Graphs

hi yorkmanz

Here's what I think.

For section A the temperature is going up (positive).  The line is straight meaning the rate of increase is constant.  Then at 20 minutes there is a sudden change to a steeper line, so the rate is still positive and constant but at a greater value.  At C the temperature isn't changing so the rate of change is zero.  Finally at D the temperature is going down so the rate is now negative.  The curve here isn't straight so the rate is changing.  Heat loss is fastest to start with and then, as the curve levels off, the rate of loss is less and less.

To get the final answer the temperature has increased by 30 degrees C in 20 minutes. The rate of change is measured by dividing the 'up' by the 'across', ie 30/20 and the units are degrees C per minute.

Note:  3) had two letters

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: Interpreting Graphs

I have to have an issue with you ganesh. All the answers are incorrect except the first one and partly the answer of question three. This is so because the rate of change of the temperature at a particular point on the temporal curve of the temperature is the slop of the curve at that point. With this fact on our mind, since the slop of the curve at C is zero the first answer is correct. However, since all the curve parts are line segments (which have constant slops) except the D part which is a continuous curve and hence with changing slop, then the correct answer for question 2 is D. Now since the slop of the curve in the D and C parts are negative and zero, respectively, while it is positive in the A and B parts then the answer of the third question is A and B. Finally, since the slop of the curve is negative in D and Zero in C while the slop of B greater than that of A and since the absolute value of the rate of change at the starting point of D is equal to the slop in B then the correct answer of Four is B and the starting point of D. Therefore in summary the answer will be as follows:

1- C
2- D
3- A and B
4- B and at the starting of segment D

I hope that will help. By the way ganesh your answer for question five is correct.

Last edited by Grantingriver (2019-04-04 22:36:27)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Interpreting Graphs

hi Grantingriver

I was just about to add that the slope at the start of D is the same as B and so it is arguable that both are 'greatest'.  It depends whether you interpret 'greatest' as 'most steep and positive' or just 'most steep'.  What do you think?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: Interpreting Graphs

Hi bob bundy, I think the greatest is B since it is possitive and any possitive value is geater than the negtive value. In fact, the geatest rate of change is in the B part of the curve and the least rate of change is at the start of section D. On the other hand, regardless of the previous argument there is a logical reason to interpret the answer in this manner since otherwise the stituation will be inconclusive which enforce that interpretation.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Interpreting Graphs

Ok, thanks

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: Interpreting Graphs

To err on the caution side, I think the bob bundy suggestion is the more rational one, since the rate of change measure the amount of variance in a quantity therefore there are no plausible reason to distinguish between the negative and positive rate of changes if they have the same absolute value and hence it is more suitable that the answer of 4 to be fixed to “B and at the starting of D”. I will amend the answer above.

Last edited by Grantingriver (2019-04-04 21:01:30)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Interpreting Graphs

Here's a bit of the graph to show what we're talking about:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

yorkmanz

Member

Registered: 2019-01-12

Posts: 13

Re: Interpreting Graphs

hi yorkmanz

Here's what I think.

For section A the temperature is going up (positive).  The line is straight meaning the rate of increase is constant.  Then at 20 minutes there is a sudden change to a steeper line, so the rate is still positive and constant but at a greater value.  At C the temperature isn't changing so the rate of change is zero.  Finally at D the temperature is going down so the rate is now negative.  The curve here isn't straight so the rate is changing.  Heat loss is fastest to start with and then, as the curve levels off, the rate of loss is less and less.

To get the final answer the temperature has increased by 30 degrees C in 20 minutes. The rate of change is measured by dividing the 'up' by the 'across', ie 30/20 and the units are degrees C per minute.

Note:  3) had two letters

Hope that helps,

Bob

For 3) since its going positive i t should be A AND B?

so C IS STOPS

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Interpreting Graphs

hi yorkmanz

Yes, that's right.  Do you need more help with the rest?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

yorkmanz

Member

Registered: 2019-01-12

Posts: 13

Re: Interpreting Graphs

hi yorkmanz

Yes, that's right.  Do you need more help with the rest?

Bob

thanks much.
for Question 5 any formula i can use to solve it
thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Interpreting Graphs

Yes, there is.  When a question asked for a rate of change, what you need is the gradient of the line.

If the end points of the line (if it's straight) are (x1, y1) and (x2, y2) then the gradient is

(y2 - y1) / (x2 - x1)

That's (how much the temperature has changed) / (how much time has changed)

https://www.mathsisfun.com/data/straigh … graph.html

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob