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March 30, 2024, 12:34:29 am

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EEEEEEP

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Re: Mathematics Question Thread
« Reply #165 on: July 13, 2016, 03:06:44 pm »
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Just in case I am confusing, I hope this helps everyone out
THe original equation  is different from the first differentiation.

The first differentiation which is 3x^2, shows the gradients (which also happens to be the rate of change).  Both equations should look different.

What else don't you get?
« Last Edit: October 10, 2017, 10:40:27 pm by EEEEEEP »

conic curve

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Re: Mathematics Question Thread
« Reply #166 on: July 13, 2016, 03:09:12 pm »
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I told you, do NOT relate the y-coordinates of the derivative, to the y-coordinates of the original function.

Draw a tangent on y=x3. The GRADIENT of the TANGENT, is the y-coordinate on the derivative.

Using this: http://www.teacherschoice.com.au/Maths_Library/Calculus/tangents_and_normals.htm

RuiAce

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Re: Mathematics Question Thread
« Reply #167 on: July 13, 2016, 03:10:52 pm »
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Using this: http://www.teacherschoice.com.au/Maths_Library/Calculus/tangents_and_normals.htm
According to the website you gave, the derivative is a measure of the GRADIENT of the TANGENT at the point (to the curve). Anything else?

Obviously the gradient of the tangent at the point does not have to resemble that of the actual curve. The tangent to y=x2 at (1,1) is 2. What does that have to do with the original curve? Nothing.

The derivative is not a tilted graph of the original thing. It ONLY measures the gradient of the tangent. If you want a function whose derivative is itself y=ex is your answer and you do that in Yr 12.

conic curve

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Re: Mathematics Question Thread
« Reply #168 on: July 13, 2016, 03:16:00 pm »
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According to the website you gave, the derivative is a measure of the GRADIENT of the TANGENT at the point (to the curve). Anything else?

Obviously the gradient of the tangent at the point does not have to resemble that of the actual curve. The tangent to y=x2 at (1,1) is 2. What does that have to do with the original curve? Nothing.

Okay I think I am very confusing

ANyways, going back to basics, if you were to differentaite y=x, you would get y=1 right? This is finding the gradient of the tangent (i.e. the rate of change). As you can see, the gradient of the tangent is "visible" on this graph

For the example I posted originally, it was y=x^3 and if that was differentiated (i.e. the rate of change was found) it was y=3x^2 and that did not touch the graph at all except for the origin. Is this case shouldn't of 3x^2 of had been the gradient of the tanngent to x^3

If I am very confusing then just forget about this because I feel bad making all of you guys do this to me


RuiAce

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Re: Mathematics Question Thread
« Reply #169 on: July 13, 2016, 03:18:09 pm »
+1
Okay I think I am very confusing

ANyways, going back to basics, if you were to differentaite y=x, you would get y=1 right? This is finding the gradient of the tangent (i.e. the rate of change). As you can see, the gradient of the tangent is "visible" on this graph

For the example I posted originally, it was y=x^3 and if that was differentiated (i.e. the rate of change was found) it was y=3x^2 and that did not touch the graph at all except for the origin. Is this case shouldn't of 3x^2 of had been the gradient of the tanngent to x^3

If I am very confusing then just forget about this because I feel bad making all of you guys do this to me
Ok. Let's clear one thing up.

x is not necessarily a number. x is a variable. We have to let x = a certain number, to get the gradient of the tangent, at that number.

The plot of the derivative shows the gradient of the tangent, EVERYWHERE on the original curve.

It is not immediately obvious that 3x2 is the derivative of x3. The reason why this is the case is that


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Re: Mathematics Question Thread
« Reply #170 on: July 13, 2016, 03:22:11 pm »
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Ok. Let's clear one thing up.

x is not necessarily a number. x is a variable. We have to let x = a certain number, to get the gradient of the tangent, at that number.

The plot of the derivative shows the gradient of the tangent, EVERYWHERE on the original curve.

It is not immediately obvious that 3x2 is the derivative of x3. The reason why this is the case is that



Oh....Right, I get it now thank you thank you thank you  ;D

Sorry for making you go through the pain in answering this  :'(

RuiAce

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Re: Mathematics Question Thread
« Reply #171 on: July 13, 2016, 03:24:22 pm »
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Oh....Right, I get it now thank you thank you thank you  ;D

Sorry for making you go through the pain in answering this  :'(
Glad that we eventually got there

shivali

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Re: Mathematics Question Thread
« Reply #172 on: July 13, 2016, 07:21:06 pm »
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Question: "A radioactive substance decays by 10% after 80 years. By how much will it decay after 500 years?"

My working:
T0 = 100
T80 = 90
Tn=T0e^(kn)
T80 = T0e^(80k)
90 = 100e^(80k)
k = (ln(0.9))/80

T500 = 100e^500k
T500 = 51.72655

Therefore the substance will decay by 51.7% in 500 years?




RuiAce

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Re: Mathematics Question Thread
« Reply #173 on: July 13, 2016, 07:39:40 pm »
+1
Question: "A radioactive substance decays by 10% after 80 years. By how much will it decay after 500 years?"

My working:
T0 = 100
T80 = 90
Tn=T0e^(kn)
T80 = T0e^(80k)
90 = 100e^(80k)
k = (ln(0.9))/80

T500 = 100e^500k
T500 = 51.72655

Therefore the substance will decay by 51.7% in 500 years?


Permit k to be negative in your working out.



shivali

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Re: Mathematics Question Thread
« Reply #174 on: July 13, 2016, 07:48:02 pm »
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Permit k to be negative in your working out.




The correct answer was 48.2% ? In the textbook

RuiAce

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Re: Mathematics Question Thread
« Reply #175 on: July 13, 2016, 08:15:41 pm »
+4
Edit: No never mind. This is exactly what happens when you try to rush.

51.76...% of the original mass is whatever is left behind.

100% - 51.76%... of the original mass is what has actually decayed.

jakesilove

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Re: Mathematics Question Thread
« Reply #176 on: July 14, 2016, 09:04:17 am »
+4
Edit: No never mind. This is exactly what happens when you try to rush.

51.76...% of the original mass is whatever is left behind.

100% - 51.76%... of the original mass is what has actually decayed.

Can we all just appreciate that Rui has answered about 100 questions in the past three days. An Atar Notes legend,who deserves all of our thanks. You're an absolute king, and hundreds of HSC students are better off with you around!

Jake
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ehatton2016

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Re: Mathematics Question Thread
« Reply #177 on: July 14, 2016, 12:12:21 pm »
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Hey Jake!

I have like 2 and a bit weeks to trials and have been pumping our past 2U papers but my marks in each has not improved at all!!

I've done the whole, do extra revision on stuff you get wrong but IT ISN'T WORKING!!!  :(

What do I do? I'm usually a band 6 student in maths, so this is really annoying me!!

Thank you!!

RuiAce

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Re: Mathematics Question Thread
« Reply #178 on: July 14, 2016, 12:14:53 pm »
+1
Hey Jake!

I have like 2 and a bit weeks to trials and have been pumping our past 2U papers but my marks in each has not improved at all!!

I've done the whole, do extra revision on stuff you get wrong but IT ISN'T WORKING!!!  :(

What do I do? I'm usually a band 6 student in maths, so this is really annoying me!!

Thank you!!
When you do past papers, do you struggle on questions? Because doing past papers "ineffectively" is the same thing as ineffective studying habits.

Or are you saying that you struggle out of exam pressure.

jakesilove

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Re: Mathematics Question Thread
« Reply #179 on: July 14, 2016, 12:17:35 pm »
+1
Hey Jake!

I have like 2 and a bit weeks to trials and have been pumping our past 2U papers but my marks in each has not improved at all!!

I've done the whole, do extra revision on stuff you get wrong but IT ISN'T WORKING!!!  :(

What do I do? I'm usually a band 6 student in maths, so this is really annoying me!!

Thank you!!

Hey!

Firstly, welcome to the forums! Nice job studying for trials; sounds like you're really putting the hours in.

Firstly, two and a bit weeks is ages. You could learn the entire Maths curriculum from scratch in that time.

It looks like you've identified what areas you are weak in, because you have tried doing revision for topics that you lose marks in. What kind of sections are you struggling with? At the end of the day, if there is a section you're not very confident with, and you just do a billion questions of that type, you might not improve at all. That's because, in those sections, it might come down to UNDERSTANDING, before repetition. If you struggle to understand a concept, doing it wrong 100 times won't improve your mark.

Past papers is really all you can do. Write out questions you get incorrect, and redo them once a day for a few days until you can do them with ease. This will solidify the methodology in your mind, and make sure that none of your time is wasted. Again, if you let us know where you are specifically struggling with, maybe we can help!

Keep at it. You have so much time left, and doing past papers DOES help even if it feels like it doesn't. There's no like secret trick or anything, nothing I can tell you right now that will get you 100% in every paper you do. But past papers helps you improve, and identifying areas of weakness will help you improve. If you have any specific questions, post them here, and we can talk them through with you in a way that will hopefully help you understand the fundamental underlying mathematics as well as the answer itself.

You'll be fine! Keep at it.

Jake
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