Mathematics Question Thread

[jakesilove]

Okay cool! Thank you I see now!

Another question haha,
Which term of the series 8, -4 , + 2.... is 1/128?

I'm just particularly struggling with dealing with a negative r value and using log to solve for n
thanks!

Mod Edit [Aaron]: Merged double post. Please edit your previous post if you want to add something.

Hey! So we know that, for a geometric series,

Where a is the first term, r is the geometric difference between two terms, and n is the term number. Thus,

is the definition of each term for this series.

Now, we want to find


So,




The last line literally means -1/2 to the power of WHAT (ie. n-1) is equal to 1/1024 (at least, that's how I think of logs). Let's keep going

Actually, this is more difficult than it needs to be. Let's take a step back




The negative here doesn't matter; as long as n-1 is even, the term becomes positive.



Let's just check this in the original equation


As expected

[RuiAce]

Thanks so much.

What would the answer for b) be?

http://i68.tinypic.com/10ynmkn.png

I told you what to sketch at the bottom of my post

[JuliaPascale123]

I told you what to sketch at the bottom of my post

Thanks you!

[HotDiggity]

Hi  ,

Sorry about the picture quality fam .



Jennifur :p

[RuiAce]

Hi  ,

Sorry about the picture quality fam .

(Image removed from quote.)

Jennifur :p

Technology.

[1937jk]

Hey! So we know that, for a geometric series,

Where a is the first term, r is the geometric difference between two terms, and n is the term number. Thus,

is the definition of each term for this series.

Now, we want to find


So,




The last line literally means -1/2 to the power of WHAT (ie. n-1) is equal to 1/1024 (at least, that's how I think of logs). Let's keep going

Actually, this is more difficult than it needs to be. Let's take a step back




The negative here doesn't matter; as long as n-1 is even, the term becomes positive.



Let's just check this in the original equation


As expected

awesome! thank you so much! I understand now

[HotDiggity]

Technology.

Cheers Rui, but your link does not work for the graph and all the graphs im looking at dont intercept at 0.495
https://www.wolframalpha.com/input/?i=graph+(t%5E2%2Bcost)%2F(t%5E4%2B1)

[jamonwindeyer]

Cheers Rui, but your link does not work for the graph and all the graphs im looking at dont intercept at 0.495
https://www.wolframalpha.com/input/?i=graph+(t%5E2%2Bcost)%2F(t%5E4%2B1)

Hey! Yeah I agree with your sketch, and that means there is a \(y\) intercept at \(\left(0,1\right)\), and there are no \(x\)-intercepts

[RuiAce]

Cheers Rui, but your link does not work for the graph and all the graphs im looking at dont intercept at 0.495
https://www.wolframalpha.com/input/?i=graph+(t%5E2%2Bcost)%2F(t%5E4%2B1)

Not sure what was going on the link

(@ Jamon as well) I believe the question asked to sketch the velocity, not the displacement.

You input the graph of s(t) into WolframAlpha in your link.

[_____]

Got a dumb questions about ACPW. Currently on exponential growth/decay. The question is:

"Newton's Law of Cooling states that the rate of decrease in temperature is proportional to the temperature difference between the body and its surroundings.

A batch of scones are removed from an oven whose temperature is 320 degrees Celsius. The rack onto which they are placed is surrounded by air at 20 degrees Celsius. They cool at a rate of 30% per minute.

What is the temperature of the scones after:
a) 2 minutes
b) 10 minutes"

I've done questions like this before where the temperatures would change from 320 > 0 for example. The equation if this were the case would be:
T = 320e^(0.3t). But how do I account for the temperature difference in this instance, where it is 20 degrees rather than 0 degrees in the new environment? I tried (320-20)e^(0.3t) but this returned ~16 degrees which must be wrong.

[jamonwindeyer]

Got a dumb questions about ACPW. Currently on exponential growth/decay. The question is:

Hey! Definitely not a dumb question - That is a 3U question, do you do 3U? Happy to explain it if it is relevant to you

Edit: If you want to have a crack at the Math, the formula should be:



Knowing where this comes from and actually using things like it in exams is left to the 3U students

[_____]

Hey! Definitely not a dumb question - That is a 3U question, do you do 3U? Happy to explain it if it is relevant to you

Edit: If you want to have a crack at the Math, the formula should be:



Knowing where this comes from and actually using things like it in exams is left to the 3U students

That's odd, I'm only doing 2 units. I've got to do this question anyway but I'll be sure to note that down (and look at the syllabus more closely).

Thanks for the equation, if you get the chance could you explain how you got 310e rather than using 300e or 320e? I understand why you'd add 20 but I thought you'd have to either keep the multiple the same (320) or reduce the multiple by 20 because the difference is 20 (300).

[jamonwindeyer]

That's odd, I'm only doing 2 units. I've got to do this question anyway but I'll be sure to note that down (and look at the syllabus more closely).

Thanks for the equation, if you get the chance could you explain how you got 310e rather than using 300e or 320e? I understand why you'd add 20 but I thought you'd have to either keep the multiple the same (320) or reduce the multiple by 20 because the difference is 20 (300).

You're absolutely right - I mistyped, it should be 300 as that second number, fixed it above! Sorry!

[_____]

You're absolutely right - I mistyped, it should be 300 as that second number, fixed it above! Sorry!

NP thanks for the help!

[sophiegmaher]

Yooo so with superannuation questions: On 31st January 1990 Hayden joined a superannuation fund by investing $5000 at 6%p.a. compound interest. He added $5000 to the fund on 31st January each year and intends to continue to do so until, but not including, the day he intends to retire 31/1/2010. Find the total accumulated value of his investment, to the nearest dollar, on that day.
- I'm confused about the "but not including" part? Would that mean that the final formula used for the final year would be 5000(1.06)^0 ?