Mathematics HL/SL/Studies Help

[Slovakov]

All you need to do is calculate the definite integrals from these functions in the given intervals.

I'm not sure how correct I am with my calculations, but more or less it should look like this:

[puyol9]

All you need to do is calculate the definite integrals from these functions in the given intervals.

I'm not sure how correct I am with my calculations, but more or less it should look like this:

Integrals look right to me, and I checked them with calculator. However, for both questions it is a question about whether the algebraic area or the geometrical area is to be found, as both questions have functions which cross the x-axis within the intervals.

Edit: Pretty sure you would be looking for the geometric area, in which case you would have to take the two integrals (one with limits 0 and pi/4 and one with limits pi/4, 3pi/4) and add the absolute value of both of these integrals together

Edited June 20, 2011 by puyol9

[nametaken]

We've begun Differentiation 3- Applications, and I can't seem to get the answer to this question. Can anyone please help me out?

Q) The population, P, of termites varies with time t hours according to the formula P=N₀e^3m where N₀ is the initial population of termites and m is a variable given by m=3e^sint.

Find the rate of change of the termite population after 6 hours, giving your answer in terms of N₀.

I'm pretty sure it's surprisingly simple and that I've missed something here.

Thanks!

[dessskris]

known:

P in terms of m

m in terms of t

t=6

can be found:

dP/dm

dm/dt

need to find:

dP/dt

answer:

dP/dt = dP/dm * dm/dt

[ZiggyM]

Hi !

I'm doing a question at the moment and it's asking the volume of revolution - I know the formula however that is just for the volume around the x-axis isn't it? The question is asking the volume around the y=x line. How would you do this? Thanks

[dessskris]

Hi !

I'm doing a question at the moment and it's asking the volume of revolution - I know the formula however that is just for the volume around the x-axis isn't it? The question is asking the volume around the y=x line. How would you do this? Thanks

wow, that's pretty tough... is there any way to somehow rotate/shift the curve so that you could find the volume of revolution about the x or y axis?

[Procrastination]

Hello, I've been trying to find the nth term for the following sequence but I've not been able to obtain it! Please help me, I know it may not be that hard but anyways I'm kinda blocked right now.

So the sequence goes like this:

{-2,6,-12,20,-30,...}. I have to find the n th term help

[kiwi.at.heart]

Hello, I've been trying to find the nth term for the following sequence but I've not been able to obtain it! Please help me, I know it may not be that hard but anyways I'm kinda blocked right now.

So the sequence goes like this:

{-2,6,-12,20,-30,...}. I have to find the n th term help

Is this part of an option topic at all? Because it doesn't work with any core work as it doesn't follow a GP or AP.

The only pattern I can find is you add 2n (n being the term) to the previous term then multiply it by (-1)^n to account for the alternating negatives. But dont ask me how to put that into a formula for the nth term.

[ILM]

The general formula fr this is :

(-1)ⁿ * n * (n+1)

for example when n=1 then

-1 * 1 * 2 = -2

n=2

1 * 2*3 = 6

n=3

-1 * 3 * 4 = -12

n=4

1* 4 *5 = 20

n=5

-1 * 5 *6 = -30

and yu can observe that when n is odd the number is negative whereas when it is even then the number is positive

[Procrastination]

Hello, I've been trying to find the nth term for the following sequence but I've not been able to obtain it! Please help me, I know it may not be that hard but anyways I'm kinda blocked right now.

So the sequence goes like this:

{-2,6,-12,20,-30,...}. I have to find the n th term help

Is this part of an option topic at all? Because it doesn't work with any core work as it doesn't follow a GP or AP.

The only pattern I can find is you add 2n (n being the term) to the previous term then multiply it by (-1)^n to account for the alternating negatives. But dont ask me how to put that into a formula for the nth term.

Well, I'm studying it as part of progressions. And believe it or not that was actually very helpful.

Edited August 23, 2011 by Procrastination

[ksguru]

Hi

I am currently doing HL math. I need help with these problems.

1.The height in cm of a cylindrical piston above its central position is given by h = 16sin4t, where t is the time in seconds, 0 <= t <= pi/4.

a) what is the ht after 1/2 sec?

b) Find the first time at which the height is 10 cm.

In this problem the 't' is said to be in secs , but it varies from 0 to pi/4. how does one do the conversion?Kindly explain.

thanks!

[dessskris]

if they say 0 <= t <= pi/4, then the t is expressed in radians, but yes the unit of the time is still second. just calculate the height with radians mode instead of degrees mode.

a)

are you asking for height but you shortened it to ht, or are you asking for height*time?

anyhow, after 0.5 s,

h=16sin(4*0.5)

h=16sin(2)

h=14.5 cm

b)

h=16sin(4t)

when h=10,

10=16sin(4t)

sin(4t)=0.625

4t=0.675

t=0.169 s

[MR.AHM]

I think he meant is that How it varies at that range..

You can convert it into decimals where pi/4 = 0.785.... seconds

and the answer Desy Galu gave you are within the range and the 0.5 seconds too

I hope this explains what you mean !!

[Hexa]

What I'm doing is Chapter 9B problem 7c in http://ispmath.wikispaces.com/file/view/New+Math+Book_Part1.pdf (pg 241). And I can't seem to solve the problem.

I'm trying to turn (2^(2-k))/((2k=1)(k!)) into (8(2^-k))/((k+1)!) but I can't do this.

If anyone can work this out for me I would appreciate it strongly.

[MR.AHM]

What I'm doing is Chapter 9B problem 7c in http://ispmath.wikispaces.com/file/view/New+Math+Book_Part1.pdf (pg 241). And I can't seem to solve the problem.

I'm trying to turn (2^(2-k))/((2k=1)(k!)) into (8(2^-k))/((k+1)!) but I can't do this.

If anyone can work this out for me I would appreciate it strongly.

Is this Haese and Harris book?

Edited September 9, 2011 by MR.AHM

[Hexa]

What I'm doing is Chapter 9B problem 7c in http://ispmath.wikispaces.com/file/view/New+Math+Book_Part1.pdf (pg 241). And I can't seem to solve the problem.

I'm trying to turn (2^(2-k))/((2k=1)(k!)) into (8(2^-k))/((k+1)!) but I can't do this.

If anyone can work this out for me I would appreciate it strongly.

Is this Haese and Harris book?

Yes the second edition HL.

[MR.AHM]

What I'm doing is Chapter 9B problem 7c in http://ispmath.wikispaces.com/file/view/New+Math+Book_Part1.pdf (pg 241). And I can't seem to solve the problem.

I'm trying to turn (2^(2-k))/((2k=1)(k!)) into (8(2^-k))/((k+1)!) but I can't do this.

If anyone can work this out for me I would appreciate it strongly.

Is this Haese and Harris book?

Yes the second edition HL.

Hello Hexa, I just saw your reply, and started working on the question.

first thing, you are wrong. You are not trying to turn it into (8(2^-k))/((k+1)!)

You are actually trying to turn it into 2^1-n/(n+1)!

I think I don't have to go through the first step which is making sure that P₁ is true. And it is.

However, lets go to the point:

If P_k is true then u_k=2^2-k/k!

and u_k+1 = u_k / 2(n+1)

= 2^2-k / k! / (2(k+1)

= 2^2-k / 2(k+1)k!

from this you can see that 2^2-k * 2^-1 = 2^2-k-1= 2^1-k

And (k+1)* k! = (k+1)!

So after all it is = 2^1-n/(n+1)!

I hope this explained it

Edited September 9, 2011 by MR.AHM

[Hexa]

I'm probably going to end up abusing this, but whatever. Thanks for the help

k Next question is 14c in the same book.

I got as far as

(8k^3) ≥ (k^3)+(3k^2)+3k+1

but how would I prove that to be true?

Full question is to prove 8^n ≥ n^3 through PMI.

Edited September 12, 2011 by Hexa

[dessskris]

what's PMI?

ignoring this PMI sht that I do not know,

(8k^3) ≥ (k^3)+(3k^2)+3k+1

(7k^3) ≥ (3k^2)+3k+1

on your GDC, plot y=7x^3

plot y=3x^2+3x+1 on the same axes

if you see the first function lies above or touches the second function then it's proven.

[Hinuku]

Hi, Can anyone explain this problem to me? :

Probability Problems

I am talking about problem no. 7. Thanks

I'd also appreciate some help with question 48 on this web site:

Probability Problems 2

Edited September 14, 2011 by Hinuku