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h = 38(1 - e^-0.049t)

Divide both sides by 38

h/38 = 1 - e^-0.049t

Add e^-0.049t to both sides

h/38 + e^-0.049t = 1

Subtract h/38 from both sides

e^-0.049t = 1 - h/38

Take natural logs of both sides

ln(e^-0.049t) = ln(1 - h/38)

-0.049t = ln(1 - h/38)   because ln(e^a) = a

Divide both sides by -0.049

t = -(1/0.049)*ln(1 - h/38)

$$\\-2-x>5\\
-2+2-x>5+2\\
-x>7\\
x<-7$$

Thanks Dragon.  

Hi Pyramid,

You are asking some good questions.   

You can use any letter to stand for an unknown number.  It does not have to be x.

You  are right, x is commonly used, I wonder if there really is a good reason for this.   

There are some good reasons for this in the artical that dragon has pasted in.  

I don't think I ever really thought about it before.  Thanks Dragon.    

Calculus involves some new concepts which take a while to understand.  

It is very powerful and once you get a bit of an understanding it is a lot of fun.   :)

You could just use the factorial button on any scientific calculator too.   

Thanks Alan, I did not know that.    

I found out that the dollar sign is \.

We all really appreciate your answers geno but Dragon is right - don't burn yourself out!     

What does that mean?

arc sine is the same as inverse sin SO

on thid calc it is 2nd asin

1.Click "Home" which is on the top of the screen

2.Click the arrow which is at the bottom-right corner of the scientific calculator.

3.Click "Create calclet" which is near the arrow.

For large values of n you can get a good approximation by using Stirling's approximation:

    n! ≈ (2pi*n)^1/2*e^-n*nⁿ

Is it the notation I've used that is confusing?

f(x) = (1 + x)^1/2 is the square root of (1+x), so putting x = 0, f(x)_{at x = 0} = 1

df(x)/dx = (1/2)(1 + x)^-1/2 so putting x = 0, df(x)/dx_{at x=0} = 1/2

d( df(x)/dx )/dx = -(1/4)(1 + x)^-3/2 so putting x = 0,  d( df(x)/dx )/dx_{at x = 0} = -1/4

and so on.

Putting these back into the Maclaurin series f(x) = 1 + x/2 - x²/8 ... 

Notice that f(x) is not exactly 1 + x/2.  This is just a first-order approximation.

9+-4--3

=9-4+3

=8

If α is the linear coefficient of thermal expansion then

 α = change in length/(original length*temperature change)

Note:  Edited and corrected thanks to Melody's more carefully thought through analysis below!

$$\\t_1 = 1,\;\;t_2 = 2,\;\;t_3 = 3\\
so\\
t_n=n$$

integers are whole numbers, positive negative or 0.

3 and 4   

-1 and -2

These are examples of consecutive integers.

Let one of them be x and the other bigger one be x+1

little one + 3*bigger one = 43

becomes

x+3(x+1)=43

now you have to solve it to find the numbers.     

How hard is calculus? I've never done it before.

Because x⁵ = 160x + 128 the sum of the fifth powers of the five roots will be 160*(p+q+r+s+t) + 5*128

Numerically, the p+q+r+s+t seems to be 0 (I used Mathcad's symbolic calculator with 200 significant figures and got a number around 10^-204 for the sum).  If so then the sum p⁵+q⁵+r⁵+s⁵+t⁵ = 5*128 = 640.

I think you've missed a l. What's a two step equation?

if x= 1 then (2*1/7)+4/5, 2/7 + 4/5 = 1.09

if x= 2 then (2*2/7)+4/5, 4/7 + 4/5 = 1.37

if x= 3 then (2*3/7)+4/5, 6/7 + 4/5 = 1.66

if x= 4 then (2*4/7)=4/5, 8/7 + 4/5 = 1.94

etcetra

btw, im sure calculus could take 7 pages to solve some equations, and some many many more pages and much time. 

I think it could be maths using this ... http://en.wikipedia.org/wiki/Aleph_number

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