# simple function problem

• Aug 17th 2007, 09:02 PM
dla
simple function problem
I have just started uni maths and never having done it before I'm having trouble with real simple things (I think)

this is a question from the washington book

one is this:

f(T) = 10.0 + 0.10T + 0.001T^2

t is temperature increases by 10 so f(T + 10)

f(T + 10) = 10 + 0.10(T + 10) + 0.001(T + 10)^2
= 10.0 + 0.10T + 1.0 + 0.001T^2 +0.02T + 0.1

I get how the first half works out but the second bit in bold I have no idea how that is possible, as I said its probably very simple but I've been staring at it for ages and can't figure it out...

Would really appreciate any help
• Aug 17th 2007, 09:22 PM
ticbol
Quote:

Originally Posted by dla

f(T + 10) = 10 + 0.10(T + 10) + 0.001(T + 10)^2
= 10.0 + 0.10T + 1.0 + 0.001T^2 +0.02T + 0.1

I get how the first half works out but the second bit in bold I have no idea how that is possible, as I said its probably very simple but I've been staring at it for ages and can't figure it out...

Would really appreciate any help

:). The book skipped one step.
It should have shown that the (T +10)^2 is expanded to
(T^2 +20T +100).

The book can skip one step, two steps, etc., depending on how it assumes the reader can follow the solution.
• Aug 17th 2007, 09:27 PM
CaptainBlack
Quote:

Originally Posted by dla
I have just started uni maths and never having done it before I'm having trouble with real simple things (I think)

this is a question from the washington book

one is this:

f(T) = 10.0 + 0.10T + 0.001T^2

t is temperature increases by 10 so f(T + 10)

f(T + 10) = 10 + 0.10(T + 10) + 0.001(T + 10)^2
= 10.0 + 0.10T + 1.0 + 0.001T^2 +0.02T + 0.1

I get how the first half works out but the second bit in bold I have no idea how that is possible, as I said its probably very simple but I've been staring at it for ages and can't figure it out...

Would really appreciate any help

What you need to know is that:

$0.001(T + 10)^2=.001(T + 10)(T + 10)$

Now we multiply out the brackets:

$0.001(T + 10)^2=0.001(T + 10)(T + 10)=0.001(T^2+20T+100)$

and now multiply through by the $0.001$:

$0.001(T + 10)^2=0.001(T + 10)(T + 10)=0.001(T^2+20T+100)=0.001T^2+0.02T+0.1$

RonL