christinajane
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Just a couple of basic questions....

I am not sure how they got the extra 1.04 in the second line???

80000 x .04^n-1 = 125000 x 1.04^n - 125000

80000 x 1.04^n-1 = 125000 x 1.04 x 1.04^n-1 -125000


Also different of two squares in this trig question...

cos^4theta - sin^4theta

factorised

(cos^2theta + sin^2theta)(cos^2theta - sin^2theta)

When you expand this wouldnt you be left with cos^4theta - sin^4theta again anyway coz you would at the 2's up?

In the book it says its - cos^2theta - sin^2theta

Just want to make it clear in my head because I thought you added the powers up when you multiply them.... doesn't seem to apply in this case???
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Zacken
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(Original post by christinajane)
Just a couple of basic questions....

I am not sure how they got the extra 1.04 in the second line???

80000 x .04^n-1 = 125000 x 1.04^n - 125000

80000 x 1.04^n-1 = 125000 x 1.04 x 1.04^n-1 -125000[
We have 1.04^n = 1.04^1 \times 1.04^{n-1}. Like you said, when you multiply, you add the powers and 1 + n-1 = n.

What don't you understand about this?
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joostan
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(Original post by christinajane)
x
For the first: a^n=a \times a^{n-1} essentially by definition.
For the second think trig identities.
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Zacken
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(Original post by christinajane)

Also different of two squares in this trig question...

cos^4theta - sin^4theta

factorised

(cos^2theta + sin^2theta)(cos^2theta - sin^2theta)
Yes, this is correct.

When you expand this wouldnt you be left with cos^4theta - sin^4theta again anyway coz you would at the 2's up?
Of course you'd get \cos^4 \theta - \sin^4 \theta again, that's the whole point of factorising, to write something in a factored way, when you expand it, you'd better hope to :dolphin::dolphin::dolphin::dolphin: that you get the same thing again. If not, then something's gone wrong.

If I write x^2 + 2x  +1  = (x+1)^2 then when I expand (x+1)^2 I had better get x^2 + 2x + 1 again...

in the book it says its - cos^2theta - sin^2theta
We have (\cos^2 \theta + \sin^2 \theta)(\cos^2 \theta - \sin^2 \theta). Remember that handy little identity in your formula booklet that tells you \cos^2 \theta + \sin^2 \theta = 1?

This means (\cos^2 \theta + \sin^2 \theta)(\cos^2 \theta - \sin^2 \theta) = (1)(\cos^2 \theta - \sin^2 \theta) = \cos^2 \theta - \sin^2 \theta .


Just want to make it clear in my head because I thought you added the powers up when you multiply them.... doesn't seem to apply in this case???
This is always true. (as long as the bases are the same, obviously).
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