Indices

Announcements Posted on
How helpful is our apprenticeship zone? Have your say with our short survey 02-12-2016
    • Thread Starter
    Offline

    2
    ReputationRep:
    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???
    Offline

    3
    ReputationRep:
    (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?
    Offline

    3
    ReputationRep:
    (Original post by christinajane)
    x
    For the first: a^n=a \times a^{n-1} essentially by definition.
    For the second think trig identities.
    Offline

    3
    ReputationRep:
    (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).
 
 
 
Write a reply… Reply
Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: April 3, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Today on TSR
Poll
Would you rather have...?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read here first

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.