Hey there! Sign in to join this conversationNew here? Join for free

Indices Watch

Announcements
    • 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???
    Online

    22
    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

    11
    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.
    Online

    22
    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).
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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.