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Math Help - Numerical Methods

  1. #1
    Newbie Tom G's Avatar
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    Numerical Methods

    I'm struggling with these two qusetions and would appreciate some help.

    7. The dimensions of a cuboid are X x Y x Z, where X is length, Y is width and Z is height. The Volume of the cubiod is 200cm3 and its length is twice its width.

    a/Write down 3 equations involving X,Y and Z.
    I've got these equations, can someone check that i have the correct answers please. 2Y=X , 3YZ=200 , 2ZY+2XY+2ZX=240.


    I have no idea how to do this question so any help will be appreciated.

    8. £1,000 is invested in a bank account on 1st Jan 1994. A further £1,000 pounds is invested at the start of each year, the final pament was on 1st Jan 2003. When the account was closed on 1st Jan 2004 it was worth £15,000.

    a/ Annual interest rate is p% and r=1+p/100. Show that r + r2 + ...+ 16r = 15

    Thanks.
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  2. #2
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    Hello, Tom!

    7. The dimensions of a cuboid are: x (length), y (width), z (height).
    The Volume of the cubiod is 200 cm³ and its length is twice its width.

    a) Write down 3 equations involving x,\,y,\,z.
    You left out a fact: .The total surface area is 240 cm².


    The equations would be:

    . . . . . . . . . . . x \:=\:2y

    . . . . . . . . . . xyz \:=\:200

    . . 2xy + 2yz + 2xz \:=\:240



    8. £1,000 is invested in a bank account on 1st Jan 1994.
    A further £1,000 is invested at the start of each year.
    The final pament was on 1st Jan 2003.
    When the account was closed on 1st Jan 2004 it was worth £15,000.

    a) Annual interest rate is p% and r \,=\,1+\frac{p}{100}

    Show that: . r + r^2 + \cdots + {\color{blue}16r} \:= \:15
    . . . . . . . . . . . . . . . . . .?
    That equation is wrong . . . Please check the original problem.

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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Tom G View Post
    I'm struggling with these two qusetions and would appreciate some help.

    7. The dimensions of a cuboid are X x Y x Z, where X is length, Y is width and Z is height. The Volume of the cubiod is 200cm3 and its length is twice its width.

    a/Write down 3 equations involving X,Y and Z.
    I've got these equations, can someone check that i have the correct answers please. 2Y=X , 3YZ=200 , 2ZY+2XY+2ZX=240.
    where does 3YZ=200 come from?

    2Y=X,\ XYZ=200,\ 2Y^2Z=200

    RonL
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Tom G View Post

    8. £1,000 is invested in a bank account on 1st Jan 1994. A further £1,000 pounds is invested at the start of each year, the final pament was on 1st Jan 2003. When the account was closed on 1st Jan 2004 it was worth £15,000.

    a/ Annual interest rate is p% and r=1+p/100. Show that r + r2 + ...+ 16r = 15

    Thanks.
    I don't know what you intend "r + r2 + ...+ 16r = 15" to mean but:

    1st Jan 94 the balance is: B(94) = 1000
    1st Jan 95 the balance is: B(95) = 1000 + rB(94) = (1+r)1000
    1st Jan 96 the balance is: B(96) = 1000 + rB(95) = (1 + r + r^2)1000

    :
    :

    1st Jan 03 the balance is: B(03) = 1000 + rB(02) = (1 + r + r^2 + .. + r^9)1000

    1st Jan 04 the balance is: B(04) = rB(03)

    RonL
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  5. #5
    Newbie Tom G's Avatar
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    Sorry, I made a mistake on question 8.

    the correct question is:

    A man invested £1000 into a high interest bank account on 1st Jan 1994. He puts £1000 into this account at the beginning of each year - his final payment was on 1st January 2003. He closed the Account on 1st Jan 2004 when it was worth £15000.

    a/ If the annual rate of interest is p% and r = 1 + p/100 then show that
    r + r2 + ... + r10 = 15.

    I'm really confused, especially as the interest rate is not given - is there enough information to solve?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by CaptainBlack View Post
    I don't know what you intend "r + r2 + ...+ 16r = 15" to mean but:

    1st Jan 94 the balance is: B(94) = 1000
    1st Jan 95 the balance is: B(95) = 1000 + rB(94) = (1+r)1000
    1st Jan 96 the balance is: B(96) = 1000 + rB(95) = (1 + r + r^2)1000

    :
    :

    1st Jan 03 the balance is: B(03) = 1000 + rB(02) = (1 + r + r^2 + .. + r^9)1000

    1st Jan 04 the balance is: B(04) = rB(03)

    RonL
    Quote Originally Posted by Tom G View Post
    Sorry, I made a mistake on question 8.

    the correct question is:

    A man invested £1000 into a high interest bank account on 1st Jan 1994. He puts £1000 into this account at the beginning of each year - his final payment was on 1st January 2003. He closed the Account on 1st Jan 2004 when it was worth £15000.

    a/ If the annual rate of interest is p% and r = 1 + p/100 then show that
    r + r2 + ... + r10 = 15.

    I'm really confused, especially as the interest rate is not given - is there enough information to solve?
    So going back to what I wrote you get the equation:

    B(04)= 15000 = (r + r^2 + ... + r^10) 1000,

    which on rearrangement gives the required answer.

    RonL
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