1. ## 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.

2. Hello, Tom!

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

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

The equations would be:

. . . . . . . . . . . $\displaystyle x \:=\:2y$

. . . . . . . . . .$\displaystyle xyz \:=\:200$

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

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 $\displaystyle r \,=\,1+\frac{p}{100}$

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

3. Originally Posted by Tom G
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?

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

RonL

4. Originally Posted by Tom G

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

5. 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?

6. Originally Posted by CaptainBlack
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
Originally Posted by Tom G
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