Random Q. for Half yearly study... (1 Viewer)

[-pari-]

[*]A compound interest housing loan for $200 000 is taken over a period of 15 years at 9% p.a.

1. Find the size of the monthly repayments I can do this – no trouble
2. How much interest is paid over the duration of this loan –this is ok too
3. What is the loan outstanding after one year? Answer: $193389.54
4. How much of the loan has been repaid after 1 year? Answer: $6610.63
5. What percentage of the first year’s repayments went towards interest ? answer: 72.8%

[*]give the maximum value of 5 – (x-7)<SUP>2</SUP>[/LIST]Answer says max value is 5 - it’s shown no working. How do you tell straight away that the max value is 5 without solving the equation?
a. for which value of x does it occur?

1. Find the locus of a point P(x,y) which lies above the x-axis so that the sum of its distances to the origin and the x-axis is 2.

Answer: x^2 = -4 (y – 1)

1. For which values of k will the equation: 2x^2 + kx – 43 = 0 have real and distinct roots? Answer: all values of x – I know that real and distinct mean that the discriminant > 0, but I’m a bit confused…

 

[robotguy002]

Hope this isn't too late. Not sure on the first few, last one I can though. I presume the answer is meant to be for all values of k, not x.
For which values of k will the equation: 2x^2 + kx – 43 = 0 have real and distinct roots?

Discriminant > 0 for real and distinct roots
discriminant = b^2-4ac
= k^2 - 4*2*-43 >0
=k^2 + 344 > 0

k^2 is allways going to be positive for all real values of k
therefore k^2 + 344 > 0 for all real values of k.
therefore 2x^2 + kx – 43 = 0 has real, distinct roots for all values of k.

 

[kokodamonkey]

[*]give the maximum value of 5 – (x-7)2[/list]Answer says max value is 5 - it’s shown no working. How do you tell straight away that the max value is 5 without solving the equation?

Just by looking at it... think about it. sub any number as x, it gets squared, which means its always going to be positive. and your taking it away from a number. there forore that number is the biggest it will ever be.. (which is when x = 7)