1. ## Help please! thnk u

I have being doing an old maths test paper to practise and i have done most of it but i am struggling with these last few Q's and i just cnt figure then out! its stressing me out! lol Any help will be much appricated thnx

1) I need to make C the subject of this formula... P= C
_____
C+4

2) We have practised doing algebracic long division, and from x^3+3x+k divided by x-1,it has a reminder of 6. But from this how can i find k?

3)finally, a circle intersepts the line with equation x+y=3 at 2 points, A and B. How can i algebraically find the coordinates of A and B.

and also show that the distance AB is squareroot 162

Thank you!! to everyone that helps!

2. Originally Posted by Chez_
2) We have practised doing algebracic long division, and from x^3+3x+k divided by x-1,it has a reminder of 6. But from this how can i find k?
$\displaystyle f(x) = x^3 + 3x + k$

$\displaystyle f(1) = 6$

$\displaystyle f(1) = 1^3 + 3(1) + k$

$\displaystyle 1 + 3 + k = 6$

$\displaystyle k = 6 - 4 = 2$

Easy as pie

3. Originally Posted by Chez_
1) I need to make C the subject of this formula... P= C
_____
C+4
$\displaystyle P = \frac{C}{C + 4}$

$\displaystyle P(C + 4) = C$

$\displaystyle PC + 4P = C$

$\displaystyle PC - C = -4P$

$\displaystyle (P - 1)C = -4P$

$\displaystyle C = -\frac{4P}{P - 1}$

-Dan

4. Originally Posted by Chez_
3)finally, a circle intersepts the line with equation x+y=3 at 2 points, A and B. How can i algebraically find the coordinates of A and B.

and also show that the distance AB is squareroot 162
We need more information about the circle. Do you have the circle's equation, or do you have the center and radius of the circle?

-Dan

5. Originally Posted by Chez_
I have being doing an old maths test paper to practise and i have done most of it but i am struggling with these last few Q's and i just cnt figure then out! its stressing me out! lol Any help will be much appricated thnx

1) I need to make C the subject of this formula... P= C
_____
C+4
P(C + 4) = C

PC + 4P = C

4P = C - CP

4P = C(1 - P)

$\displaystyle \frac{4P}{1 - P} = C$

Originally Posted by Chez_

3)finally, a circle intersepts the line with equation x+y=3 at 2 points, A and B. How can i algebraically find the coordinates of A and B.

and also show that the distance AB is squareroot 162
Okay, you said the equation is: $\displaystyle x^2 + y^2 = 45$

And we are told that $\displaystyle y = -x + 3$

$\displaystyle x^2 + (-x + 3)^2 = 45$

$\displaystyle x^2 + (x^2 - 6x + 9) = 45$

$\displaystyle 2 x^2 - 6x - 36 = 0$

$\displaystyle x^2 - 3x - 18 = 0$

$\displaystyle (x - 6)(x + 3) = 0$

So x = 6 or x = -3

Set those values back into the circle's equation to find the corresponding y-values.
When you have those, use the distance formula to find the length of AB.

6. Originally Posted by topsquark
$\displaystyle P = \frac{C}{C + 4}$

$\displaystyle P(C + 4) = C$

$\displaystyle PC + 4P = C$

**
$\displaystyle PC - C = 4P$
**

$\displaystyle (P - 1)C = 4P$

$\displaystyle C = \frac{4P}{P - 1}$

-Dan
Topsquark, shouldn't that be a -4P ? (Between the asterisks i put in the quote)

7. Chez, i edited my post above to finish the circle problem.