and have to show that P lies on C, would I just substitute the numbers in?
2006-11-27 08:40:44 · 9 answers · asked by Andy P 1 in Science & Mathematics ➔ Mathematics
ok
2006-11-27 08:43:12 · answer #1 · answered by mummy to thomas n summer 5 · 0⤊ 0⤋
Yes, do the substitution. As for the presentation...
y=1/3x³-4x²+8x+3
RHS
= (1/3)(3)^3 - 4(3)^2 + 8(3) + 3
= 9 - 36 + 24 + 3
= 0
= LHS (Proven)
So Point P is on the curve.
[Note: RHS - right hand side and LHS is left hand side.]
2006-11-27 10:20:51 · answer #2 · answered by Kemmy 6 · 0⤊ 0⤋
y' = 2x^2 - 2x + 4 y'(3) = 18 - 6 + 4 = 16 so discover x such that 2x^2 - 2x + 4 = 16 => 2x^2 - 2x - 12 = 0 divide with the help of two x^2 - x - 6 = 0 (x - 3)(x + 2) = 0 x = 3 or x = - 2 so Q is (-2 , y(-2)) y(-2) = -16/3 - 4 - 8 - 3 = - 16/3 - 15 = - sixty one/3 so Q is (-2 , -sixty one/3)
2016-11-27 02:14:10 · answer #3 · answered by ? 4 · 0⤊ 0⤋
Substitute x in and find the value of y:
so x = 3 => y = (working) = 0
2006-11-27 08:51:01 · answer #4 · answered by Anonymous · 0⤊ 0⤋
plug in x=3 so that y=9-36+24+3=0
2006-11-27 08:50:31 · answer #5 · answered by ploppytheplopper 1 · 0⤊ 0⤋
y=1/3x³-4x²+8x+3
plug in y=0
1/3x³-4x²+8x+3=0
x^3-12x+24x+9=0
(x-3)(x^2-9x-3)=0
therefore, at y=0,x=3
hence,P(3,0) lies on the curve C
i hope that this helps
2006-11-27 08:54:55 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Yes
0=?1/3* 3^3-4*3^2+8*3+3=9-36+24+3=0
so it is.
2006-11-27 09:29:54 · answer #7 · answered by yupchagee 7 · 0⤊ 0⤋
Yes!!!
3 is substituted in whereever you see an 'x'.
The answer must come to zero '0'.
If it does not come to zero then P (3,0) does not lie on the curve.
2006-11-30 09:15:16 · answer #8 · answered by lenpol7 7 · 0⤊ 0⤋
Yes. That is all it takes.
2006-11-27 08:43:16 · answer #9 · answered by Anonymous · 0⤊ 0⤋