The axis of symmetry can be found by finding the average of the zeros, a derivation from the conservation of energy :P, or by finding the point when the velocity is equal to zero.
df/dx=-6x+12 so df/dx, velocity, equals zero when:
-6x+12=0
6x=12
x=2 so the axis of symmetry is the vertical line x=2
....
average of zeros...
3x^2-12x+6=0
x^2-4x+2=0
x^2-4x=-2
x^2-4x+4=2
(x-2)^2=2
x-2=±√2
x=2±√2 so the average of the zeros is obviously 2.
....
conservation of energy
vf-vi=at When vf=0, this is the maximum value for f(x)...
-vi=at, vi=b and a(acceleration)=2a(from quadratic) and t=x
-b=2ax
x=-b/(2a) in this case
x=-12/(2(-3))
x=-12/-6
x=2
Answer:
(-3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.
1) Volume = area * height => height = volume / area
2)
x^4 + 4x^3 + 3x^2 + 8x + 4
height = --------------------------------------
x^3 + 3x^2 + 8
That division is not exact
The result of this division is x + 1 plus a residue of - 8x^2 + 8x - 4.
It was expected an exact division, so likely some of the terms is not properly written. Now you know the procedure and can perform it with the right terms.
