A cylindrical flower vase has a diameter of 6cm and a volume of 171cm^(3) Determine the height of the vase.

h = 6.05 cm

Step-by-step explanation:

Volume of a cylinder = πr²h

Where,

Pi, π = 3.14

Radius, r = diameter/2 = 6 cm/2

= 3 cm

Height, h = ?

Volume if the cylinder = 171 c ³

Volume of a cylinder = πr²h

171 = 3.14 * 3² * h

171 = 3.14 * 9 * h

171 = 28.26 * h

171 = 28.26h

h = 171/28.26

h = 6.0509554140127

Approximately,

h = 6.05 cm

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this