Twenty seven is b, not sure about the rest. we learn it different
By completing the square: x²-8x+19 = (x-4)²-16+19 = (x-4)²+3 so minimum point = (4,3)
By calculus: f'(x) = 2x-8. (minimum point occurs when f'(x)=0 therefore)
2x-8 = 0 means x=4 and the corresponding y value is 3.
The minimum value of this function (y) is 3 and this occurs when x = 4.
The equations

and

are really the same, we're just setting
, or
.

So we get

Answer:
The height of right circular cone is h = 15.416 cm
Step-by-step explanation:
The formula used to calculate lateral surface area of right circular cone is: 
where r is radius and h is height.
We are given:
Lateral surface area s = 236.64 cm²
Radius r = 4.75 cm
We need to find height of right circular cone.
Putting values in the formula and finding height:

So, the height of right circular cone is h = 15.416 cm