Answer:
Converting the equation 
into completing the square method we get: 
Step-by-step explanation:
we are given quadratic equation:
And we need to convert it into completing the square method.
Completing the square method is of form: 
Looking at the given equation
We have a = x
then we have middle term 20x that can be written in form of 2ab So, we have a=x and b=? Multiplying 10 with 2 we get 20 so, we can say that b = 20
So, 20x in form of 2ab can be written as: 2(x)(10)
So, we need to add and subtract (10)^2 on both sides
So, converting the equation into completing the square method we get:
Answer:
The maximum revenue is $900, obtained with 30 people
Step-by-step explanation:
Naturally, the answer should be a number equal or higher than 20, because up to 20 persons, each one pays the same. Lets define a revenue function for x greater than or equal to 20.
f(x) = x*(40-(x-20)) = -x²+60x
Note that f multiplies the number of persons by how much would they pay (here, assuming that there are more than 20).
f is quadratic with negative main coefficient and its maximum value will be reached at the vertex.
The value of the x coordinate of the vertex is -b/2a = -60/-2 = 30
for x = 30, f(x) = 30*(40-(30-20))=30*30=900
So the maximum revenue is $900.
Volume of a cone = (1/3) pi x r^2 x h
Volume of a cylinder = pi x r^2 x h
Volume of the cylinder = pi x 2^2 x 3 = 37.68 cubic inches
Now set the volume for the cone to the volume of the cylinder and solve for the height.
37.68 = (1/3) x pi x r^2 x h
37.68 = (1/3) x pi x 3^2 x h
37.68 = (1/3) x pi x 9 x h
37.68 = 9.42 x h
h = 37.68 / 9.42
h = 4
The height of the cone is 4 cm.
