The golden ratio is a solution to a quadratic equation. a. Find the precise value for Φ by solving Φ2 − Φ − 1 = 0.

b. Which method of solving a quadratic equation did you use? Explain your reasoning.

c. What type of number is Φ? Why can it only be approximated by a decimal value?

Below.

Step-by-step explanation:

a.    Φ^2 − Φ − 1 = 0

Φ2 − Φ = 1

(Φ - 0.5)^2 - 0.25 = 1

(Φ - 0.5)^2 = 1.25

Φ - 0.5 = √(1.25)      (We only take the positive root).

Φ  = 0.5 + √(1.25)

b. I used Completing the square.

c.  Φ is irrational That is it cannot be represented as a fraction a/b and because of this it can only be approximated by a decimal.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

d is the only accurate one

step-by-step explanation: