Answer:
diameter of the pizza = 21.88 centimeters
Step-by-step explanation:
Given:
C = d^2 – 2d + 447
where
C = cost of the pizza
d = diameter of the pizza
If the pizza costs $12.00, then what is a reasonable estimate for the diameter of the pizza?
12 = d^2 – 2d + 447
d^2 - 2d = 447 - 12
d^2 - 2d = 435
d^2 - 2d - 435 = 0
Solve the quadratic equation using formula
a = 1
b = -2
c = -435
d = -b +or- √b^2 - 4ac / 2a
= -(-2) +or- √(-2)^2 - (4)(1)(-435) / 2(1)
= 2 +or- √4 - (-1740) / 2
= 2 +or- √4 + 1740 / 2
= 2 +or- √1744 / 2
= 2 +or- 4√109 / 2
= 2/2 +or- 4√109/2
= 1 +or- 2√109
d = 1 + 2√109 or d = 1 - 2√109
= 1 + 2(10.44) or d = 1 - 2(10.44)
= 1 + 20.88 or d = 1 - 20.88
d = 21.88 or -19.88
diameter of the pizza = 21.88 centimeters
Therefore, the estimated diameter of the pizza can not be negative. So, diameter of the pizza = 21.88 cm
