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
The diameter of the given pizza would be 27.56 cm. Check below how Middle Term Factors work.
Factorization by Splitting the Middle Term is the method of dividing the middle term into two factors. We know that composite numbers can be expressed as the product of prime numbers. For example, [tex]42 = 2 \times 3 \times 7[/tex]Here, 2, 3, and 7 are the prime factors of 42.
The given function is,
[tex]C=d^2-2d+447[/tex]
As the given cost of the pizza is $12.00 then from the given equation we get,
[tex]d^2-2d+447=1200[/tex]
Now, solving the above by the formula quadratic equation,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Now, applying the obtained equation to the above formula we get,
[tex]d^2-2d+447=1200\\d^2-2d-753=0\\d=\frac{-(-2)\pm2 \sqrt{754} }{2} \\d=1+\sqrt{754}\\ or\ d=1-\sqrt{754}[/tex]
So, the required diameter of the given equation is,
[tex]d=1+\sqrt{754}\\d=27.46 cm[/tex]
Learn more about the topic Middle Term Factor:
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