Question

Zachary's cornfields are irrigated in circular regions. Zachary records data on the com production from various irrigated circular regions.
Radius (ft) Bushels of Corn

500

2,705

1,000

10,818

1,500

24,341

2,000

43 273

2,500

67 613

Use the equation f(x) = 0.01x2 + =

A about 3,000 ft

X+0.2 to estimate what radius Zachary would need to irrigate 250.000 bushels of com

B. about 4 875 ft

C. about 3,967 ft

D. about 5,000 ft

Answer 1

Answer:

D. about 5,000 ft

Step-by-step explanation:

Given the equation: $f(x)=0.01x^2+x+0.2$

We want to estimate what radius Zachary would need to irrigate 250,000 bushels of corn.

Substituting f(x)=5000, we have

$250000=0.01x^2+x+0.2\\0.01x^2+x+0.2-250000=0\\0.01x^2+x-249999.8=0$

Using the quadratic formula

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

$a=0.01, b=1, c=-249999.8\\x=\dfrac{-1\pm\sqrt{1^2-4(0.01)(-249999.8)} }{2(0.01)}\\=\dfrac{-1\pm\sqrt{1+9999.992} }{0.02}\\=\dfrac{-1\pm\sqrt{10000.992} }{0.02}\\x\approx \dfrac{-1\pm100 }{0.02}\\x\approx \dfrac{-1+100 }{0.02}\: or\:\dfrac{-1-100 }{0.02}\\\\x\approx4950\: or\: -5050 \\ Therefore x\approx 5000ft$

The correct option is D