Answer:
D. about 5,000 ft
Step-by-step explanation:
Given the equation: f(x)=0.01x^2+x+0.2f(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
\begin{gathered}250000=0.01x^2+x+0.2\\0.01x^2+x+0.2-250000=0\\0.01x^2+x-249999.8=0\end{gathered}
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}x=
2a
−b±
b
2
−4ac
\begin{gathered}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\end{gathered}
The correct option is D
