Answer:
D. about 5,000 ft
Step-by-step explanation:
Given the equation: [tex]f(x)=0.01x^2+x+0.2[/tex]
We want to estimate what radius Zachary would need to irrigate 250,000 bushels of corn.
Substituting f(x)=5000, we have
[tex]250000=0.01x^2+x+0.2\\0.01x^2+x+0.2-250000=0\\0.01x^2+x-249999.8=0[/tex]
Using the quadratic formula
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]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[/tex]
The correct option is D
