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 48,273 2,500 67,613 What type of function best models the given data set? A constant B. exponential C. linear D quadratic

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

d. vertex

step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)