2The elevation E in feet of a highway x feet along a hill is

2.The elevation E in feet of a highway x feet along a hill is modeled by E(X)=-0.0002x2+500, where, -2000 x 2000. Determine the x-values where the elevation is 338 feet. The x-values where the elevation is 338 are_________

Substitute 338 for E(x) into E(X)=-0.0002x2+500,

Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution (s) is/are y (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. There is no solution

Solution

1)Given equation y^3+y^2=25y+25 .This can be factorised as y^2(y+1)=25(y+1)

(y+1)(y^2-25)=0

(y+1)(y+5)(y-5)=0

So the roots of the given equation are y=-1,-5,1(solutions)

B) E(X)=-0.0002x^2+500,

Given that the elevation is 338 feet ,substituting in the above equation gives.

-0.0002x^2+500=338,

0.0002x^2=162

x^2=810000

x=900,-900(values of x)