SOLUTION: 0.57060=y+(q^2)/2gy^2)) where q=0.4 g=9.81 need help finding y and the second root of y

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 0.57060=y+(q^2)/2gy^2)) where q=0.4 g=9.81 need help finding y and the second root of y      Log On


   

Question 312066: 0.57060=y+(q^2)/2gy^2))
where q=0.4
g=9.81
need help finding y and the second root of y
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
0.57060=y%2B%28q%5E2%29%2F%282gy%5E2%29
q=0.4
g=9.81
0.57060=y%2B%28%280.4%29%5E2%29%2F%282%289.8%29y%5E2%29
0.57060=y%2B%28%280.4%29%5E2%29%2F%282%289.8%29y%5E2%29
0.57060=y%2B%280.16%29%2F%2819.6y%5E2%29
0.57060=y%2B%280.16%29%2F%2819.6y%5E2%29
11.1837y%5E2=19.6y%5E3%2B0.16
f%28x%29=19.6y%5E3-11.1837y%5E2%2B0.16=0
df%2Fdx=176.4y%5E2-22.3674y
Using Newton's method with a starting value of x0=-0.5, you get
highlight%28x1=-0.10955%29
+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+19.6x%5E3-11.1837x%5E2%2B0.16%29+
Using Newton's method with a starting value of x0=0.5, you get
highlight%28x2=0.542895%29
The final root I did by hand using an Excel spreadsheet,
highlight%28x3=0.13725%29