Find y as a function of t if y" + 14y' + 85y = 0, y(0) = 9, y'(0) = 8. y(t) =

Step-by-step explanation:

The Given diffrential equation can be written as follows

Solving the auxiliary equation we get

Comparing with the standard quadratic equation we get

Using the values we get the roots as

The roots are imaginary and conjugate

For a auxillary equation with roots the solution is given by

Applying values we get the solution of the equation as

....................(i)

here are constants whose values shall be obtained using the given boundary conditions y(0) = 9 ; y'(0) = 8

In equation i putting x = 0 we get

9 =

Now we have

Now y'(0) = 8

Thus we get

Solving for we get

Thus the solution becomes

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

step-by-step explanation:

what grade level is this? need to know so i can look in my old textbooks!