Question

The path of water from a hose on a fire tugboat can be approximated by the equation y=-0.0055x^2 +1.15x + 5, where y is the height above the ocean and x is the distance from the tugboat. When the water is 6 ft above the ocean how far is it from the tugboat

Answer 1

The water is 208.22ft from the tug boat

Explanation:

The governing equation is
`y=-0.0055x^2 +1.15x + 5`

y is the height above the ocean

x is the distance from the tugboat

if y= 6ft, the equation will now become

`6=-0.0055x^2 +1.15x + 5`

we can arrange this properly to form a quadratic equation by grouping like terms.

`-0.0055x^2 +1.15x -1=0`

solving quadratically we have two values of x as 208.22ft and 0.873 ft.

We can take a more realistic value as a solution to our problems:

208.22ft