If you stand on a ship in a calm sea, then your height x (in feet) above sea level is related to the farthest distance y (in miles) that you can see by the equation: y=sqrt (1.5x + (x/5280) ^2) how high up do you have to be to be able to see 10mi?

We are given the relation between the height (in feet) and the distance (in miles) as follows:

y = sqrt (1.5x + (x/5280) ^2).

We want to know the height (x) that makes the distance (y) = 10 miles

So, we will simply substitute in the above equation with y = 10 and calculate x as follows:

10 = sqrt (1.5x + (x/5280) ^2)

we will square both sides to get rid of the root:

100 = 1.5x + (x/5280) ^2

1.5x + (x/5280) ^2 - 100 = 0

(x-66.11475) (x+7986.1147) = zero

either x = 66.11475 feet (accepted solution)

or x = - 7986.1147 feet (rejected solution as no height is in negative)