Question

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?

Answer 1

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)