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?

Question

Arias

Mathematics

17 June, 23:40

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?

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Faulkner · 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)