The hull speed of a boat when given by the function v = 1.34√l, makes the expression represent the speed of Santa Monica, v = a√b, with a = 1.34, and b = ln - 10, where lₙ is the length of the Nina Pinta. The restriction on lₙ is that lₙ > 10.
In the question, we are asked to express the speed of the boat of Santa Monica in terms of the length, lâ‚™ of the Nina Pinta.
We are informed that the function is represented as v = a√b, for the speed of Santa Monica.
We are given that the hull speed of a boat of length l is given as v = 1.34√l.
Comparing, the speed of Santa Monica v = a√b, to the general formula v = 1.34√l, we get:
a = 1.34, and
b = the length of the boat of Santa Monica.
The length of the boat of Santa Monica is 10 ft. shorter than of Nina Pinta.
Thus, b = lâ‚™ - 10, where lâ‚™ is the length of the boat of Nina Pinta.
Since b has to be positive, as the function involves square root over b, lâ‚™ - 10 > 0, or, lâ‚™ > 10, is the restriction on the length of the boat of Nina Pinta.
Thus, the hull speed of a boat when given by the function v = 1.34√l, makes the expression represent the speed of Santa Monica, v = a√b, with a = 1.34, and b = ln - 10, where lₙ is the length of the Nina Pinta. The restriction on lₙ is that lₙ > 10.
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