a=1.34,
b=[tex]l_n-10\\[/tex], and
the restriction on [tex]l_n\\[/tex] is [tex]l_n\geq 10[/tex].
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The hull speed of a boat is approximated by the function
[tex]v=1.34\sqrt l[/tex],
where l is the hull length in feet and v is the hull speed in knots.
Suppose the Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta. What expression represents the hull speed of the Santa Monica in terms of length, lâ‚™ of the Nina Pinta?
[tex]v_s=a\sqrt b[/tex]
Where a=(...), and b=[tex]l_n+[/tex](...)
What are the restrictions on lâ‚™?
lâ‚™> (...)
What is a knot?
The term "knot" is used to describe the speed of currents and is defined as one nautical mile per hour.
1 nautical mile = 1.15 miles = 1.85 km
1 knot = 1.15 miles per hour = 1.85 kmph
What is hull?
Hull is the body of boat.
How to fill the blanks?
Let
[tex]l_s[/tex] = hull length of Santa Monica
[tex]l_n[/tex] = hull length of Nina Pinta
[tex]v_s[/tex] = speed of Santa Monica
[tex]v_n[/tex] = speed of Nina Pinta
The hull length of Santa Monica is 10 ft shorter than that of Nina Pinta that means [tex]l_s=l_n-10[/tex]
We are given [tex]v=1.34\sqrt l[/tex]
so,
[tex]v_s=1.34\sqrt l_s\\ =1.34\sqrt {ln-10}[/tex]
Note: Santa Monica and Nina Pinta are names of boats.
Hence, we conclude that if  [tex]v_s=a\sqrt b[/tex] then,
a=1.34, and
b= [tex]l_n[/tex]-10, and
[tex]l_n[/tex] has the restriction that [tex]l_n > 10[/tex]
because to have a real value of [tex]v_s[/tex] we need
[tex]l_n-10\geq 0[/tex]
[tex]\implies l_n\geq 10[/tex].
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