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, lₙ of the Nina Pinta?
[tex]v_s=a\sqrt b[/tex]
Where a=(...), and b=[tex]l_n+[/tex](...)
What are the restrictions on lₙ?
lₙ> (...)
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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