Question

the hull speed of a boat is approximated by the function
$v = 1.34\sqrt{l}$,
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 the length, $l_n$ of the nina pinta?

$v_s = a\sqrt{b}$

where $a = \square$ and $b = l_n \square$

what are the restrictions on $l_n$?

$l_n > \square$

done

Explanation:

Step1: Determine the hull length of Santa Monica

The hull length of Santa Monica, \( l_s \), is 10 ft shorter than that of Nina Pinta (\( l_n \)). So, \( l_s = l_n - 10 \).

Step2: Substitute \( l_s \) into the hull speed formula

The hull speed formula is \( v = 1.34\sqrt{l} \). Substituting \( l = l_s = l_n - 10 \) into the formula, we get the hull speed of Santa Monica, \( v_s = 1.34\sqrt{l_n - 10} \). Comparing with \( v_s = a\sqrt{b} \), we have \( a = 1.34 \) and \( b = l_n - 10 \).

Step3: Determine restrictions on \( l_n \)

For the square root to be defined (in the real - number system), the expression inside the square root must be positive. So, \( l_n - 10>0 \). Solving this inequality for \( l_n \), we add 10 to both sides: \( l_n>10 \).

Answer:

• For \( a \): \( 1.34 \)
• For \( b \): \( l_n - 10 \) (so the operation for \( b \) is subtraction of 10, i.e., \( b = l_n-10 \))
• For the restriction on \( l_n \): \( l_n>10 \)