The hull speed, y, in nautical miles per hour of a sailboat can be found using the formula: y = 1.35√xwhere x is the length in feet of the boat at the surface of the water. Find the length of the boat if it has a speed of 10 nautical miles per hour.
To find the length of the boat, we need to substitute the given speed (10 nautical miles per hour) into the equation and solve for x.
y = 1.35√x
10 = 1.35√x
Divide both sides of the equation by 1.35:
10/1.35 = √x
7.407 = √x
Square both sides of the equation:
(7.407)^2 = x
54.833649 = x
Therefore, the length of the boat is approximately 54.833649 feet.
To find the length of the boat when it has a speed of 10 nautical miles per hour, we can use the given formula:
y = 1.35√x
In this case, we know that y (the hull speed) is 10 nautical miles per hour. Let's substitute this value into the formula:
10 = 1.35√x
To isolate the square root of x on one side of the equation, we can divide both sides of the equation by 1.35:
10/1.35 = √x
Now, we can square both sides of the equation to eliminate the square root:
(10/1.35)^2 = (√x)^2
Simplifying the left side of the equation:
(100/1.8225) = x
Now, we can calculate the value of x:
x ≈ 54.983
Therefore, the length of the boat, x, is approximately 54.983 feet.
To find the length of the boat, we can rearrange the formula and substitute the given speed:
y = 1.35√x
10 = 1.35√x
Divide both sides of the equation by 1.35:
10/1.35 = √x
Simplify the left side of the equation:
7.407 = √x
Square both sides of the equation to eliminate the square root:
(7.407)^2 = (√x)^2
54.76 = x
So, the length of the boat is approximately 54.76 feet.