A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 60 ft is given by the following.
y= 155-(1/40)(x-50)^2
and the question...?
Find the distance traveled by the kite
I am wondering what rule you are using...
I suspect it is Simpsons Rule, if so do that. That will give you the distance of the path.
see http://answers.yahoo.com/question/index?qid=20101016110803AAKwID9
To solve for the height of the kite above the ground, we need to substitute the values of x into the equation y = 155 - (1/40)(x - 50)^2.
Let's find the height of the kite at x = 0 ft.
Substituting x = 0 into the equation:
y = 155 - (1/40)(0 - 50)^2
y = 155 - (1/40)(-50)^2
y = 155 - (1/40)(2500)
y = 155 - (1/40)(2500)
y = 155 - 62.5
y = 92.5 ft
The height of the kite at x = 0 ft is 92.5 ft.
Now, let's find the height of the kite at x = 60 ft.
Substituting x = 60 into the equation:
y = 155 - (1/40)(60 - 50)^2
y = 155 - (1/40)(10)^2
y = 155 - (1/40)(100)
y = 155 - 2.5
y = 152.5 ft
The height of the kite at x = 60 ft is 152.5 ft.
Therefore, the height of the kite above the ground from x = 0 ft to x = 60 ft is decreasing from 92.5 ft to 152.5 ft.