Answer:
[tex]-11.67 ft^{2}/s[/tex]
Step-by-step explanation:
The area is given by:
[tex]A=\frac{x.y}{2}[/tex]
The rate is given by the derivative of that function:
[tex]\frac{dA}{dt}=\frac{1}{2} *(\frac{dx}{dt} *y + x*\frac{dy}{dt} )[/tex] (1)
From the original question we know that
[tex]\frac{dx}{dt}=10feet[/tex] (2)
We also know the relation between x and y:
[tex]y=\sqrt{5^{2}-x^{2}}[/tex]
If we derive this function and evaluate for x=4feet:
[tex]\frac{dy}{dt} =-\frac{40}{3}[/tex] (3)
Replacing (2) and (3) into (1):
[tex]\frac{dA}{dt}=-\frac{70}{6}=-11.6666[/tex]
