Answer:
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
Step-by-step explanation:
From the question we are told that:
Slant height [tex]h=13ft[/tex]
Velocity [tex]v=\frac{dx}{dt}=8[/tex]
Distance [tex]d=12ft[/tex]
Generally the equation for area is mathematically given by
[tex]A=0.5*x*sqrt(169 - x^2)[/tex]
Differentiating
[tex]\frac{da}{dx}=\frac{169-2 x^2}{(2 sqrt(169-x^2))}[/tex]
Multiplying through by dx/dt
[tex]\frac{da}{dx}*\frac{dx}{dt}=\frac{169-2 x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-2x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-(2*12^{2})}{2*\sqrt{(169-12^{2})}}*8[/tex]
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
