Answer:
The speed of planes is 419.31 miles per hours
Explanation:
Given that
[tex]\dfrac{dS}{dt}=-400\ miles/hr[/tex]
S= 10 miles
And we have to find [tex]\dfrac{dx}{dt}[/tex].
From triangle ABC
[tex]AC^2=AB^2+BC^2[/tex]
[tex]S^2=x^2+3^2}[/tex]
by differentiating with respect to time t
[tex]2S\dfrac{dS}{dt}=2x\dfrac{dx}{dt}[/tex]
[tex]S\dfrac{dS}{dt}=x\dfrac{dx}{dt}[/tex]
Now when S=10 miles then
[tex]10^2=x^2+3^2}[/tex]
x= 9.53 miles
So
[tex]S\dfrac{dS}{dt}=x\dfrac{dx}{dt}[/tex]
[tex]10\times (-400)=9.53\times \dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt}=-419.31\ miles/hr[/tex]
So the speed of planes is 419.31 miles per hours
