Answer:
The rate of change of the distance is 14.89.
Explanation:
Given that,
Distance = 145 miles
Speed of car = 42 miles/hr
Distance covered by car = 55 miles
We need to calculate the the rate of change of the distance
According to figure,
Let OA is x, and AB is y.
Now, using Pythagorean theorem
[tex]x^2=y^2+145^2[/tex]
On differentiating
[tex]2x\dfrac{dx}{dt}=2y\dfrac{dy}{dt}[/tex]
[tex]\dfrac{dx}{dt}=\dfrac{y}{x}\dfrac{dy}{dt}[/tex]
[tex]\dfrac{dx}{dt}=\dfrac{55\times42}{\sqrt{55^2+145^2}}[/tex]
[tex]\dfrac{dx}{dt}=14.89\ miles/hr[/tex]
Hence, The rate of change of the distance is 14.89.
