Respuesta :
Answer:
27.63 mph
Step-by-step explanation:
First we find the distance, p between the Car and the house using Pythagoras theorem.
[tex]p^2=x^2+y^2\\p^2=7^2+9^2\\p^2=49+81=130\\p=\sqrt{130} miles[/tex]
Taking derivatives of:
[tex]p^2=x^2+y^2\\2p \frac{dp}{dt} =2x \frac{dx}{dt} + 2y \frac{dy}{dt}[/tex]
Since the farmhouse does not move, its speed [tex]\frac{dy}{dt}=0[/tex]
Therefore:
[tex]2*\sqrt{130} *\frac{dp}{dt} =2*7*45 + 2y*0\\2*\sqrt{130} *\frac{dp}{dt}=630\\\frac{dp}{dt}=\frac{630}{2\sqrt{130}}\\\frac{dp}{dt}=27.63 mph[/tex]
The distance between the automobile and the farmhouse is increasing at a rate of 27.63mph.
Answer:
27.63 mph
Step-by-step explanation:
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