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One airplane is approaching an airport from the north at 124 km/hr. A second airplane approaches
from the east at 223 km/hr. Find the rate at which the distance between the planes changes when
the southbound plane is 34 km away from the airport and the westbound plane is 15 km from the
airport.
 one year ago
 one year ago
One airplane is approaching an airport from the north at 124 km/hr. A second airplane approaches from the east at 223 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 34 km away from the airport and the westbound plane is 15 km from the airport.
 one year ago
 one year ago

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backpack799Best ResponseYou've already chosen the best response.0
Think of it as a triangle: one side has a length of 34  124x, and the other side has a length of 15 223x. The distance between them is the hypotenuse of the triangle, while you find using Pythagorean theorem. Now that you have the equation for the distance, derive it, and that's it.
 one year ago

backpack799Best ResponseYou've already chosen the best response.0
*which you can find, bahh typos.
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
\[r^2 = x^2 +y^2\] \[2r \frac{ dr }{ dt} = 2x \frac{ dx}{ dt} + 2y \frac{ dy}{ dt} \] \[ \frac{ dr }{ dt} =\frac{ 1 }{ r} (x \frac{ dx}{ dt} + y \frac{ dy}{ dt} )\]
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
x=15 dx/dt = 223 y= 34 dy/dt = 124 r = sqrt(34^2 + 15^2)
 one year ago
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