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anonymous
 5 years ago
ALKJFSALJF. Two small planes approach an airport, one flying due west at 120mi/hr and the other flying due north at 150mi/hr. Assuming they fly at the same constant elevation, how fast is the distance between the planes changing when the westbound plane is 180mi from the airport and the northbound plane is 225mi from the air port?
anonymous
 5 years ago
ALKJFSALJF. Two small planes approach an airport, one flying due west at 120mi/hr and the other flying due north at 150mi/hr. Assuming they fly at the same constant elevation, how fast is the distance between the planes changing when the westbound plane is 180mi from the airport and the northbound plane is 225mi from the air port?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey, you keep posting problems i can't catch up, which do you want to work on?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha sorry! i'm flustered. whatever you're heart desires to work on is good enough for me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0with these types of problems i always start by drawing the picture, did you do that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me know if youre still here

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, you still there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so what does your picture look like? the question is asking for the rate of change of the distance. so we need an equation for the distance and take the derivative. how can we get an equation for the distance?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i kind of made a triangle between the two planes. i'm use to doing rate of change of distance with a point and equation of a line given

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0triangle sounds good, what kind of triangle

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, so we are given rate of change of the sides of the triangle, so we want an equation for the distance as a function of the sides of the triangle

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0basically we want d = (something with x's and y's), because we know x,y, dx/dt, dy/dt, so if we take the derivative we can find dd/dt

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0say a is 180x and b is 225y then d(ba)/dt=(180)x+(225)y just a guess

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmm, now a and b is what you are using for the sides of the triangle?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i was using x and y for that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so if you want you can take everything i said and substitute a for x and b for y, it's the same thing

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now don't confuse 180,225 and the variables. it's 180 at a certain time, and x (or a), when you don't know what it is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what's a formula for d in terms of a and b

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know the pythagorean theorem?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so what is c here in our problem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait 225^2 + 180^2 =83025 then take the square of that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what does c stand for though

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes that is what c is when a and b are those numbers

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the distance between planes

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so what's the equation for the distance between the planes in terms of a and b

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the distance formula is a^2 + b^2 = c^2 and we want to derive with respect to time: (d/dt)(x^2) + (d/dt)(y^2) = (d/dt)(c^2) (dx/dt)(2x) + (dy/dt)(2y) = (dc/dt)(2c) To clean this up: (dx/dt) = x'; (dt/dt) = y'; and (dc/dt) = c'. x'2x + y'2y = c'2c solve for c': x'2x + y'2y  = c' 2c the twos cancel to give us: x'(x) + y'(y)  = c' c y' = 150; x'=120; and c = whatever you got with the pythag. theorum. x and y values are their current values of x=180; y=225 So lets plug those in: 120(180) + 150(225)  = c' 288.14

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0192mi/hr. i never would have gotten that

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol....(dy/dt) = y' :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0was I right is what I want to know :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha i have to find that out....
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