They are traveling at right angles to each other so we can say one is traveling north to south and the other west to east. Then we can say that there positions, y and x are:
y=150-600t x=200-800t
By using the Pythagorean Theorem we can find the distance between these two planes as a function of time:
d^2=y^2+x^2, using y and x from above
d^2=(150-600t)^2+(200-800t)^2
d^2=22500-180000t+360000t^2+40000-320000t+640000t^2
d^2=1000000t^2-500000t+62500
d=√(1000000t^2-500000t+6250)
So the rate of change is the derivative of d
dd/dt=(1/2)(2000000t-500000)/√(1000000t^2-500000t+6250)
dd/dt=(1000000t-250000)/√(1000000t^2-500000t+6250)
So the rate depends upon t and is not a constant, so for the instantaneous rate you would plug in a specific value of t...
...
To find how much time the controller has to change the airplanes flight path, we only need to solve for when d=0, or even d^2=0...
1000000t^2-500000t+62500=0
6250(16t^2-8t+1)=0
6250(16^2-4t-4t+1)=0
6250(4t(4t-1)-1(4t-1))=0
6250(4t-1)(4t-1)=0
6250(4t-1)^2=0
4t-1=0
4t=1
t=1/4 hr
Well technically, the controller has t<1/4 because at t=1/4 impact will occur :)
Answer:
The diagram of the plotting point 
is attached below.
Step-by-step explanation:
Given the points
as
so the point can be visualized as:
Now, we can check the point x = 3.5, and determine the corresponding value y = 2.75 and plot the point at the location (x, y) = (3.5, 2.75)
The diagram of the plotting point is attached below.
Answer:
The system of the equations has no solution; the two lines are parallel.
Step-by-step explanation:
The equations have the same slope. In standard form, this can be seen as the same coefficients for x and y. We will multiply the second equation by -12 to reveal this.
This means the equations are parallel and will never cross. There is no solution.
Answer:
15
Step-by-step explanation:
hope this helps
Answer:
1 to 10 = Pointer Finger
1 to 100 = Ring Finger
1 to 1000 = Ring Finger
Step-by-step explanation:
Every time she counts 10 on her fingers starting from 1 it either lands on her Index Finger or Ring Finger in a pattern of starting first on her index finger for 10 then ending up on her Ring Finger for 20 and 30 the going back to her Index finger for 40 and 50 and so on. Using this you can figure out 100 and 1000.
