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 :)
<span>Solution
m = {-13, -1}</span>
Answer:
y=19/3
Step-by-step explanation:
Answer:
total payment = $563,760
Interest = $383,760
Principal part = $66
Step-by-step explanation:
(a) total payment:
n = 30 years = 360 months
monthly payment = $1,566
Total payment = $1,566 * 360 months = $563,760
(b) interest:
Total payment = $563,760
Principal = $180,000
Total payment = Principal + Interest
Interest = Total payment - Principal
Interest = $563,760 - $180,000 = $383,760
(c) part of first payment applied to the principal:
First payment = $1,566
Principal = $180,000
Interest rate = 10% yearly = 10% / 12 = 0.8333% = 0.008333 monthly
Monthly interest = Principal * Interest rate = $180,000 * 0.008333 = $1,500
Principal part = $1,566 - $1,500 = $66
Hope this helps!
