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:
x>5
Step-by-step explanation:
2x - 7 > 3
Add 7 to both sides
2x - 7 +7 > 3+7
2x > 10
Divide both sides by 2
2x/2 > 10/2
x > 5
I hope this was helpful, please mark as brainliest
The answer would be D) x = 11.
Add 5 to both sides (5x = 50 + 5)
Simplify 50 + 5 to 55 (5x = 55)
Divide both sides by 5 (x = 55/5)
Simplify 55/5 to 11 (x = 11)
Yes it is. It is the only even number that is prime that is multiplied by 1.
Answer:
Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, 6/24, 7/28, 8/32, 9/36, 10/40.
those are the ones i know so far
