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 correct answer is option B and D.
Step-by-step explanation:
A. Shawn owed 40% of his tuition bill, b, after paying $6.00
= 40%of (b-6)
B. The amount donated to the school was 40% more that $6.00.
Amount donated to the school = b
b=6+40% of b
C. The cost for a coat was 40% of the sum of b and $6.00.
= 40%(b+6)
D. Summer paid $6.00 more than 40% of b.
Amount by summer = x
= 40%b+6
Answer:
Just substitue every 't' with -4
Step-by-step explanation:
g(-4) = 3*(-4)*(-4) + 2*(-4) + 1
g(-4) = 64-8+1
g(-4) = 57
The equation of a circumference is 2
r. Since we know that r=17, we plug that into the formula, and get an answer of C. 34
The awnser is 6(4t-3) I hope this helps u
