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:
y =8.7
Step-by-step explanation:
y + 8.5 = 17.2
Subtract 8.5 from each side
y +8.5 -8.5 = 17.2 -8.5
y =8.7
Answer:
3/4
Step-by-step explanation:
The total number of children is 8 and the number of girls is 6. This can be represented as 6/8.
You would then need to simplify...
6/2=3
8/2=4
which which lead you to 3/4!
Volume ratio = 1331/729 which is the cube of the linear scale factor.
To find the linear scale factor, let find the cubic root of the numerator & the denominator:
∛1331 = ∛11³ = 11
& ∛729 = ∛9³ = 9
So the linear scale is 11/9 ==> then the ratio of their surface area will be:
11²/9² ==> 121/81.
Note, if you have a linear scale, then the surface will be the square othis scale & the volume will be the cube of the linear scale
