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:
Dilate, Reflect
Not congruent, dilations are used
Step-by-step explanation:
Dilate the figure by a scale factor of 1/3
Reflecting the resulting shape will map the figure
Step 1: Dilate by 1/3
Step 2: Reflect over the y-axis
Since dilations are used, the figures are not the same, as it changes area and side lengths.
-Chetan K
Answer:
Let x represents the Sara eat pancake and y represents the Phil eat the pancake.
As per the statement:
Phil ate three less than twice as many pancakes as Sara.
"Twice as many pancake as Sara" means 2x
"three less than twice as many pancakes as Sara" means 2x -3
⇒
.....[1]
It is also given that together they combined to eat 15 pancakes.
⇒
.....[2]
Substitute equation [1] into [2] we get;
Combine like terms;
3x-3 =15
Add 3 to both sides we get;
3x = 18
Divide both sides by 3 we get;
x = 6
Substitute the value of x in [1] we get;
y = 2(6)-3 = 12-3 =9
y = 9
Therefore, the pancakes did each eat are;
Sara eat pancake = 6 and Phil eat pancake = 9
