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 :)
It will take one person for the venues to equal the same amount. This is simply done by multiplying 1 x the per person amount then adding it to the reservation cost.
Answer:
A
Step-by-step explanation:
We know that the growth of a linear function will always be constant. So, that eliminates B and C.
A quadratic function can be a function such as 
, or 
, etc.
An exponential function wouldn't be , it would be 
! Or 
, or 
, etc. Therefore, D is eliminated.
So, the answer is 
and we're done!
Answer: b. 14ft
Step-by-step explanation:
In the rectangle, the opposite sides are equal. The diagonal divides the rectangle into two equal right angle triangles. The diagonal represents the hypotenuse of both right angle triangles. The length and width represents the opposite and adjacent sides of the right angle triangles.
To determine the length, L of the rectangle, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
16² = L² + 7²
256 = L² + 49
L² = 256 - 49 = 207
L = √207
L = 14.38
the closest to the length of this rectangle in feet is
14ft
Answer:
20.94021
Step-by-step explanation:
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