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:
-14
Step-by-step explanation:
First of all, we know that 5x^2+ ax+7x +5=0 only has one root. That means that b^2 - 4ac=0, and we can use this to find the discriminant, ax + 7x.
Now, if we simplified 5x^2+ ax+7x +5=0, by dividing it all by 5, it would be x^2+(a+7)/5x + 1 = 0.
After, we can plug what we know into the formula, b^2 - 4ac=0. It would be:
(a+7)^2 / 25 - 4 = 0
(a+7)^2 / 25 = 4
(a+7)^2 = 100
Since this is a square root, a+7 can be both negative or positive.
a+7= 10, or a+7 = -10
a=3, or a=-17
The question asks for the sum of a, which is 3 + (-17) = -14
Therefore, the answer is -14.
:) have fun with your rsm problems, assuming you got this from the portal.
Answer:Triangle Inequality Theorem. The sum of the lengths of any two sides of a triangle is greater than the length of the third side
Step-by-step explanation:
First you need to make a multiplier:
1-(12/100) = 0.78
Then you multiply the price by 1.12 to get the final answer;
22 * 0.78 = 17.16
This means it cost $17.16 after the 12% sales tax.
Hope this helps! :)
Answer:
-30
Step-by-step explanation:
-|-30-(10-20)|-|5-(10-15)|=-|-30-(-10)|-|5-(-5)|
=-|-30+10|-|5+5|
=-|-20|-|10|
=-(20)-(10)
= -20-10
= -30
