Answer:
Your answer is 40%
Step-by-step explanation:
It is 20 units between Z and B.
We add 2 more points, and one of them is at the the halfway point of the entire line.(M)
One of them is only 2 units away from B.(N)
That means our line is halved, so from 20/20 possible places a point could go and land in the right area is now 10/20.
Minus 2 from that; to take into count of the N to B, and you have 8/20
8/20 is just 40%
4 yrs
Step-by-step explanation:
Formulae for simple interest is;
A= P (1 + rt) Whereby;
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
15300 = 3200 (1 + 106.5/100 *t)
15300/3200 = 1 + 1.065t
4.78125 – 1 = 1.065t
3.78125 = 1.065t
3.78125/1.065 = t
3.55 = t
Rounded off to the nearest whole number;
= 4
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 :)
The coefficient of x in the equation is 1/(300 grams). Multiply by the reciprocal of that, which is (300 grams).
x = (300 grams)×(2 grams)/(100 grams) = (300×2/100) grams = 6 grams
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This is the way you solve any equation where x is multiplied by some value in the only term on one side of the equal sign.
