Answer:
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
Step-by-step explanation:
After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.
This means that the amount of caffeine after t hours is given by:
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.
1 - 0.2722 = 0.7278, thus, 
. We use this to find k.
Then
What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?
We have to find find A(5), as a function of A(0). So
The decay factor is:
1 - 0.8531 = 0.1469
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
4.16 / 5.20 = 1 / x.....4.16 lbs to $ 5.20 = 1 lb to $x
cross multiply because this is a proportion
(4.16)(x) = (5.20)(1)
4.16x = 5.20
x = 5.20 / 4.16
x = 1.25 per lb <==
No because it only works with addition and multiplication
9+(-6-3)=(9-6)-3 is true tho
9-(6-3)=9-(3)=6
(9-6)-3=(3)-3=0
so not equivilent
Answer:
Step-by-step explanation:
(x-1)(x+2)/x^2(x-1)+2(x-1)
(x-1)(x+2)/(x-1)(x^2+2)
(x+2)/(x^2+2)
You need to find the acceleration once the rope starts acting.
For that, first you need the velocity, V, when Karen ends the 2.0 m free fall
V^2 = Vo^2 + 2gd = 0^2 + 2* 9.81m/s^2 * 2.0 m = 39.24 m^2 / s^2 => V = 6.26 m/s
From that point, the rope starts acting with a net force that produces a constant acceleration, modeled as per these values and equation:
Vo = 6.26m/s
Vf = 0
Vf^2 = Vo^2 + 2ad => a = [Vf^2 - Vo^2] / 2d = [0^2 - (6.26 m/s)2 ] /2(1m) = -19.62 m/s^2
That acceleration is due to the difference of the force applied by the rope - the weight of Karen:
Weight of Karen: mg
Weight of karen - Force of the rope = Net force = ma
mg - Force of the rope = ma
Force of the rope = mg - ma = m(g -a) = m [9.81m/s^2 - (-19.62m/s^2) ]= 29.43m
To express it as a multiple of her weight, divide it by her weight (mg = 9.81m) =>
29.43m / 9.81m = 3.0
Answer: 3.0 times.
