Answer:
a. dQ/dt = -kQ
b.
c. k = 0.178
d. Q = 1.063 mg
Step-by-step explanation:
a) Write a differential equation for the quantity Q of hydrocodone bitartrate in the body at time t, in hours, since the drug was fully absorbed.
Let Q be the quantity of drug left in the body.
Since the rate of decrease of the quantity of drug -dQ/dt is directly proportional to the quantity of drug left, Q then
-dQ/dt ∝ Q
-dQ/dt = kQ
dQ/dt = -kQ
This is the required differential equation.
b) Solve your differential equation, assuming that at the patient has just absorbed the full 9 mg dose of the drug.
with t = 0, Q(0) = 9 mg
dQ/dt = -kQ
separating the variables, we have
dQ/Q = -kdt
Integrating we have
∫dQ/Q = ∫-kdt
㏑Q = -kt + c
when t = 0, Q = 9
So,
c) Use the half-life to find the constant of proportionality k.
At half-life, Q = 9/2 = 4.5 mg and t = 3.9 hours
So,
taking natural logarithm of both sides, we have
d) How much of the 9 mg dose is still in the body after 12 hours?
Since k = 0.178,
when t = 12 hours,
Answer: y= -3/2 -5
explanation:
The slope is 3/-2, and it slopes down. making it a negative slope/fraction
And the point is on -5 on the Y axis.
Making the answer y= -3/2-5
Answer: 4m
Step-by-step explanation:
Note : midpoints divide a line into two equal parts.
To calculate the length of SA;
We can consider the large triangle QRS with
Two midpoints :
A on the line QS, QA = 4m ;
and B on the line RS with RB = 3m
Fron the definition of midpoint :
QS = QA + AS
where QA = AS
QS = 2QA = 2AS
Therefore,
QA = QS
4m = 4m
Subtract the 5x to get
3y=-5x+7
Then divide the whole equation by 3 to finally get
Y=-5/3x+ 7/3
Answer:
6cm
Step-by-step explanation:
Given data
Width= 4.6cm
Length= 9cm
Volume= 82.8cm^3
The expression for the volume is given as
V= lwh/3
82.8= 9*4.6*h/3
cross multiply
82.8*3= 9*4.6*h
248.4= 41.4h
h= 248.4/41.4
h= 6cm