The <u>correct answer</u> is:
The scale drawing is larger.
Explanation:
A scale for a scale drawing is written as a ratio in the form
(scale size):(actual size).
For example, on a map you may have a scale that says 1 in: 2 mi. This means that 1 inch on the scale is equal to 2 miles on the map.
The scale for this problem is 10 cm: 1 mm. This means that 10 cm on the scale drawing represents 1 mm on the actual object.
10 cm is larger than 1 mm, so the scale drawing is larger.
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,
34 x 17 = 578
they would eat 578 kgs a day
This question can be solved primarily by L'Hospital Rule and the Product Rule.
I) Product Rule and L'Hospital Rule:
II) Product Rule and L'Hospital Rule:
III) Product Rule and L'Hospital Rule:
IV) Product Rule and L'Hospital Rule:
V) Using the Definition of Limit: