Complete the square to rewrite y = x2 - 6x + 15 in vertex form. Then state
1 answer:
Since is the square of x and 6x is twice the product between x and 3, the second square must be 3 squared, i.e. 9.
So, if we think of 15 as 9+6, we have
Which is the required vertex form. This form tells us imediately that the vertex is the point (3,6).
Since the leading coefficient is 1, the parabola is facing upwards (it's U shaped), so the vertex is a minimum.
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Answer:
a)
b)
c) the steady state mass of the drug is 2000 mg
d) t ≅ 153.51 minutes
Step-by-step explanation:
From the given information;
At time t= 0
an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500
The inflow rate is 0.06 L/min.
Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.
The objective of the question is to calculate the following :
a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.
From above information given :
Therefore;
with respect to x(0) = 0
b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.
By Using Integration Method:
However; if x(0) = 0 ;
Then
C = -2000
Therefore
c) What is the steady-state mass of the drug in the blood?
the steady-state mass of the drug in the blood when t = infinity
x = 2000 - 0
x = 2000
Thus; the steady state mass of the drug is 2000 mg
d) After how many minutes does the drug mass reach 90% of its stead-state level?
After 90% of its steady state level; the mas of the drug is 90% × 2000
= 0.9 × 2000
= 1800
Hence;
t = 153.5056729
t ≅ 153.51 minutes