3. Furnace repair bills are normally distributed with a mean of 269 dollars and a standard

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

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 :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

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

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

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;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

2 years ago

What is the relation between the sine and cosine values of angles in each quadrant? How would you use the 60° angle to find sine

Masja [62]

<span>The sine, cosine, and tangent of 60 deg. is the same as 120, 240, and 300. 30 deg, 45 deg, and 60 deg. can each be matched to other counter parts across the quadrants. The only ones that have their own sin, cos, and tan are 90, 180, 270, and 360. The pi over 4 is a radian and can be found using an equation= π/4*180/π The two πs will cancel out and you are left with 180/4 which will give you the degrees. You would do the same equation for the π/6. This can also be used in reverse and you can find the radian using the degrees. Just multiply the degrees by pi/180 and then find a common multiple to reduce the fraction/radian down. pi will stay in your answe</span>

3 0

2 years ago

Determine whether the value given below is from a discrete or continuous data set. The volume of cola in a can is 11.1 oz. nothi

mars1129 [50]

Answer:

The given variable is a continuous variable.

Step-by-step explanation:

We are given the following variable in the question:

Variable: "The volume of cola in a can is 11.1 oz"

Discrete variable:

These can be expressed in whole numbers and cannot take value in decimals
They are counted not measured.
They cannot take any value within an interval.

Continuous Variable:

These can be expressed in decimal numbers.
They are measured not counted.
They can take any value within an interval.

Thus, the given variable which is volume is measured and can tale any value within an interval.

Thus, it is a continuous variable.

3 0

2 years ago

Give an example of a 2x2 matrix whose determinant is 13.

elixir [45]

<span>If all your entries are integers, the determinant is also an integer.
</span>For this problem, 1 0
0 13

For this question, you should just fix 3 values and make the 4th value an unknown and solve it.
I hope my answer helped you somehow.

5 0

2 years ago

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paper clips are sold in boxes of 1000. each box costs £15.40. ethan orders 5 boxes of paper clips. work out the discount ethan g

torisob [31]

Step-by-step explanation:

Total money = 15.40 × 5 = 77

Ethan gets 5 boxes for 77

4 0

2 years ago

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