Wribreeminsl
2021-01-02
Answered

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Suppose the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. 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 mg/L. 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. a. Write an initial value problem that models the mass of the drug in the blood, for $t\text{}\ge \text{}0$ . Solve the initial value problem, and graph both the mass of the drug and the concentration of the drug. c. What is the steady-state mass of the drug in the blood? d. After how many minutes does the drug mass reach 90% of its steady-state level?

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Clelioo

Answered 2021-01-03
Author has **88** answers

Step 1 a) Use stirred tank model with constants

Step 2

b) Solution is given with

Step 3

Graph of concentration of the drug

Step 4

c) From the first graph it is visible that steady state mass of the drug is 2000 mg.

Step 5 c) 90% of steady state level drug mass is 1800. Solve

asked 2021-09-17

The function $y=3.5x+2.8$ represents the cost y (in dollars) of a taxi ride of x miles.

a. Identify the independent and dependent variables.

b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

a. Identify the independent and dependent variables.

b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

asked 2021-09-07

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe.

asked 2021-12-06

Express as a polynomial.

$(4x-5)(2{x}^{2}+3x-7)$

asked 2022-06-05

Need help with a proof concerning zero-free holomorphic functions.

Suppose $f(z)$ is holomorphic and zero-free in a simply connected domain, and that $\mathrm{\exists}g(z)$ for which $f(z)=$ exp$(g(z))$

The question I am answering is the following:

Let $t\ne 0$ be a complex number. Prove that $\mathrm{\exists}h(z)$ holomorphic such that $f(z)=(h(z){)}^{t}$

I see that the idea makes sense, but a nudge in the right direction would be appreciated.

Suppose $f(z)$ is holomorphic and zero-free in a simply connected domain, and that $\mathrm{\exists}g(z)$ for which $f(z)=$ exp$(g(z))$

The question I am answering is the following:

Let $t\ne 0$ be a complex number. Prove that $\mathrm{\exists}h(z)$ holomorphic such that $f(z)=(h(z){)}^{t}$

I see that the idea makes sense, but a nudge in the right direction would be appreciated.

asked 2022-01-29

How do you write y=(-5x)+2 in standard form?

asked 2022-03-02

How do I prove that

$2{b}^{2}-3abc+d{a}^{2}=0$

if the roots of the polynomial

$f\left(x\right)=a{x}^{3}+3b{x}^{2}+3cx+d$

are in arithmetic progression?

if the roots of the polynomial

are in arithmetic progression?

asked 2022-07-06

Let, $\frac{P(x)}{Q(x)}$ and $\frac{M(x)}{N(x)}$ be two rational functions consisting of polynominals $P(x),Q(x),M(x),N(x)$. The polyniminals are defined with respect to variable x. Now, if a rational function is formed by summation of the rational functions, does there exist a general way to evaluate the zeros of $\frac{P(x)}{Q(x)}+\frac{M(x)}{N(x)}$? If yes, where will the zeros of $\frac{P(x)}{Q(x)}$ and $\frac{M(x)}{N(x)}$ map to?

Edit 1: I know that, roots of $P(x)N(x)$ will be union of the roots of P(x) and N(x), and so on so forth for $Q(x)M(x)$. So, few possible roots can be calculated by taking the intersection of the roots of $P(x)N(x)$ and $Q(x)M(x)$. But I am not interested in them, I want solution in general.

Edit 2: What if, $\frac{P(x)}{Q(x)}$ is a Pade approximant of order (m,n)?

Edit 1: I know that, roots of $P(x)N(x)$ will be union of the roots of P(x) and N(x), and so on so forth for $Q(x)M(x)$. So, few possible roots can be calculated by taking the intersection of the roots of $P(x)N(x)$ and $Q(x)M(x)$. But I am not interested in them, I want solution in general.

Edit 2: What if, $\frac{P(x)}{Q(x)}$ is a Pade approximant of order (m,n)?