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Chapter 7: Problem 41

For exercises \(41-44\), the formula \(R=\frac{V C}{T}\) describes the flow rate of fluid \(R\) through an intravenous drip. Is the relationship of the given variables a direct variation or an inverse variation? $$ V \text { and } T \text { are constant; the relationship of } R \text { and } C \text {. } $$

Short Answer

Expert verified
Direct variation

Step by step solution

01

Identify Constants

It is given that variables \( V \) and \( T \) are constants.
02

Rewrite the Formula

Rewrite the formula \( R = \frac{V C}{T} \) to show the relationship between \( R \) and \( C \). Since \( V \) and \( T \) are constants, let's denote them as \( k = \frac{V}{T} \).
03

Substitute Constants

Substitute \( k \) into the formula: \( R = kC \).
04

Identify the Variation Type

The equation \( R = kC \) indicates a direct variation because \( R \) changes directly with \( C \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fluid flow rate
The fluid flow rate, represented by the variable \(R\), refers to how quickly fluid passes through a system or apparatus. In medical contexts, it is crucial to regulate the flow rate of intravenous (IV) fluids accurately. The formula \(R = \frac{VC}{T}\) allows healthcare professionals to calculate this rate.
Here:
  • \(R\): Flow rate of the fluid
  • \(V\): Volume of the fluid
  • \(C\): Concentration of the solution
  • \(T\): Time to deliver the volume
Accurate calculation and control of fluid flow rates ensure that patients receive the correct dosage of medication, avoiding potential complications.
intravenous drip formula
The intravenous drip formula is given by \(R = \frac{VC}{T}\). This formula helps in determining the rate at which fluid needs to be administered intravenously. It combines several factors:
  • Volume of the fluid (\(V\))
  • Concentration of the fluid (\(C\))
  • Time period (\(T\))
By keeping the volume and time constant, and varying the concentration, professionals can directly understand the effects on the flow rate. For example, doubling the concentration (\(C\)) will double the flow rate (\(R\)). This makes the formula immensely useful in healthcare to ensure fluid delivery meets medical needs.
constant variables
In the formula \(R = \frac{VC}{T}\), the variables \(V\) (Volume) and \(T\) (Time) are constant. Constants are values that do not change during the process of calculation. By identifying and using constant variables:
  • \

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Most popular questions from this chapter

For exercises 61-64, the completed problem has one mistake. (a) Describe the mistake in words or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: The relationship of the number of weeks a box of garbage bags is used, \(x\), and the number of bags left in the box, \(y\), is an inverse variation. When \(x\) is 8 weeks, \(y\) is 168 bags. Find the constant of proportionality, \(k\). Incorrect Answer: \(k=\frac{y}{x}\) $$ k=\frac{168 \text { bags }}{8 \text { weeks }} $$

When the radiation is constant, the relationship of the current in an X-ray tube, \(x\), and the exposure time, \(y\), is an inverse variation. When the current is 600 milliamp, the exposure time is \(0.2 \mathrm{~s}\). Write an equation that represents this variation. Include the units.

The relationship of the taxable value of a property, \(x\), and the annual property tax, \(y\), is a direct variation. When the taxable value of a property is \(\$ 250,000\), the annual property tax bill is \(\$ 5375\). a. Find the constant of proportionality, \(k\). b. Write an equation that represents this relationship. c. Find the taxable value of a property with an annual property tax bill of \(\$ 8062.50\). d. Find the tax owed for a property with an assessed value of \(\$ 185,000\). Round to the nearest whole number. e. What does \(k\) represent in this equation?

For exercises 1-10, (a) solve. (b) check. $$ \frac{3}{5} x-\frac{1}{4}=\frac{9}{10} $$

If both sides of the equation \(\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\) are multiplied by \(x(x-1)\), the simplified equation is \(1 x+2(x-1)=x^{2}\). Rewriting in standard form and factoring, the equation is \((x-2)(x-1)=0\) and its solutions are \(x=1\) or \(x=2\). Explain why the solution \(x=1\) is extraneous.
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