Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

14th Edition

ISBN: 9780134677972

Author: Barnett

Publisher: PEARSON

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Textbook Question

Chapter 1, Problem 32RE

Graph y = m x + b and y = − 1 m x + b simultaneously in the same coordinate system for b fixed and several different values of m, m ≠ 0 . Describe the apparent relationship between the graphs of the two equations.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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Chapter 1, Problem 31RE

Chapter 1, Problem 33RE

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Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final…

Question 3: A sealed flask at room temperature contains a mixture of neon (Ne) and nitrogen (N2) gases. Ne has a mass of 3.25 g and exerts a pressure of 48.2 torr. . N2 contributes a pressure of 142 torr. • What is the mass of the N2 in the flask? • Atomic mass of Ne = 20.1797 g/mol • Atomic mass of N = 14.0067 g/mol Solution: We will use the Ideal Gas Law to determine the number of moles of each gas and calculate the mass of N2. PV = nRT where: • P = total pressure • V volume of the flask (same for both gases) n = number of moles of gas • R 0.0821 L atm/mol K • T = Room temperature (assume 298 K) Since both gases are in the same flask, their partial pressures correspond to their mole fractions. Step 1: Convert Pressures to Atmospheres 48.2 PNe = 0.0634 atm 760 142 PN2 = = 0.1868 atm 760 Step 2: Determine Moles of Ne nNe = mass molar mass 3.25 nNe 20.1797 nne 0.1611 mol Step 3: Use Partial Pressure Ratio to Find n

Chapter 1 Solutions

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Ch. 1.1 - According to equality property 2, multiplying both...Ch. 1.1 - Replace ? with < or > in each of the following:...Ch. 1.1 - The solution to Example 5B shows the graph of the...Ch. 1.1 - Solve and check: 3x2(2x5)=2(x+3)8 Ch. 1.1 - Solve and check: x+13x4=12 Ch. 1.1 - Matched Problem 3 If a cardboard box has length L,...Ch. 1.1 - Replace each question mark with either < or >....Ch. 1.1 - (A) Write 7,4 as a double inequality and graph....Ch. 1.1 - Solve and graph: 3(x1)5(x+2)5 Ch. 1.1 - Solve and graph: 83x57

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