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mathematics
college mathematics for business
College Mathematics For Business Economics, Life Sciences, And Social Sciences 14th Edition Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker - Solutions
In Problem find the indicated function f of a single variable.f(y) = K(4, y) for K(x, y) = 10xy + 3x - 2y + 8
In Problem M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means.M(22, 40)
In Problem use Theorem 2 to find the local extrema.f(x, y) = xey + xy + 1 THEOREM 2 Second-Derivative Test for Local Extrema If 1. z = f(x, y) 2. fx(a, b) = 0 and f(a, b) = 0 [(a, b) is a critical point] 3. All second-order partial derivatives of fexist in some circular region containing (a, b) as
In Problem evaluate each integral. Graph the region of integration, reverse the order of integration, and then evaluate the integral with the order reversed. 1-x SfxVy dy dx
In Problem M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means.M(32, 50)
In Problem find the volume of the solid under the graph of each function over the given rectangle. f(x, y) = 2x² - y²; R = {(x, y) |0 ≤x≤ 1, 0≤ y ≤ 1}
In Problem use Theorem 2 to find the local extrema.f(x, y) = y ln x + 3xy THEOREM 2 Second-Derivative Test for Local Extrema If 1. z = f(x, y) 2. fx(a, b) = 0 and f(a, b) = 0 [(a, b) is a critical point] 3. All second-order partial derivatives of fexist in some circular region containing (a, b) as
In Problem evaluate each integral. Graph the region of integration, reverse the order of integration, and then evaluate the integral with the order reversed. 4x (1 + 2y) dy dx
In Problem find the volume of the solid under the graph of each function over the given rectangle. f(x, y) = 5x; R = {(x, y) |0 ≤ x ≤ 5, 0≤ y ≤ 5}
In Problem find the indicated function f of a single variable.f(y) = M(y, y) for M(x, y) = x2y - 3xy2 + 5
In Problem M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means.M(22, 50)
The global land–ocean temperature index, which measures the change in global surface temperature (in °C) relative to 1951–1980 average temperatures, is given in the table for the years 1955 through 2015.(A) Find the least-squares line for the data using x = 0 for 1950.(B) Use the least-squares
In Problem evaluate each integral. Graph the region of integration, reverse the order of integration, and then evaluate the integral with the order reversed. √x/2 Sox dy dx 0Jx/4
In Problem find the volume of the solid under the graph of each function over the given rectangle. f(x, y) = 4 - y²; R = {(x, y) |0 ≤ x ≤ 2, 0 ≤ y ≤ 2}
In Problem M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means.Mx(32, 50)
Three pens of the same size are to be built along an existing fence (see the figure). If 400 feet of fencing is available, what length should x and y be to produce the maximum total area? What is the maximum area? X Existing fence X
Data on U.S. organic food sales (in billions of dollars) are given in the table for the years 2005 through 2015.(A) Find the least-squares line for the data using x = 0 for 2000.(B) Use the least-squares line to estimate U.S. organic food sales in 2025. U.S. Organic Food
In Problem evaluate each integral. Graph the region of integration, reverse the order of integration, and then evaluate the integral with the order reversed. 2Vy Sov (1 + 2xy) dx dy 0 Jy²/4
In Problem find the volume of the solid under the graph of each function over the given rectangle. f(x, y) = e¯¯³; R = {(x, y) |0 ≤ x ≤ 1, 0≤ y ≤ 1}
Find a formula for the function D(x, y) of two variables that gives the square of the distance from the point (x, y) to the origin (0, 0).
In Problem M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means.My (32, 50)
In Problem find the volume of the solid under the graph of f (x, y) over the region R bounded by the graphs of the indicated equations. Sketch the region R; the solid does not have to be sketched. f(x, y) = 4 - x - y; R is the region bounded by the graphs of x + y = 4, y = 0, x = 0
Evaluate each double integral in Problem Select the order of integration carefully; each problem is easy to do one way and difficult the other. [[x em đội xey dA; R = {(x, y) |0 ≤ x ≤ 1, 1 ≤ y ≤ 2} R
Find a formula for the function V(d, h) of two variables that gives the volume of a right circular cylinder of diameter d and height h.
In Problem find the indicated second-order partial derivative for each function f(x, y).fxx(x, y) if f(x, y) = 6x - 5y + 3
In Problem find the volume of the solid under the graph of f (x, y) over the region R bounded by the graphs of the indicated equations. Sketch the region R; the solid does not have to be sketched. f(x, y) = (x - y)²; R is the region bounded by the graphs of y = x, y = 2, x = 0
Find a formula for the function C(n, w) of two variables that gives the number of calories in n cookies, each weighing w ounces, if there are 35 calories per ounce.
In Problem find the volume of the solid under the graph of f (x, y) over the region R bounded by the graphs of the indicated equations. Sketch the region R; the solid does not have to be sketched. f(x, y) = 4; R is the region bounded by the graphs of y = 1x² and y = 0 for 0 ≤ x ≤ 1
In Problem find the indicated second-order partial derivative for each function f(x, y).fyx(x, y) if f(x, y) = -2x + y + 8
Evaluate each double integral in Problem Select the order of integration carefully; each problem is easy to do one way and difficult the other. J 2y + 3xy² 1 + x² -dA; R R = {(x, y) |0 ≤x≤1, −1≤y≤ 1}
Find a formula for the function N(p, r) of two variables that gives the number of hot dogs sold at a baseball game, if p is the price per hot dog and r is the total amount received from the sale of hot dogs.
In Problem find the volume of the solid under the graph of f (x, y) over the region R bounded by the graphs of the indicated equations. Sketch the region R; the solid does not have to be sketched. f(x, y) y = V1 4xy; R is the region bounded by the graphs of = x² and y = 0 for 0 ≤ x ≤ 1 -
In Problem find the indicated second-order partial derivative for each function f(x, y).fxy(x, y) if f(x, y) = 4x2 + 6y2 - 10
A firm produces two types of earphones per year: x thousand of type A and y thousand of type B. If the revenue and cost equations for the year are (in millions of dollars)R(x, y) = 2x + 3yC(x, y) = x2 - 2xy + 2y2 + 6x - 9y + 5determine how many of each type of earphone should be produced per year
A store sells two brands of camping chairs. The store pays $60 for each brand A chair and $80 for each brand B chair. The research department has estimated the weekly demand equations for these two competitive products to bewhere p is the selling price for brand A and q is the selling price for
Find a formula for the function S(x, y, z) of three variables that gives the average of three test scores x, y, and z.
In Problem find the indicated second-order partial derivative for each function f(x, y).fyy(x, y) if f(x, y) = x2 + 9y2 - 4
In Problem reverse the order of integration for each integral. Evaluate the integral with the order reversed. Do not attempt to evaluate the integral in the original form. S. 0 4 4x 1 + y² 2 dy dx
Find a formula for the function W(x1, x2, x3, x4) of four variables that gives the total volume of oil that can be carried in four oil tankers of capacities x1, x2, x3, and x4, respectively.
In Problem reverse the order of integration for each integral. Evaluate the integral with the order reversed. Do not attempt to evaluate the integral in the original form. S. S V1-x² dx dy
In Problem find the indicated second-order partial derivative for each function f(x, y).fxy(x, y) if f(x, y) = exy2
Find a formula for the function L(d, h) of two variables that gives the volume of a right circular cone of diameter d and height h.
In Problem find the indicated second-order partial derivative for each function f(x, y). fxx(x, y) if f(x, y) = 3 ln x 2 y²
In Problem find the indicated second-order partial derivative for each function f(x, y). fyy(x, y) if f(x, y) In x y
In Problem find the indicated second-order partial derivative for each function f(x, y).fyx(x, y) if f(x, y) = e3x + 2y
In Problem reverse the order of integration for each integral. Evaluate the integral with the order reversed. Do not attempt to evaluate the integral in the original form. 0 1 y2 4ye dx dy
Find a formula for the function T(x, y, z) of three variables that gives the square of the distance from the point (x, y, z) to the origin (0, 0, 0).
In Problem reverse the order of integration for each integral. Evaluate the integral with the order reversed. Do not attempt to evaluate the integral in the original form. 2 VF √3x + y² dy dx
In Problem use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate the indicated integral correct to
Suppose that Congress enacts a onetime- only 10% tax rebate that is expected to infuse $y billion, 5 ≤ y ≤ 7, into the economy. If every person and every corporation is expected to spend a proportion x, 0.6 ≤ x ≤ 0.8, of each dollar received, then, by the multiplier principle in economics,
Find a formula for the function K(C, h) of two variables that gives the volume of a right circular cone of circumference C and height h.
In Problem use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate the indicated integral correct to
In Problem find the indicated second-order partial derivative for each function f(x, y).fxx(x, y) if f(x, y) = (2x + y)5
Let F(x, y) = 2x + 3y - 6. Find all values of y such that F(0, y) = 0.
In Problem find the indicated second-order partial derivative for each function f(x, y).fyx(x, y) if f(x, y) = (3x - 8y)6
In Problem use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate the indicated integral correct to
Let F(x, y) = 5x - 4y + 12. Find all values of x such that F(x, 0) = 0.
In Problem find the indicated second-order partial derivative for each function f(x, y).fxy(x, y) if f(x, y) = (x2 + y4)10
In Problem use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate the indicated integral correct to
If an industry invests x thousand labor-hours, 10 ≤ x ≤ 20, and $y million, 1 ≤ y ≤ 2, in the production of N thousand units of a certain item, then N is given byN(x, y) = x0.75y0.25What is the average number of units produced for the indicated ranges of x and y? Set up a double integral
Let F(x, y) = 2xy + 3x - 4y - 1. Find all values of x such that F(x, x) = 0.
In Problem find the indicated second-order partial derivative for each function f(x, y).fyy(x, y) if f(x, y) = (1 + 2xy2)8
In Problem use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate the indicated integral correct to
Let F(x, y) = xy + 2x2 + y2 - 25. Find all values of y such that F(y, y) = 0.
In order to study the population distribution of a certain species of insect, a biologist has constructed an artificial habitat in the shape of a rectangle 16 feet long and 12 feet wide. The only food available to the insects in this habitat is located at its center. The biologist has determined
Let F(x, y) = x2 + exy - y2. Find all values of x such that F(x, 2) = 0.
For the function f(x, y) = x2 + 2y2, find f(x + h,y)-f(x, y) h
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cx (x, y)
In Problem use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate the indicated integral correct to
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cy (x, y)
A heavy industrial plant located in the center of a small town emits particulate matter into the atmosphere. Suppose that the concentration of fine particulate matter (in micrograms per cubic meter) at a point d miles from the plant (see the figure) is given byC = 50 - 9d2If the boundaries of the
For the function f(x, y) = 2xy2, find f(x + h,y)-f(x, y) h
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cx (3, -2)
The floor of a glass-enclosed atrium at a football stadium is the region bounded by y = 0 and y = 100 - 0.01x2. The ceiling lies on the graph of f(x, y) = 90 - 0.5x. (Each unit on the x, y, and z axes represents one foot.) Find the volume of the atrium (in cubic feet).
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cy (3, -2)
The average value of a function f(x, y) over a regular region R is defined to beUse this definition of average value in ProblemAn industrial plant is located on the lakefront of a city. Let (0, 0) be the coordinates of the plant. The city's residents live in the region R bounded by y = 0 and y = 10
The floor of an art museum gallery is the region bounded by x = 0, x = 40, y = 0, and y = 50 - 0.3x. The ceiling lies on the graph of f(x, y) = 25 - 0.125x. (Each unit on the x, y, and z axes represents one foot.) Find the volume of the atrium (in cubic feet).
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cxx (x, y)
The intelligence quotient Q for a person with mental age x and chronological age y is given byIn a group of sixth-graders, the mental age varies between 8 and 16 years and the chronological age varies between 10 and 12 years. What is the average intelligence quotient for this group? Set up a double
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cyy (x, y)
The floor of a concert hall is the region bounded by x = 0 and x = 100 - 0.04y2. The ceiling lies on the graph of f(x, y) = 50 - 0.0025x2. (Each unit on the x, y, and z axes represents one foot.) Find the volume of the concert hall (in cubic feet).
In Problem use a graphing calculator as necessary to explore the graphs of the indicated cross sections.(A) Explain why the cross sections of the surface z = f(x, y) produced by cutting it with planes parallel to x = 0 are semicircles of radius 2.(B) Describe the cross sections of the surface in
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cxy (x, y)
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cyx (x, y)
In Problem use a graphing calculator as necessary to explore the graphs of the indicated cross sections.Let f(x, y) = x2.(A) Explain why the cross sections of the surface z = f(x, y) produced by cutting it with planes parallel to y = 0 are parabolas.(B) Describe the cross sections of the surface in
In Problem use a graphing calculator as necessary to explore the graphs of the indicated cross sections.(A) Describe the cross sections of the surface z = f(x, y) produced by cutting it with the planes y = 1, y = 2, y = 3, y = 4, and y = 5.(B) Describe the cross sections of the surface in the
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cxx (3, -2)
In Problem use a graphing calculator as necessary to explore the graphs of the indicated cross sections.(A) Explain why f(a, b) = f(c, d) whenever (a, b) and (c, d) are points on the same circle with center at the origin in the xy plane.(B) Describe the cross sections of the surface z = f(x, y)
In Problem find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.Cyy (3, -2)
In Problem S (T, r) = 50 (T - 40) (5 - r) gives an ice cream shop’s daily sales as a function of temperature T (in °F) and rain r (in inches). Find the indicated quantity (include the appropriate units) and explain what it means.S(60, 2)
In Problem use a graphing calculator as necessary to explore the graphs of the indicated cross sections.Let f(x, y) = 100 + 10x + 25y - x2 - 5y2.(A) Describe the cross sections of the surface z = f(x, y) produced by cutting it with the planes y = 0, y = 1, y = 2, and y = 3.(B) Describe the cross
In Problem S (T, r) = 50 (T - 40) (5 - r) gives an ice cream shop’s daily sales as a function of temperature T (in °F) and rain r (in inches). Find the indicated quantity (include the appropriate units) and explain what it means.S(80, 0)
In Problem use a graphing calculator as necessary to explore the graphs of the indicated cross sections.Let f(x, y) = e-(x2 + y2).(A) Explain why f(a, b) = f(c, d) whenever (a, b) and (c, d) are points on the same circle centered at the origin in the xy plane.(B) Describe the cross sections of the
At the end of each year, $5,000 is invested into an IRA earning 3% compounded annually.(A) How much will be in the account at the end of 30 years? Use the annuity formulawhereP = periodic paymenti = rate per periodn = number of payments (periods)F = FV = future value(B) Use graphical approximation
For a diver using scuba-diving gear, a marine biologist estimates the time (duration) of a dive according to the equationwhereT = time of dive in minutesV = volume of air, at sea level pressure, compressed into tanksx = depth of dive in feetFind T(70, 47) and T(60, 27). T(V,x) 33V x + 33
A small manufacturing company produces two models of a surfboard: a standard model and a competition model. If the standard model is produced at a variable cost of $210 each and the competition model at a variable cost of $300 each, and if the total fixed costs per month are $6,000, then the
In Problem find fxx (x, y), fxy (x, y), fyx (x, y), and fyy (x, y) for each function f. f(x, y) X y y X
In Problem S (T, r) = 50 (T - 40) (5 - r) gives an ice cream shop’s daily sales as a function of temperature T (in °F) and rain r (in inches). Find the indicated quantity (include the appropriate units) and explain what it means.STr(90, 1)
In Problem find fxx (x, y), fxy (x, y), fyx (x, y), and fyy (x, y) for each function f.f(x, y) = x2y2 + x3 + y
In Problem write a transition matrix for the transition diagram indicated, identify any absorbing states, and classify each Markov chain as regular, absorbing, or neither. А .1 B .7 с
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