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mathematics
calculus with applications

Calculus With Applications 12th Edition Margaret L. Lial - Solutions

Give the domain of each function defined as follows. f(x) 2 1-x²
Give the domain of each function defined as follows.ƒ(x) = (3x + 5)1/2
Give the domain of each function defined as follows.ƒ(x) = (x - 3)1/2
Give the domain of each function defined as follows.ƒ(x) = |3x – 6|
Give the domain of each function defined as follows.ƒ(x) = √4 - x2
Give the domain of each function defined as follows.ƒ(x) = (x + 3)2
Give the domain of each function defined as follows.ƒ(x) = x4
Give the domain of each function defined as follows.ƒ(x) = 2x + 3
Give the domain of each function defined as follows.ƒ(x) = 2x
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = -4x2
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = x2
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = (x - 2)(x + 2)
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = x(x + 2)
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.6x - y = -1
Which of the following rules define y as a function of x? X 9 4 1 0 1 4 9 y 32 1 0 -1 -2 -3
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.2y - x = 5
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = -3x + 9
Which of the following rules define y as a function of x? 82 23 X 17. Y 27 .6 93 14
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = 2x + 3
Which of the following rules define y as a function of x? X V 9 2 4 1 1 0 0 -1 1 -2 4 -3 9 3 32 نا انا
Which of the following rules define y as a function of x?x = y2 + 4
Which of the following rules define y as a function of x?x = y
Which of the following rules define y as a function of x? 12 54 32 9. 27 X Y 69 101 43 18
Which of the following rules define y as a function of x?y = √x
Which of the following rules define y as a function of x?y = x3 + 2
The function ƒ(x) = 0 is both even and odd.Determine whether each statement is true or false, and explain why.
The range of the function ƒ(x) = 1/x is all real numbers.Determine whether each statement is true or false, and explain why.
The equation y = x4 does not define a function because it assigns the number 16 to two different x-values, 2 and -2.Determine whether each statement is true or false, and explain why.
A function is a rule that assigns one or more elements from one set to each element in another set.Determine whether each statement is true or false, and explain why.
In Exercises, find a linear cost function.Twelve units cost $445; 50 units cost $1585.
To manufacture x thousand computer chips requires fixed expenditures of $352 plus $42 per thousand chips. Receipts from the sale of x thousand chips amount to $130 per thousand.(a) Find the linear expenditure function, E(x).(b) Find the linear receipt function, R(x).(c) For profit to be made,
For the lines in exercises which of the following is closest to the slope of the line? (a) 1 (b) 2 (c) 3 (d) 21 (e) 22(f) - 3 2 + + 2 X
In exercises, estimate the slope of the lines. -2- 2 x
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you receive the data, you must decide whether to go ahead with production of the new product.Analyze the
Graph each linear equation defined as follows.x + 3y = 0
In exercises, estimate the slope of the lines. 2 2 ++
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you receive the data, you must decide whether to go ahead with production of the new product.Analyze the
The United States is China’s largest export market. Imports from China have grown from about $100 billion in 2000 to $540 billion in 2018. This growth has been approximately linear.(a) Determine a linear equation that approximates this growth in imports in terms of t, where t represents the
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you receive the data, you must decide whether to go ahead with production of the new product.Analyze the
U.S. exports to China have grown (although at a slower rate than imports) since 2000. In 2000, about $16 billion of goods were exported to China. By 2018, this amount had grown to $120 billion. This growth has been approximately linear.(a) Determine a linear equation that approximates this growth
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you receive the data, you must decide whether to go ahead with production of the new product.Analyze the
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Vertical, through 1-6, 52
Suppose that the demand and price for a certain model of a youth wristwatch are related by p = D(q) = 16 - 1.25q, where p is the price (in dollars) and q is the quantity demanded (in hundreds). Find the price at each level of demand.(a) 0 watches(b) 400 watches(c) 800 watchesFind the quantity
The following data give the expected points for a football team with first down and 10 yards to go from various points on the field.(a) Calculate the correlation coefficient. Does there appear to be a linear correlation?(b) Find the equation of the least squares line.(c) Use your answer from part
To show that two perpendicular lines, neither of which is vertical, have slopes with a product of -1, go through the following steps. Let line L1 have equation y = m1 x + b1 , and let L2 have equation y = m2x + b2, with m1 > 0 and m2 < 0. Assume that L1 and L2 are perpendicular, and use right
Consider the equation(a) Show that this equation represents a line by writing it in the form y = mx + b.(b) Find the x- and y-intercepts of this line.(c) Explain in your own words why the equation in this exercise is known as the intercept-intercept form of a line. XI a y b = 1.
In recent decades, the median income for all U.S. households has increased in a roughly linear manner. In 1990, the median income was $29,943. By 2018, it had risen to $63,179. Source: U.S. Census Bureau.(a) Determine a linear equation that approximates the median income in terms of t, the number
Suppose that the fixed cost for a product is $400 and the break-even quantity is 80. Find the marginal profit (the slope of the linear profit function).
The supply and demand for fresh jumbo lump crabmeat in a local fish store are related by the equationsSupply: p = S(q) = 4q + 10andDemand: p = D(q) = 40 - 4q,where p represents the price in dollars per pound and q represents the quantity of crabmeat in pounds per day. Find the quantity supplied and
Suppose that the fixed cost for a product is $650 and the break-even quantity is 25. Find the marginal profit (the slope of the linear profit function).
Graph each equation.y = x - 1
Deer ticks are of concern because they can carry the parasite that causes Lyme disease. One study found a relationship between the density of acorns produced in the fall and the density of deer tick larvae the following spring. The relationship can be approximated by the linear function ƒ(x) = 34x
In Exercises, find a linear cost function.Eight units cost $300; fixed cost is $60.
Graph each equation.y = 4x + 5
The U.S. Centers for Disease Control and Prevention projects that tobacco could soon be the leading cause of death in the world. In 1990, 35 million years of healthy life were lost globally due to tobacco. This quantity was rising linearly at a rate of about 28 million years each decade. In
In Exercises, find a linear cost function.Fixed cost is $2000; 36 units cost $8480.
Graph each equation.y = -4x + 9
Use the formula for conversion between Fahrenheitand Celsius derived in Example 8 to convert each temperature.(a) 58°F to Celsius (b) -20°F to Celsius(c) 50°C to Fahrenheit
Graph each equation.y = -6x + 12
You may have heard that the average temperature of the human body is 98.6°. Recent experiments show that the actual figure is closer to 98.2°. The figure of 98.6 comes from experiments done by Carl Wunderlich in 1868. But Wunderlich measured the temperatures in degrees Celsius and rounded the
Find the temperature at which the Celsius and Fahrenheit temperatures are numerically equal.
In Exercises, find a linear cost function.Thirty units cost $1500; 120 units cost $5640.
Graph each equation.2x - 3y = 12
A report estimated the cost to build a new 30% carbon sequestration coal-generated electricity plant with a capacity of 650 MW to be $3.308 billion, with a marginal cost of $7.17 for each MWh of electricity produced.(a) Find a formula for the cost, C(x), to build a plant and generate x MWh of
The cost of producing x cartons of CDs is C(x) dollars, where C(x) = 200x + 1000. The CDs sell for $400 per carton.(a) Find the break-even quantity.(b) What revenue will the company receive if it sells just that number of cartons?
Graph each equation.3x - y = -9
The cost function for flavored coffee at an upscale coffeehouse is given in dollars by C(x) = 3x + 160, where x is in pounds. The coffee sells for $7 per pound.(a) Find the break-even quantity.(b) What will the revenue be at that point?
Graph each equation.3y - 7x = -21
The average new car cost (in dollars) from 2002 to 2018 is given in the table.(a) Find a linear equation for the average new car cost in terms of t, the number of years since 2000, using the data for 2012 and 2018.(b) Repeat part (a), using the data for 2014 and 2018.(c) Find the equation of the
Graph each equation.5y + 6x = 11
The U.S. per capita consumption (in pounds) of beef, pork, and chicken for 2000 and 2016 is given in the following table. Assume that the changes in consumption are approximately linear.(a) Determine three linear functions, b(t), p(t), and c(t), which approximate the pounds of beef, pork, and
Graph each equation.y = -2
In general, people tend to live longer in countries that have a greater supply of food. Listed in the table below is the 2013 daily calorie supply and 2010–2015 life expectancy at birth for 10 randomly selected countries.(a) Find the correlation coefficient. Do the data seem to fit a straight
Grandfather clocks use pendulums to keep accurate time. The relationship between the length of a pendulum L and the time T for one complete oscillation can be determined from the data in the table.(a) Plot the data from the table with L as the horizontal axis and T as the vertical axis.(b) Find the
The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. The index was 100 for the three-year period centered on 1983. For simplicity, we will assume that the CPI was exactly 100 in 1983. Then the CPI of 251.1 in 2018 indicates that an item that cost $1.00 in 1983
In exercises, find an equation in slope-intercept form for each line.Through (8, -1) and (4, 3)
While shopping for an air conditioner, Manuel consulted the following table, which gives a machine’s BTUs and the square footage (ft2) that it would cool.(a) Find the equation for the least squares line for the data.(b) To check the fit of the data to the line, use the results from part (a) to
Find an equation in the form y = mx + b for each line.Through (2, -10), perpendicular to a line with undefined slope
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.x-intercept -2, y-intercept 4
Assume that each situation can be expressed as a linear cost function. Find the cost function in each case.Marginal cost: $120; 700 items cost $96,500 to produce.
Find an equation in the form y = mx + b for each line.Through (-2, 5); slope = 0
The table shows the men’s and women’s outdoor world records (in seconds) in the 800-m run.Let x be the year, with x = 0 corresponding to 1900.(a) Find the equation for the least squares line for the men’s record (y) in terms of the year (x).(b) Find the equation for the least squares line for
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (3, -4), parallel to 4x - 2y = 9
Let the supply and demand functions for butter pecan ice cream be given bywhere p is the price in dollars and q is the number of 10-gallon tubs.(a) Graph these on the same axes.(b) Find the equilibrium quantity and the equilibrium price. p = S(q) = IN 2 59 and P = D(q) = 120 4 59,
Suppose that the demand and price for strawberries are related by p = D(q) = 6 - 0.25q, where p is the price (in dollars) and q is the quantity demanded (in hundreds of quarts). Find the price at each level of demand.(a) 0 quarts(b) 400 quarts(c) 840 quartsFind the quantity demanded for the
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Horizontal, through 18, 72
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (0, 5), perpendicular to 8x + 5y = 3
Let the supply and demand functions for sugar be given bywhere p is the price per pound and q is the quantity in thousands of pounds.(a) Graph these on the same axes.(b) Find the equilibrium quantity and the equilibrium price. p= S(q) = 1.4q 0.6 p= D(q)-2q + 3.2, P and
An analysis similar to that of the previous exercise can be done for the 100-meter sprint, for which the winning times in the Summer Olympic Games since 1928 are listed in the table below. Let x be the number of years since 1900.(a) Find the least squares line for the men’s winning time.(b) Find
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through 1-4, 62, parallel to 3x + 2y = 13
If you think a marathon is a long race, consider the Hardrock 100, a 100.5 mile running race held in southwestern Colorado. The chart which follows lists the times that the 2018 winner, Jeff Browning, arrived at various mileage points along the way.(a) What was Browning’s average speed?(b) Graph
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (-1, 4); undefined slope
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (7, -6), parallel to a line with undefined slope
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through 12, -52, parallel to 2x - y = -4
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (3, -5), parallel to y = 4
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through 13, -42, perpendicular to x + y = 4
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (-3, 5), perpendicular to y = -2
An interesting phenomenon occurred with the 2000 New York Yankees. The following table shows the number of base hits, triples, and home runs for those Yankees with at least 300 at-bats.(a) Find the correlation coefficient between the number of hits and the number of triples.(b) Find the correlation
Suppose that the supply function for honey is p = S(q) = 0.3q + 2.7, where p is the price in dollars for an 8-oz container and q is the quantity in barrels. Suppose also that the equilibrium price is $4.50 and the demand is 2 barrels when the price is $6.10. Find an equation for the demand
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through 1-2, 62, perpendicular to 2x - 3y = 5

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