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mathematics
applied calculus
Calculus And Its Applications 14th Edition Larry Goldstein, David Lay, David Schneider, Nakhle Asmar - Solutions
Factor the polynomials.x5 - x4 - 2x3
Factor the polynomials.x2 - 16
LetandExpress the following as rational functions.f (x)g(x) f(x) = X x-2' g(x)= 5-x 5 + x'
If f (x) = x2 - 2x, find f (a + 1) and f (a + 2).
Consider a rectangular corral with a partition down the middle, as shown in Fig. 14. Assign letters to the outside dimensions of the corral. Write an equation expressing the fact that 5000 feet of fencing is needed to construct the corral (including the partition). Write an expression for the total
Compute the numbers.(.01)-1
Determine the intercepts of the graphs of the following equations.x - 5y = 0
Give two methods for finding the zeros of a quadratic function.
LetandExpress the following as rational functions.g(x)h(x) f(x) = X x-2' g(x)= 5-x 5 + x'
Find the zeros of the quadratic function y = 5x2 - 3x - 2.
Consider a rectangular corral with two partitions, as in Fig. 15. Assign letters to the outside dimensions of the corral. Write an equation expressing the fact that the corral has a total area of 2500 square feet. Write an expression for the amount of fencing needed to construct the corral
Factor the polynomials.x2 - 1
If f (x) = 3x + 2 and h ≠ 0, findSimplify your answer as much as possible. f(3 +h)-f(3) h
If h(s) = s/(1 + s), find h(1/2), h( - 3/2), and h(a + 1).
Compute the numbers.(-5)-1
Determine the intercepts of the graphs of the following equations.2 + 3x = 2y
State the six laws of exponents.
Find the zeros of the quadratic function y = -2x2 - x + 2.
If f (x) = x2 and h ≠ 0, findSimplify your answer as much as possible. f(1 +h)-f(1) h
If the rectangle in Exercise 1 has a perimeter of 40 cm, find the area of the rectangle.Exercise 1Assign variables to the dimensions of the geometric object. Rectangle with height=3 width
Factor the polynomials.3x2 + 12x + 12
In some cities, you can rent a car for $24 per day and $.45 per mile.(a) Find the cost of renting the car for one day and driving 200 miles.(b) If the car is to be rented for one day, express the total rental expense as a function of the number x of miles driven. (Assume that for each fraction of a
Find the points of intersection of the pairs of curves.y = x2 - 4x + 4, y = 12 + 2x - x2
Consider the corral of Exercise 16. If the fencing for the boundary of the corral costs $10 per foot and the fencing for the inner partitions costs $8 per foot, write an expression for the total cost of the fencing.Exercise 16Consider a rectangular corral with two partitions, as in Fig. 15. Assign
LetandExpress the following as rational functions.f (x)/g(x) f(x) = X x-2' g(x)= 5-x 5 + x'
Compute the numbers.84/3
LetandExpress the following as rational functions.h(s)/f (s) f(x) = X x-2' g(x)= 5-x 5 + x'
In the formula A = P(1 + i)n, what do A, P, i, and n represent?
Find the points of intersection of the curves y = 5x2 - 3x - 2 and y = 2x - 1.
Factor the polynomials.2x2 - 12x + 18
Consider the rectangular box of Exercise 3. Assume that the box has no top, the material needed to construct the base costs $5 per square foot, and the material needed to construct the sides costs $4 per square foot. Write an equation expressing the fact that the total cost of materials is
Compute the numbers.163/4
A gas company will pay a property owner $5000 for the right to drill on his land for natural gas and $.10 for each thousand cubic feet of gas extracted from the land. Express the amount of money the landowner will receive as a function of the amount of gas extracted from the land.
Explain how to solve f (x) = b geometrically from the graph of y = f (x).
Find the points of intersection of the curves y = -x2 + x + 1 and y = x - 5.
Factor the polynomials.30 - 4x - 2x2
LetandExpress the following as rational functions.f (x + 1)g(x + 1) f(x) = X x-2' g(x)= 5-x 5 + x'
The boiling point of tungsten is approximately 5933 Kelvin.(a) Find the boiling point of tungsten in degrees Celsius, given that the equation to convert x°C to Kelvin is k(x) = x + 273.(b) Find the boiling point of tungsten in degrees Fahrenheit. (Tungsten, also known as wolfram, has the highest
Compute the numbers.(25)3/2
LetandExpress the following as rational functions.f (x + 2) + g(x + 2) f(x) = X x-2' g(x)= 5-x 5 + x'
In 2010, a patient paid $700 per day for a semiprivate hospital room and $1900 for an appendectomy operation. Express the total amount paid for an appendectomy as a function of the number of days of hospital confinement.
Explain how to find f (a) geometrically from the graph of y = f (x).
Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions.f (x) + g(x)
Factor the polynomials.15 + 12x - 3x2
If the cylinder in Exercise 6 has a volume of 54π cubic inches, find the surface area of the cylinder.Exercise 4Assign variables to the dimensions of the geometric object. Rectangular box with height = length
An office supply firm finds that the number of laptop computers sold in year x is given approximately by the function f (x) = 150 + 2x + x2, where x = 0 corresponds to 2015.(a) What does f (0) represent?(b) Find the number of laptops sold in 2020.
Compute the numbers.(27)2/3
Describe the domain of the function. f(x) 8.x (x - 1)(x - 2)
When a baseball thrown at 85 miles per hour is hit by a bat swung at x miles per hour, the ball travels 6x - 40 feet (This formula assumes that 50 ≤ x ≤ 90 and that the bat is 35 inches long, weighs 32 ounces, and strikes a waist-high pitch so that the plane of the swing lies at 35∘ from the
Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions.f (x) - g(x)
Factor the polynomials.3x - x2
LetandExpress the following as rational functions. f(x) = X x-2' g(x)= 5-x 5 + x'
Compute the numbers.(1.8)0
Let f (x) be the cost–benefit function. If 70% of the pollutant has been removed, what is the added cost to remove another 5%? How does this compare with the cost to remove the final 5% of the pollutant?
Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions.f (x)h(x)
Describe the domain of the function. f(t) = 1 Vi
Suppose that the cost (in millions of dollars) to remove x percent of a certain pollutant is given by the cost–benefit function(a) Find the cost to remove 85% of the pollutant.(b) Find the cost to remove the final 5% of the pollutant. f(x) = 20x 102 - x for 0≤x≤ 100.
LetandExpress the following as rational functions. f(x) = X x-2' g(x)= 5-x 5 + x'
A specialty shop prints custom slogans and designs on T-shirts. The shop’s total cost at a daily sales level of x T-shirts is C(x) = 73 + 4x dollars.(a) At what sales level will the cost be $225?(b) If the sales level is at 40 T-shirts, how much will the cost rise if the sales level changes to 50
Factor the polynomials.4x2 - 1
LetandExpress the following as rational functions. f(x) = X x-2' g(x)= 5-x 5 + x'
Describe the domain of the function. g(x) = 1 √3-x
Compute the numbers.91.5
Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions.f (x)g(x)
Describe the domain of the function. g(x) 4 x(x + 2)
A college student earns income by typing term papers on a computer, which she leases (along with a printer). The student charges $4 per page for her work, and she estimates that her monthly cost when typing x pages is C(x) = .10x + 75 dollars.(a) What is the student’s profit if she types 100
Factor the polynomials.6x - 2x3
Compute the numbers.160.5
In biochemistry, such as in the study of enzyme kinetics, we encounter a linear function of the form f (x) = (K/V)x + 1/V, where K and V are constants.(a) If f (x) = .2x + 50, find K and V so that f (x) may be written in the form f (x) = (K/V)x + 1/V.(b) Find the x-intercept and y-intercept of the
Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions.f (x)/h(x)
LetandExpress the following as rational functions. f(x) = X x-2' g(x)= 5-x 5 + x'
A frozen yogurt stand makes a profit of P(x) = .40x - 80 dollars when selling x scoops of yogurt per day. (a) Find the breakeven sales level, that is, the level at which P(x) = 0.(b) What sales level generates a daily profit of $30?(c) How many more scoops of yogurt will have to be sold to
Factor the polynomials.16x + 6x2 - x3
Compute the numbers.(81)0.75
Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions.g(x)h(x)
A cellular telephone company estimates that, if it has x thousand subscribers, its monthly profit is P(x) thousand dollars, where P(x) = 12x - 200.(a) How many subscribers are needed for a monthly profit of 160 thousand dollars?(b) How many new subscribers would be needed to raise the monthly
Letand h(x) = x3 - 5x2 + 1. Calculate the following functions.f (g(x)) 1 − x' (x)8'9x = (x) f
Factor the polynomials.x3 - 1
Each quadratic function has the form y = ax2 + bx + c. Identify a, b, and c. x² - 6x + 2 2 3
Sketch the graph of the function.f (x) = x2 + 1
Compute the numbers.4-1/2
Letand h(x) = x3 - 5x2 + 1. Calculate the following functions.h(f (t)) 1 − x' (x)8'9x = (x) f
Each quadratic function has the form y = ax2 + bx + c. Identify a, b, and c.y = 3x2 - 4x
Compute the numbers. -100 8 -2/3
Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.f (x) - g(x)
Sketch the graph of the function. I + x^ = (x)ƒ
An average sale at a small florist shop is $21, so the shop’s weekly revenue function is R(x) = 21x, where x is the number of sales in 1 week. The corresponding weekly cost is C(x) = 9x + 800 dollars.(a) What is the florist shop’s weekly profit function?(b) How much profit is made when sales
Factor the polynomials.x3 + 125
Sketch the graph of the function.f (x) = 2x2 - 1
Letand h(x) = x3 - 5x2 + 1. Calculate the following functions.h(g(x)) 1 − x' (x)8'9x = (x) f
The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.What is the cost of constructing a cylinder of radius 6 inches? 400 350 300 250 200 150 100 50 (1,330) (3, 162) (6.87, 330) y = f(r) 0 1 2
Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.f (x) - g(x + 1)
A catering company estimates that, if it has x customers in a typical week, its expenses will be approximately C(x) = 550x + 6500 dollars, and its revenue will be approximately R(x) = 1200x dollars.(a) How much profit will the company earn in 1 week when it has 12 customers?(b) How much profit is
Factor the polynomials.8x3 + 27
Compute the numbers.(.01)-1.5
Sketch the graph of the function. 1 f(x) = x + 1
Letand h(x) = x3 - 5x2 + 1. Calculate the following functions.g(f (x)) 1 − x' (x)8'9x = (x) f
Each quadratic function has the form y = ax2 + bx + c. Identify a, b, and c.y = 3x - 2x2 + 1
Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.g(x) - h(x)
Decide which curves are graphs of functions. y X
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