Calculate the compound amount from the given data. principal = $50,000, compounded quarterly, 10 years, annual rate = 9.5%
> Refer to 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 (1, 330) (6.87, 3
> 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 whe
> 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
> 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 subscri
> 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 s
> 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
> 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 t
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. h(s) / f (s)
> If the cylinder in Exercise 6 has a volume of 54p cubic inches, find the surface area of the cylinder. Cylinder in Exercise 6: Cylinder with height = diameter
> Decide which curves are graphs of functions.
> If the rectangle in Exercise 1 has a perimeter of 40 cm, find the area of the rectangle. Rectangle in Exercise 1: Rectangle with height = 3- width
> Cost of an Open Box 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
> 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. Corral of Exercise 16: Figure 15
> 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 fe
> 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
> Consider the cylinder of Exercise 6. Write an equation expressing the fact that the surface area is 30Ï€ square inches. Write an expression for the volume. Cylinder with height = diameter
> Consider the cylinder of Exercise 5. Write an equation expressing the fact that the volume is 100 cubic inches. Suppose that the material to construct the left end costs $5 per square inch, the material to construct the right end costs $6 per square inch
> Consider the closed rectangular box in Exercise 4. Write an expression for the surface area. Write an equation expressing the fact that the volume is 10 cubic feet. Rectangular box with height =- length
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x) / g(x)
> Consider the rectangular box in Exercise 3, and suppose that it has no top. Write an expression for the volume. Write an equation expressing the fact that the surface area is 65 square inches. Rectangle with height = 3 - width
> Consider the Norman window of Exercise 2. Write an expression for the perimeter. Write an equation expressing the fact that the area is 2.5 square meters. Norman window: Rectangle topped with a semicircle
> Decide which curves are graphs of functions. -x
> Consider a circle of radius r. Write an expression for the area. Write an equation expressing the fact that the circumference is 15 centimeters.
> Consider the rectangle in Exercise 1. Write an expression for the area. Write an equation expressing the fact that the perimeter is 30 centimeters. Rectangle with height = 3- width
> Consider the rectangle in Exercise 1. Write an expression for the perimeter. If the area is 25 square feet, write this fact as an equation. Rectangle with height = 3- width
> Assign variables to the dimensions of the geometric object. Cylinder with height = diameter
> Assign variables to the dimensions of the geometric object. Сyinder
> Compute the numbers. 025
> Compute the numbers. 1100
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. g(x)h(x)
> Compute the numbers. (-2)3
> Compute the numbers. 33
> Convert the numbers from graphing calculator form to standard form (that is, without E). 8.23E-6
> Decide which curves are graphs of functions.
> Convert the numbers from graphing calculator form to standard form (that is, without E). 1.35E13
> Convert the numbers from graphing calculator form to standard form (that is, without E). 8.103E-4
> Convert the numbers from graphing calculator form to standard form (that is, without E). 5E-5
> Velocity When a car’s brakes are slammed on at a speed of x miles per hour, the stopping distance is 1 20x2 feet. Show that when the speed is doubled the stopping distance increases fourfold.
> Semiannual Compound Assume that a $1000 investment earns interest compounded semiannually. Express the value of the investment after 2 years as a polynomial in the annual rate of interest r.
> Assume that a $500 investment earns interest compounded quarterly. Express the value of the investment after 1 year as a polynomial in the annual rate of interest r.
> Use intervals to describe the real numbers satisfying the inequalities. x ≥ 12
> Assume that a couple invests $4000 each year for 4 years in an investment that earns 8% compounded annually. What will the value of the investment be 8 years after the first amount is invested?
> Assume that a couple invests $1000 upon the birth of their daughter. Assume that the investment earns 6.8% compounded annually. What will the investment be worth on the daughter’s 18th birthday?
> Calculate the compound amount from the given data. principal = $1500, compounded daily, 3 years, annual rate = 6%
> Calculate the compound amount from the given data. principal = $1500, compounded daily,1 year, annual rate = 6%
> Decide which curves are graphs of functions.
> Calculate the compound amount from the given data. principal = $500, compounded monthly,1 year, annual rate = 4.5%
> Calculate the compound amount from the given data. principal = $100, compounded monthly, 10 years, annual rate = 5%
> Calculate the compound amount from the given data. principal = $20,000, compounded quarterly, 3 years, annual rate = 12%
> Calculate the compound amount from the given data. principal = $700, compounded annually, 8 years, annual rate = 8%
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x)g(x)
> Calculate the compound amount from the given data. principal = $500, compounded annually, 6 years, annual rate = 6%
> Evaluate f (4). f (x) = x0
> Evaluate f (4). f (x) = x-5/2
> Evaluate f (4). f (x) = x-1/2
> Evaluate f (4). f (x) = x3/2
> Decide which curves are graphs of functions. -x
> Draw the following intervals on the number line. [ -2, √2)
> Evaluate f (4). f (x) = x1/2
> Evaluate f (4). f (x) = x-1
> Evaluate f (4). f (x) = x3
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (t) - h(t)
> Evaluate f (4). f (x) = x2
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a/√b = √ (a/b).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a * √b = √(ab).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √ (x/y) - √ (y/x) = √xy ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. x-1/4 + 6x1/4 = x-1/4( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. 2x2/3 - x-1/3 = x-1/3 ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √x – 1/√x = 1/√x ( )
> Decide which curves are graphs of functions.
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (f (x))
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x) - g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g (f (x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. 3√ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)/ g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)g(x)]3
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)]3g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(x) / f (x)
> Sketch the graph of the function. f (x) = 1 / f(x) = x + 1
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x) / g(x)
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 6 / x – 6, g(x) = x – 6 / x + 6
> Use intervals to describe the real numbers satisfying the inequalities. x ≥ -1 and x < 8
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x)g(x)
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-32y-5)3/5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-27x5)2/3 / x3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (25xy)3/2 / x2y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √x (1/4x)5/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-8y9)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (16x8)-3/4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1 / yx-5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 2x / √x
> Sketch the graph of the function. f (x) = √(x + 1)
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 5 / x – 10, g(x) = x / x + 10
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x2 / x5y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (3x2 / 2y)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
