Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Algebra (MindTap Course List)
Maximizing height A ball is thrown straight up from the top of a building 144 ft. tall with an initial velocity of 64 ft per second. The height s(t) in feet of the ball from the ground, at time t in seconds, is given by s(t)=144+64t16t2. Find the maximum height attained by the ball.Flat-screen television sets A wholesaler of appliance finds that she can sell (1200x) flat-screen television sets each week when the price is x dollars. What price will maximize revenue?Maximizing revenue A seller of contemporary disks finds that he can sell (820x) desks each month when the price is x dollars. What price will maximize revenue?Minimizing cost A company that produces and sells digital cameras has determined that the total weekly cost C(x), in dollars of producing x digital cameras is given by the function C(x)=1.5x2144x+5856. Determine the production level that minimizes the weekly cost for producing the digital cameras and find that weekly minimum cost.78EFinding mass transit fares The Municipal Transit Authority serves 150,000 commuters daily when the fare is 1.80. Market research has determined that every penny decrease in the fare will result in 1000 new riders. What fare will maximize revenue?Selling concert tickets Tickets for a concert are cheaper when purchased in quantity. The first 100 tickets are priced at 10 each, but each additional block of 100 tickets purchased decreases the cost of each ticket by 50. How many blocks of tickets should be sold to maximize the revenue?Finding hotel rates A 300-room hotel is two-thirds filled when the nightly room rate is 90. Experience has shown that each 5 increase in cost results in 10 fewer occupied rooms. Find the nightly rate that will maximize income.82EAn object is tossed vertically upward from ground level. Its heights(t), in feet, at time t seconds is given by the position function s(t)=16t2+80t. Use the position function for Exercise 8386. In how many seconds does the object reach its maximum height?An object is tossed vertically upward from ground level. Its heights(t), in feet, at time t seconds is given by the position function s(t)=16t2+80t. Use the position function for Exercise 8386. In how many seconds does the object return to the point from which it was thrown?An object is tossed vertically upward from ground level. Its heights(t), in feet, at time t seconds is given by the position function s(t)=16t2+80t. Use the position function for Exercise 8386. What is the maximum height reached by the object?86E87E88E89E90E91E92EAlligators The length in inches and weight in pounds of 25 alligators is shown in the table. Find the quadratic function that best fits the data. Round a,b, and c to six decimal places. Use the regression function to estimate the weight of an alligator that is 130 inches long. Round the weight to the nearest pound. Length Weight Length Weight Length Weight 94 130 72 38 90 106 74 51 128 366 89 84 147 640 85 84 68 39 58 28 82 80 76 42 86 80 86 83 114 197 94 110 88 70 90 102 63 33 72 61 78 57 86 90 74 54 69 36 61 44Alligators Refer to Exercise 93. If an alligator weighs 125 pounds, what is its approximate length? Round to the nearest inch. 93. Alligators The length in inches and weight in pounds of 25 alligators is shown in the table. Find the quadratic function that best fits the data. Round a,b, and c to six decimal places. Use the regression function to estimate the weight of an alligator that is 130 inches long. Round the weight to the nearest pound. Length Weight Length Weight Length Weight 94 130 72 38 90 106 74 51 128 366 89 84 147 640 85 84 68 39 58 28 82 80 76 42 86 80 86 83 114 197 94 110 88 70 90 102 63 33 72 61 78 57 86 90 74 54 69 36 61 4495E96EWhat is an axis of symmetry of a parabola?98E99E100E101E102E103E104E105E106E107E108E109EDetermine if the statement is true or false. If the statement is false, then correct it and make it true. The axis of symmetry of the parabola f(x)=44x2888x+222 is x=1.Determine whether or not the functions are polynomial function. For those that are, state the degree. a. f(x)=2x436x2+1 b. g(x)=1x2+5x5Find the zeros of each polynomial function. a. f(x)=x3x22x b. f(x)=2x4+2x23SC4SC5SCShow that P(x)=2x39x2+7x+6 has at least one real zero between 1and0.1EFill in the blanks. Peaks and valleys on a polynomial graph are called _________ points.3E4E5E6E7E8EFill in the blanks. If (x+5)3 occurs as a factor of a polynomial function, then the ________ of the zero x=5 is 3.Fill in the blanks. The graph of a nth degree polynomial function can have at most ________ turning points.11EFill in the blanks. If P(x) has real coefficients and P(a) and P(b) have opposite sings, there is at least one number r in (a,b) for which________.Determine whether or not the functions are polynomial functions. For those that are, state the degree. f(x)=12x55x3+3x10Determine whether or not the functions are polynomial functions. For those that are, state the degree. f(x)=0.8x65x32x+5Determine whether or not the functions are polynomial functions. For those that are, state the degree. f(x)=11x73x2+11x1Determine whether or not the functions are polynomial functions. For those that are, state the degree. f(x)=2x863x42x3+2x917E18E19EDetermine whether or not the functions are polynomial functions. For those that are, state the degree. f(x)=73x39x2+|x|Determine whether or not the graph of the functions shown are polynomial functions.22E23E24EFind the zero of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=4x225Find the zero of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=649x2Find the zero of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=2x2+7x15Find the zero of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=6x2x2Find the zero of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. g(x)=2x37x215xFind the zero of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. g(x)=x38x2+16xFind the zeros of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. g(x)=x3+6x24x24Find the zeros of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. g(x)=x32x29x+18Find the zeros of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=x4+2x33x2Find the zeros of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=x43x3+2x2Find the zeros of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=x415x2+44Find the zeros of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. f(x)=x419x2+48Find the zeros of each polynomial function and state the multiplicity of each. State whether the graph touches the x-axis and turns or crosses the x-axis at each zero. h(x)=3x2(x+4)2(x5)38E39E40EUse the Leading Coefficient Test to determine the end behavior of each polynomial. f(x)=5x7+10x32x42E43E44E45E46E47E48EGraph each polynomial function. f(x)=x39x50EGraph each polynomial function. f(x)=x34x252EGraph each polynomial function. f(x)=x3+x254E55E56EGraph each polynomial function. f(x)=x3x24x+458EGraph each polynomial function. f(x)=x42x2+1Graph each polynomial function. f(x)=x45x2+4Graph each polynomial function. f(x)=x4+5x2462EGraph each polynomial function. f(x)=x4+6x38x264E65E66E67E68E69E70E71E72E73E74E75E76E77E78E79E80EMaximize volume An open box is to be constructed from a piece of cardboard 20 inches by 24 inches by cutting a square of length x from each corner and folding up the sides as shown in the figure. a. Write a polynomial function V(x) that expresses the volume of the constructed box as a function of x. b. Use the theory learned about graphing polynomial functions and graph V(x). c. What is the domain of the function as it relates to the application problem? d. Use a graphing calculator to graph the function, and estimate the value of x that gives the maximum volume and then estimate the maximum volume. Round to one decimal place.82E83E84E85ERoller coaster A portion of a roller coasters tracks can be modeled by the polynomial function f(x)=0.0001(x3600x2+90,000x), where 0x400.f(x) represents the height of the roller coaster in feet and x represents the horizontal distance in feet. a. Find the height of the roller coaster when x=100 yards. b. Find the values of x on the interval [0,400] at which the height of the roller coaster is 0 yards.87E88E89E90E91E92E93E94EExplain why a polynomial function of odd degree must have at least one zero.What is the purpose of the Intermediate Value Theorem?Use a graphing calculator to explore the properties of graphs of polynomial function. Write a paragraph summarizing your observations. Graph the function y=x2+ax for several values of a. How does the graph change?Use a graphing calculator to explore to properties of graphs of polynomial functions. Write a paragraph summarizing your observations. Graph the function y=x3+ax for several values of a. How does the graph change?99E100EMatch each polynomial function with its graph shown below. f(x)=(xa)(xb)2(xc)102EMatch each polynomial function with its graph shown below. g(x)=(xa)2(xb)104E105E106ESelf Check 1 Let P(x)=2x23x+5. Find P(2) and divide P(x) by x2. What do you notice about the results?2SC3SC4SC5SC6SC7SC8SC9SC1E2E3E4E5EFill in the blanks. A shortcut method for dividing a polynomial by a binomial of the form xc is called _____ division.7E8EUse long division to perform each division. 2x4+x3+2x2+15x5x+210EFind each value by substituting the given value of x into the polynomial and simplifying. Then find the value by performing long division and finding the remainder. P(x)=3x32x25x7 ; P(2)12EFind each value by substituting the given value of x into the polynomial and simplifying. Then find the value by performing long division and finding the remainder. P(x)=7x4+2x3+5x21 ; P(1)Find each value by substituting the given value of x into the polynomial and simplifying. Then find the value by performing long division and finding the remainder. P(x)=2x42x3+5x21 ; P(2)Find each value by substituting the given value of x into the polynomial and simplifying. Then find the value by performing long division and finding the remainder. P(x)=2x5+x4x32x+3 ; P(1)Find each value by substituting the given value of x into the polynomial and simplifying. Then find the value by performing long division and finding the remainder. P(x)=3x5+x43x2+5x+7 ; P(2)Use the Remainder Theorem to find the remainder that occurs when P(x)=3x4+5x34x22x+1 is divided by each binomial. x+218EUse the Remainder Theorem to find the remainder that occurs when P(x)=3x4+5x34x22x+1 is divided by each binomial. x220E21E22E23EUse the Remainder Theorem to find the remainder that occurs when P(x)=3x4+5x34x22x+1 is divided by each binomial. x+4Use the Factor Theorem to determine whether each statement is true. If the statement is not true, so indicate. x1 is a factor of P(x)=x7126E27E28E29E30E31E32E33E34EUse the division algorithm and synthetic division to express the polynomial function P(x)=3x32x26x4 in the form divisorquotient remainder for each divisor. x336EUse the division algorithm and synthetic division to express the polynomial function P(x)=3x32x26x4 in the form divisorquotient remainder for each divisor. x+138E39E40EUse synthetic division to perform each division. x3+x2+x3x142EUse synthetic division to perform each division. 7x33x25x+1x+144EUse synthetic division to perform each division. 4x43x3x+5x346E47E48ELet P(x)=5x3+2x2x+1 . Use synthetic division to find each value. P(2)Let P(x)=5x3+2x2x+1 . Use synthetic division to find each value. P(2)Let P(x)=5x3+2x2x+1 . Use synthetic division to find each value. P(5)52E53E54ELet P(x)=2x4x2+2. Use synthetic division to find each value. P(12)56ELet P(x)=2x4x2+2. Use synthetic division to find each value. P(i)58ELet P(x)=x48x3+14x2+8x15. Write the terms of P(x) in descending powers of x and use synthetic division to find each value. P(1)60ELet P(x)=x48x3+14x2+8x15. Write the terms of P(x) in descending powers of x and use synthetic division to find each value. P(3)62E63E64E65E66E67E68EUse the Factor Theorem and synthetic division to determine whether the given polynomial is a factor of the polynomial function P(x). P(x)=3x313x210x+56;x+270EUse the Factor Theorem and synthetic division to determine whether the given polynomial is a factor of the polynomial function P(x). P(x)=x43x3+4x22x+4;x172E73E74E75E76E77E78E79E80EA partial solution set is given for each polynomial equation. Find the complete solution set. x3+3x213x15=0;{1}82EA partial solution set is given for each polynomial equation. Find the complete solution set. 2x3+x218x9=0;{12}84E85E86EA partial solution set is given for each polynomial equation. Find the complete solution set. x33x2+x+57=0;{3}88E89E90E91E92EFind a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 4,594E95EFind a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 1,0,1Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 2,4,598EFind a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 1,1,2,2Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 0,0,0,3,3101E102E103E104E105E106E107E108E109EIf 0 occurs twice as a zero of P(x)=anxn+an1xn1+...+a1x+a0, find a1.If P(2)=0 and P(2)=0, explain why x24 is a factor of P(x).112E113E114E115E116E117E118E119E120ESelf Check Find a second degree polynomial function P(x) with real coefficients that has a zero of 1i2SCSelf check Find a quadratic function with a repeated zero of i .Self check Discuss the possibilities for the zeros of P(x)=5x3+2x2x+3 .5SC6SC1E2E3E4E5E6E7E8E9E10EPractice: Determine how many zeros each polynomial function has. P(x)=x101Practice: Determine how many zeros each polynomial function has. P(x)=x401Practice: Determine how many zeros each polynomial function has. P(x)=3x44x22x+7Practice: Determine how many zeros each polynomial function has. P(x)=32x111x51Practice: Determine how many zeros each polynomial function has. One zero of P(x)=x(3x42)12x is 0. How many other zeros are there?Practice: Determine how many zeros each polynomial function has. Two zeros of P(x)=3x2(x714x+3) are 0 How many other zeros are there?