Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Algebra and Trigonometry (MindTap Course List)
15CC16CCWhat is the complex conjugate of a complex number a+bi?18CCWhat is the logical first step in solving the equation x-1=x-3? Why is it important to check your answers when solving equations of this type?Explain how to solve the given type of problem aLinear inequality: 2x1 bNonlinear inequality: x-1x-40 cAbsolute value equation: 2x-5=7 dAbsolute value inequality: 2x-57How do you solve an equation i algebraically? ii graphically?How do you solve an inequality i algebraically? ii graphically?Write an equation that expresses each relationship. ay is directly proportional to x by is inversely proportional to x cz is jointly proportional to x and y.1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23.1E23.2E24.1E24.2E25.1E25.2E26.1E26.2E27.1E27.2E28.1E28.2E29.1E29.2E30.1E30.2E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65-68 Complex Numbers Evaluate the expression and write in the form of a+bi a 2-3i+1+4i b 2+i3-2i66E67E68.1E68.2E69E70E71E72E73E74E75E76E77EDimensions of a Garden A homeowner wishes to fence in three adjoining garden plots, one for each of her children, as shown in the figure. If each plot is to be 80ft2 in area and she has 88ft of fencing material at hand, what dimensions should each plot have?79E79-92 Inequalities Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line. 12-x7x81E82E83E84E85E86E87E88E89E90E91E92E93.1E93.2E94E95E96E97E98E99E100E101E102E103E104E105E106E107E108E109E110E111E112E113E114E115ERange of a Projectile The maximum range of a projectile is directly proportional to the square of its velocity. A base-ball pitcher throws a ball at 60 mi/h, with a maximum range of 242 ft. What is his maximum range if he throws the ball at 70 mi/h?aPlot the points P0, 3, Q3, 0, and R6, 3 in the coordinate plane. Where must the point S be located so that PQRS is a square? bFind the area of PQRS.2CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CTA bottle of medicine is to be stored at a temperature between 5 C and 10 C. What range does this correspond to on the Fahrenheit scale? Note: Fahrenheit F and Celsius C temperatures satisfy the relation C=59(F32).15CT16CTThe maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h and inversely proportional to its length L. a Write an equation that expresses this proportionality. b Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb. c If a 10-ft beam made of the same material is 3 in. wide and 10 in. high, what is the maximum weight it can support?Femur Length and Height Anthropologists use a linear model that relates femur length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton including the femur is found. In this problem we find the model by analyzing the data on femur length and height for the eight males given in the table. a Make a scatter plot of the data. b Find and graph a linear function that models the data. c An anthropologist finds a femur of length 58 cm. How tall was the person? Femur length cm Height cm 50.1 178.5 48.3 173.6 45.2 164.8 44.7 163.7 44.5 168.3 42.7 165.0 39.5 155.4 38.0 155.8Demand for Soft Drinks A convenience stores manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table. a Make a scatter plot of the data. b Find and graph a linear function that models the data. c Use the model to predict soft drink sales if the temperature is 95. High temperature Number of cans sold 55 340 58 335 64 410 68 460 70 450 75 610 80 735 84 780Tree Diameter and Age To estimate ages of trees, forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age which requires special tools for extracting a representative cross section of the tree and counting rings. To find the model, use the data in the table, which were collected for a certain variety of oaks. a Make a scatter plot of the data. b Find and graph a linear function that models the data. c Use the model to estimate the age of an oak whose diameter is 18 in. Diameter in. Age years 2.5 15 4.0 24 6.0 32 8.0 56 9.0 49 9.5 76 12.5 90 15.5 894P5P6P7P8P9P10P11PDemand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00If f(x)=x3+1, then a the value of f at x=-1 is f()=. b the value of f at x=2 is f()=. c the net change in the value of f between x = - 1 and x =2 is f()f()=.2E3E4E5E6E7E8E7-10 Function Notation Express the rule in function notation. For example, the rule square, then subtract 5 is expressed as the function f(x)=x25 Subtract 1, then square10E11E12E13E14E15E16E17E18E19E19-30 Evaluating Functions Evaluate the function at the indicated values. f(x)=x3+2x;f(2),f(1),f(0),f(12)21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51-54 Domain and Range Find the domain and range of the function. f(x)=3x52E53E54E55-72 Domain Find the domain of the function. f(x)=1x356E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73E74E75E76E77E78ETorricellis Law A tank holds 50 gal of water, which drains from a leak at the bottom, causing the tank to empty in 20 min. The tank drains faster when it is nearly full because the pressure on the leak is greater. Torricellis Law gives the volume of water remaining in the tank after t minutes as V(t)=50(1t20)20t20 a Find V(0) and V(20). b What do yours answer to part a represent? c Make a table of values of V(t) for t=0,5,10,15,20. d Find the net change in the volume V as t changes from 0 min to 20 min.80E81E82EBlood Flow As blood moves through a vein or an artery, its velocity v is greatest along the central axis and decreases as the distance r from the central axis increases see the figure. The formula that gives v as the function of r is called the law of laminar flow. For an artery with radius 0.5 cm, the relationship between v in cm/s and r in cm is given by the function v(r)=18,500(0.25r2)0r0.5 a Find v(0.1)andv(0.4). b What do your answers to part a tell you about the flow of blood in this artery? c Make a table of values of v(r)forr=0,0.1,0.2,0.3,0.4,0.5. d Find the net change in the velocity v as r changes from 0.1 cm to 0.5 cm.84E85E86ECost of a Hotel Stay A hotel chain charges 75 each night for the first two night and 50 for each additional nights stay. The cost T is the function of the number of nights x that a guest stays. a Complete the expressions in the following piecewise defined function. T(x)={if0x2ifx>2 b Find T(2),T(3),andT(5). c What do your answers in part b represent?88E89E90E91E92E93E94E95ETo graph the function f, we plot the points (x,) in a coordinate plane. To graph f(x)=x22, we plot the points (x,). So the point (3,) is on the graph of f. The height of the graph of f above the x-axis when x=3 is _______. Complete the table, and sketch a graph of f. x f(x) (x,y) 2 1 0 1 22E3EMatch the function with its graph. a f(x)=x2 b f(x)=x3 c f(x)=x d f(x)=|x|5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E33-46 . Graphing Piecewise Defined Functions Sketch a graph of the piecewise defined function. f(x)={1ifx11if1x11ifx140E41E