JimJackJAustinCommunityCollegeDistrict

1、jim jack (j²)math 1314 - college algebraadminclassgradingattendance1.1 numbers, data, and problem solvingnatural numbersintegersrationalirrationalpemdas1. parenthesis2. exponents3. multiplication and division, left to right4. addition and subtraction, left to rightscientific notationa real numb

2、er r is in scientific notation when r is written as , where and n is an integer.dist to sun = 93,000,000pop of world in 2050 = 9,000,000,000light travels in 1 mile = mass of the earth kgcalculator exercisefind the speed the earth travels in space relative to the sun in miles per hour.find the volume

3、 of a soda can with radius 1.4” and height 5”. can it hold 16oz?1.2 visualizing and graphing datalow temperatures in minneapolis for six nights-12-4-821189maximum, minimum, mean, mediana relation is a set of ordered pairs.portland rainfall12345678910112.32.06.4domain=ran

4、ge=202040401.6domain=range=portland rainfall12345678910112.32.06.4distance formuladistance between two moving cars100 50 kc50100linear approximationmidpoint formulathe midpoint of a line segment with endpoints and in the xy plane ispopulation of the usin 1990, t

5、he population of the us was 249 million, and in 2010, it was 308 million.find the population in 2000.a circle is the set of points equidistant from a center point.graph finding the equation of a circlea) radius = 4, center is b) center with a point on the circle a line is drawn from the point to the

6、 point . state the equation of a circle for which this line is the circles diameter.completing the squareskipfind the center and the radius of the circle:1.3 functions and their representationsthunder and lightning speed of sound=1050 ft/sec51015202512345rule: compute y by dividing x by 5meaningful

7、input domaincorresponding output rangeverbal: divide x by 5 to obtain y milesnumerical:1234560.81.01.21.4diagrammatic:51awax102bxby153cycz204zdsymbolic: leonhard euler(1707-1783)graphical:graph a function is a relation in which each element in the domain corresponds to exactly one element

8、in the range. exactly one y function (rule for finding y)ordered pairs domainrangelet domaindomainrangefind domain and range graphicallyair cools at a rate of 3.6º f per 1,000 ft altitudefigure for , where x is in thousands ft.verbal:symbolic:graphical:numerical:crutch length trial and error or

9、 (65” height) skip exsymbolic:graphical:numerical:identifying functionsvertical line test1.4 types of functions and their rates of changedescribe datamake predictionslinearnon-linearconstantwindspeed at hilo, himayjunejulyaugseptoctnovdec77777777f=a function represented by , where b is a fixed numbe

10、r, is a constant function.discrete functioncontinuous functionother constant fcns thermostat, speed controllinear functionsa car is initially located 30 miles n of the red river on i-35 traveling northbound at 60mph.0123453090150210270330f=a function represented by , where a and b are fixed, is a li

11、near function.wages earned at $8.25/hrtuition at $75/credit hr + $55 student feedistance traveled by light at 186,000 miles/sec.slope as a rate of changethe slope of the line passing through the points and ispositive slopenegative slopeno slopefind the slope of a line through and songs that can be s

12、tored on x gb of ipod memory20,000songs 80gbpass thru origin?slope?rate of change?non-linear functionsx01234f(x)014916average temperature in each monthheight of a child at age 2 through 18linear and non-linear dataskip05101520-4-2024-30369571014190123411111111110136103691215recognizing linear functi

13、onsincreasing and decreasing functionssuppose f is a function defined over interval i.for :a) f increases on i if b) f decreases on i if interval notationaverage rate of change, non-linear functionrate of change from x = 1 to x = 3rate of change of us pop, 1800 1840, 1900 1940yearpopulation180051840

14、171900761940132the difference quotientfind first, then difference quotient.ch 2 linear functions and equations2.1 equations of linespoint-slope formx intercept , y intercept slope passing through equation of a line passing through , alternate method slope-intercept formequation of a line passing thr

15、ough , apple sold 55m ipods in 2008, and 43m in 2011 determine x and y interceptsequations of horizontal and vertical linesan equation of a horizontal line with y intercept is . an equation of the vertical line with x intercept is .vertical and horizontal lines through finding parallel linestwo line

16、s with slopes and , neither of which are vertical, are parallel if and only if .find the equation of a line parallel to the line , passing through .finding perpendicular linestwo lines with slopes and , neither of which are vertical, are perpendicular if and only if their slopes have product , i.e.f

17、ind the equation of a line perpendicular to the line , passing through .determining a rectangleinterpolation and extrapolationin 2005, about $350m was spent on us musical downloads. this amount reached $1350m in 2010. model, find value in 2008, 2003.20032005200820103501350investments in cloud comput

18、ingyear20052006200720082009investments26113195299374model the dataestimate investments in 20142.2 linear equationsequation statement that two expressions are equalsolve find variable value(s) that make stmt truesolution set set of the values that make it trueequivalent two stmts with same solution s

19、etcontradiction equation with no solution setidentity equation with infinite solution seta linear equation in one variable is an equation that can be written in the form(an equation that is not linear is called non-linear)addition propertymultiplication property solving linear equations symbolically

20、solving linear equations symbolicallyeliminating fractions and decimalsthe linear function estimates ipod sales (million) during year x. when will sales reach 27 million?contradictions, identities, conditional equationsan equation with one expression on each side of the = sign can be solved by the i

21、ntersection of graphs method.using a graphing calculator; 1. set equal to the left side, and equal to the right side of the equation.2. graph both on one set of coordinates3. points of intersection are ordered pairs that make both sides true at the same time. these ordered pairs solve the equation.t

22、he market share of music on cds held from 1987 to 1998 could be modeled by . during the same period, cassette tape sales could be modeled by . (x=0 indicates year 1987)percentages: suppose 76% of all bicycle riders do not wear helmets. there are 38.7 million riders that do not wear helmets, find tot

23、al ridership.solving for a variableproblem solving1. read problem, understand it. assign variable to what you must find. write other quantities in terms of this variable.2. model it, write the equation. diagram it if necessary.3. solve the equation, state solution4. check your work.work problemsa pu

24、mp can empty a gasoline tank in 5 hours. a smaller pump can empty the same tank in 9 hours. how long will it take both pumps working together to empty the tank?motion problemsin one hour, an athlete runs 10.1 miles by running some at 8mph, the rest at 11 mph. how long did the athlete run at each spe

25、ed?similar trianglesa person 6 feet tall stands 17 feet from a streetlight, and casts an 8 ft shadow. estimate the height of the streetlight.mixturepure water is being added to 153 ml of a solution of 30% hydrochloric acid. how much pure water should be added to dilute to 13%?2.3 linear inequalities

26、sizing approximatemax takeoff weight of aircraftinterstate speeda linear inequality in one variable is an inequality that can be written in the form:, .properties of inequalitieslet a, b, and c represent real numbers1. and are equivalent.2. if , then and are equivalent.3. if , then and are equivalen

27、t.solve symbolicallysolve symbolicallysolve graphicallythe daily payment processing for the company square grew from $1m in march 2011 to $11m in march 2012. model this growth and find when daily volume was $8.5m or less.x intercept methodnumerical solutionslet cost of manufacturing be and revenue b

28、e expressed by . profit is expressed by revenue minus cost.boundary number (break even point)x171819202122230102030solve numerically.x1234567y181383-2-7-12x4.9y1.51.50-.5-1-1.5compound inequalitiesspeed limit on interstate 35sunset in bostonin boston, the sun set at 7pm on the 82nd

29、 day (22 mar), and at 8pm on the 136th day (15 may).find the days when the sun set between 7:15pm and 7:45pm. (do not include fall dates).symbolicgraphical 2.4 more modeling with functionsto model a quantity that is changing at a constant rate, with, f(x)=(const rate of chg)x + (initial value)model

30、each situation and state the domain:(a) in 2011, the average cost of attending a public college was $8200, and it is projected to increase, on average, by $600 per year until 2014.(b) a cars initial speed is 50 mph, then it begins to slow down at a constant rate of 10 mph each second.a 100 gallon ta

31、nk is initially full of water and being drained at 5 gallons per minute.formula?how much water is in the tank after 4 minutes? emissionsx miles240360680800y pounds150230435510slopes? linear? piecewise defined functionsfirst-class mail rates first ounce $0.46each additional ounce $0.20first-class mai

32、l rates weight notover(ounces) rate 1 0.46 2 0.66 domain?3 0.86 4 1.06 range?tornadofujita scale housing startsyear2000200520112012homes0.5graph, interpret, continuous? modelevaluating a piecewise-defined functionpiecewise defined functiondomain?continuous?greatest integer function, the gre

33、atest integer xdirect variationy is directly proportional to x, or y varies directly with x, if there is a non-zero number such thatthe number k is called the constant of proportionality or the constant of variation.wages $57.75 for 7 hours worksuppose t varies directly with x, and that when . find

34、t when .a 12-pound weight is hung on a spring and it stretches 2 inches.find the spring constant (const of var)how far will it stretch with a 19lb weight on it?megabytes needed for y sec of musicx (mb)0.230.491.161.275.00y (sec)10.722.855.260.246.546.547.647.4computing for each entry 3rd row, approx

35、imate constant of proportionality.using constant of proportionality, how much music would a fd hold?2.5 absolute value equations and inequalitiesabsolute value functionprimary square root if , then .absolute value equationsfor any positive number k, is equivalent to graphicalnumericaltblset symbolic

36、interstate speed limits: two absolute valuesabsolute value inequalitieslet the solutions to be and , with , and .1. is equivalent to .2. is equivalent to .absolute value inequalities (alternative method)let k be a positive number.1. is equivalent to 2. is equivalent to error tolerances on iphone 4st

37、he iphone 4s is 4.5” high. suppose actual height a of any particular phone has an error tolerance of 0.005”.model and quantifych 3 quadratic functions and equations3.1 quadratic functions and modelslinearlet a, b, and c be real numbers with . a function represented by is a quadratic function.domain

38、is , leading coefficient is a.graph parabolavertex, axis of symmetry standard formvertex formthe parabolic graph of with has vertex . its graph opens upward when , and opens downward when .vertex form from graphconverting to standard formconverting to vertex form the vertex of the graph with is the

39、point .find the vertex of .symbolic, graphical, numericalnote: for axis of symmetry ,converting to vertex form:graph a farmer is fencing a rectangular area for cattle using the straight portion of a river as one side of the rectangle. if the farmer has 2400 feet of fence, find the dimensions of the

40、rectangle that will give the maximum area for the cattle.models and applications a baseball is hit straight up with an initial velocity of feet per second and leaves the bat at an initial height of feet.write a formula for the height of the ball at t seconds. what is the height of the ball after 2 s

41、econds?what is the maximum height of the baseball?athletes heart rate024682001501109080modeling quadratic data 23456101-21103.2 quadratic equations and problem solvinga quadratic equation in one variable is an equation that can be written in the form , where a, b, and c are real numbers with .findin

42、g the x-interceptssquare root propertylet k be a nonnegative number. then the solutions to the equation are given by .determine if either equation represents a function.completing the squarethe solutions of the quadratic equation with arean athletes heart rate was modeled in the last section as . de

43、termine when the rate was 110 beats per minute.quadratic equation - paraboladiscriminantto determine the number of real solutions to the quadratic equation , with , evaluate the discriminant . is a perfect squareconstructiona box is being constructed by cutting 2 inch squares from the corners of a r

44、ectangular piece of cardboard that is 6 inches longer than it is wide. if the box has a volume of 224 cubic inches, find the dimensions of the cardboard.revenuea company charges $5 for earbud headphones, but it reduces this cost by 5¢ for each additional pair ordered (up to 50). if the total pr

45、ice is $95, how many earbuds were ordered?projectile motion0246896400576624544model it, find max height, and impact to ground 3.3 complex numbersnumbers natural roman numerals zero represent nothing? negative numbersrectangledebt properties of the imaginary unit icomplex numbersif , then .addition and subtractionmultiplicationdivisionthe conjugate of is powers of isolving quadratics3.4 quadratic inequalitiessafe stopping distancevisual distance limited to 200 feetgraphicalto solve sym