WeBWorK demonstration assignment

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1 WeBWorK demonstration assignment The main purpose of this WeBWorK set is to familiarize yourself with WeBWorK. Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK change your password. Find out how to print a hard copy on the computer system that you are going to use. Print a hard copy of this assignment. Get to work on this set right away and answer these questions well before the deadline. Not only will this give you the chance to figure out what s wrong if an answer is not accepted, you also will avoid the likely rush and congestion prior to the deadline. The primary purpose of the WeBWorK assignments in this class is to give you the opportunity to learn by having instant feedback on your active solution of relevant problems. Make the best of it!.( pt) Answer all parts of the question. Given the equation 4x 8y 3, a) the x-intercept is ; b) the y-intercept is ; c) if x is, then y ; d) if y is 5, then..( pt) A road rises.4 feet for every 00 feet travelled. How far must one travel to rise a mile (580 feet)? Answer: mile(s). 3.( pt) Write down the equation of the line through the point 3 69 which is parallel to the line through the points 5 8 and 7 4. y x. 4.( pt) Let f x 3x 3 3x x. Find f. 5.( pt) The domain of the function f x 46 9x 34 is all real numbers x except for x where x equals 6.( pt) The domain of the function f x x 9x 8 consists of one or more of the following intervals: A, A B and B where A B. Find A Find B For each interval, answer YES or NO to whether the interval is included in the solution. A A B B 7.( pt) The solution of the equation x x x 7 x 3 is. (You may enter your answer as a decimal number or as a fraction.) 8.( pt) You are hiking along the California coast and wonder about the height of a particular Giant Redwood tree. You are 5 feet and nine inches tall and your shadow is 3 feet long. The shadow of the tree is 46 feet long. How tall is the tree? Enter its height here: feet. 9.( pt) Let F denote a certain temperature in degrees Fahrenheit, and C the same temperature in degrees Celsius. Then you can convert between F and C by the formula F C Suppose the temperature is 3 degrees Celsius. Enter here the corresponding temperature in degrees Fahrenheit. 0.( pt) Suppose a mining company will supply 7000 tons of ore per month if the price is 90 dollars per ton but will supply 6500 tons per month if the price is 5 dollars per ton. Assuming the supply function is of the form y mx b, find the slope, m and y-intercept, b m : b:

2 WeBWorK demonstration assignment The main purpose of this WeBWorK set is to familiarize yourself with WeBWorK. Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK change your password. Find out how to print a hard copy on the computer system that you are going to use. Print a hard copy of this assignment. Get to work on this set right away and answer these questions well before the deadline. Not only will this give you the chance to figure out what s wrong if an answer is not accepted, you also will avoid the likely rush and congestion prior to the deadline. The primary purpose of the WeBWorK assignments in this class is to give you the opportunity to learn by having instant feedback on your active solution of relevant problems. Make the best of it!.( pt) Find the x and y intercepts and the coordinates of the vertex of the parabola f x 4 x x 6 () Then the smaller one of the x intercept is and the larger one of the x intercept is () y intercept is (3) x coordinate of the vertex h k : h = and y coordinate of the vertex h k : k =.( pt) Find the number of units sold that produces a maximum revenue from the total revenue function, R 600x 0 x (in dollars) and x is the number of units sold. Answer = 3.( pt) Solve the system. x 8y 8x 70y 3 y 4.( pt) Solve the following system. x 0 y 3 4 x 4y 5 y 5.( pt) Find the point of equilibrium if the demand function for a product is P x and the supply function is P 5 0 x Answer 6.( pt) Solve the system of linear equations x y 7z 4 x y z 3 3x 9y 36z 33 The solutions have the form a bt y c dt z t, where t is any real number. Find a b c d. a b c d 7.( pt) A chemist needs 0 liters of a 5% acid solution. The solution is to be mixed from three solutions whose concentrations are 0% 0%, and 50%. How many liters should the chemist use to satisfy the following a) Use as little as possible of the 50% solution 0% concentration solution in liters 0% concentration solution in liters 50% concentration solution in liters b) Use as much as possible of the 50% solution 0% concentration solution in liters 0% concentration solution in liters 50% concentration solution in liters c) Use liters of the 50% solution 0% concentration solution in liters 0% concentration solution in liters

3 50% concentration solution in liters 8.( pt) Solve the system x y z x 3y z 8 x y 4 y z 9.( pt) A company manufactures and sells bookcases. The selling price is 54 9 (in dollars) per bookcase. The total cost function is linear, and costs amount to (in dollars) for 000 bookcases and 3 0 (in dollars) for 800 bookcases. Find the break-even point., 0.( pt) Suppose that a company has fixed costs of 300 dollars and variable costs of 0 75x 40 dollars per unit, where x is the number of units produced. Suppose further that the selling price of its product is x dollars per unit. Then (a) find the break-even point., and, Note that the first one in x is bigger than the second one in x. (b) find the maximum revenue. (c) what price will maximise profit?

4 WeBWorK demonstration assignment The main purpose of this WeBWorK set is to familiarize yourself with WeBWorK. Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK change your password. Find out how to print a hard copy on the computer system that you are going to use. Print a hard copy of this assignment. Get to work on this set right away and answer these questions well before the deadline. Not only will this give you the chance to figure out what s wrong if an answer is not accepted, you also will avoid the likely rush and congestion prior to the deadline. The primary purpose of the WeBWorK assignments in this class is to give you the opportunity to learn by having instant feedback on your active solution of relevant problems. Make the best of it!.( pt) Find the standard form of the parabola equation, k with vertex (8,-) and passing through the point (6,4). Then h is and k is y a x h and a is:.( pt) (a) Find two quadratic functions, one that opens upward f x x bx c and one that opens downward, g x x bx c whose graphs have x-intercepts (0,0), (7,0). b = c = b = c = (b) Find the vertex of both parabolas in part (a). The vertex h k of the open upward quadratic function is h = k = and the vertex h k of the open downward quadratic function is h = k = 3.( pt) Find the turning point of the graph of f x x 0x The turning point h k has the values h = and k = 4.( pt) In this problem fill in the blanks to make a perfect square. For example, in x 6x x fill in 9 and 3 since x x 6x 9 x 3 4x x. x 8x x. x 0x x. 5.( pt) This is like the preceding problem, except that your answers may be negative x 7 3 x x. x 5 7 x x. x 3 x x. 6.( pt) This is like the preceding problem, except that you have to factor out the leading coefficient. For example, in 3x 3x 3 x fill in 3 4 and 3x 3x x x 4 3 x x 3x x. 3x x 3 x. 7.( pt) In several problems of this set you are asked to solve quadratic equations. These are of the form bx c 0 There are usually two solutions that are either of the form r s or of the form r si where i, and r ax

5 and s are real numbers. Enter r and s. Also enter i if the solution is a conjugate complex pair of numbers, if both solutions are real, or 0 if there is only one real solution. In the last case, also enter s 0. For example, the equation x x 0 has the solution 3 i Enter, sqrt 3, and i here: here. The equation has the solution x x 0 5 Enter, sqrt 5, and here: here. The equation x only has the solution x 4 0 Enter, 0, and 0 here: here. 8.( pt) The equation x x 6 0 has the solution x. 9.( pt) The equation x 6x 8 0 has the solution x. 0.( pt) The equation 3x 3 3x 7 0 has the solution.

6 %$ %$!! Young-Seon Lee WeBWorK problems. WW Prob Lib Math course-section, semester year WeBWorK assignment 4 due 403 at :00 PM..( pt) You ll need to use formatted text mode in order to do this problem: click the formatted text button at the bottom of the page and then click submit answer. If then A 5 9! AB and B 9 7 7!.( pt) You ll need to use formatted text mode in order to do this problem: click the formatted text button at the bottom of the page and then click submit answer. If then A "# 3.( pt) If A '&( Then AB,&( AB "# and B B +&( 6 3! and BA -&( 4.( pt) Solve the following matrix equation for X where Then A ! X X A B and B a b c d! ! a b c d 5.( pt) You ll need to use formatted text mode in order to do this problem: click the formatted text button at the bottom of the page and then click submit answer. If then B = A. 5 9! BA ! and

7 %$ #" %$ Young-Seon Lee WeBWorK problems..( pt) Solve the system using matrices (row operations) y x 7y 7 9x 6y 39.( pt) Solve the system using matrices (row operations) y z x y z 5x 6y z 4 4x y 6z 3 3.( pt) You ll need to use formatted text mode in order to do this problem: click the formatted text button at the bottom of the page and then click submit answer. Given the augmented matrix A, perform each row operation in order, (a) followed by (b) followed by (c). A "# a R 4r b R 3 r c R 3 r r 3 r 3 r WW Prob Lib Math course-section, semester year WeBWorK assignment 5 due 3303 at :00 PM. 4.( pt) If A and B are matrices, and C is a matrix, which of the following are defined? A. CB B. BA C. B A D. AB T E. B C F. C T 5.( pt) You ll need to use formatted text mode in order to do these problems: (Click the formatted text radio button at the bottom of the page and then click submit answer.) If A &( and Then A B,&( 4A T,&( B &(

8 ! %$ %$ Young-Seon Lee WeBWorK problems. WW Prob Lib Math course-section, semester year WeBWorK assignment 6 due 3003 at :00 PM..( pt) For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no solutions.. 5x 0y 0 7x 5y 38 A. No solutions B. Unique solution: 4 y C. Infinitely many solutions D. Unique solution: 0 y 0 E. Unique solution: y 4 F. None of the above. 4x y 4x y 3 A. Unique solution: 3 y B. Unique solution: 0 y 0 C. No solutions D. Unique solution: y 3 E. Infinitely many solutions F. None of the above 3. 5x 6y 0 5x 5y 0 A. Unique solution: 0 y 0 B. No solutions C. Unique solution: y 0 D. Unique solution: 5 y 5 E. Infinitely many solutions F. None of the above 4. x 5y 3 4x 0y 6 A. Unique solution: 0 y 0 B. No solutions 3 C. Unique solution: y 0 D. Infinitely many solutions E. Unique solution: 3 y 6 F. None of the above.( pt) You ll need to use formatted text mode in order to do this problem: click the formatted text button at the bottom of the page and then click submit answer. If then A A 3 4 5! 3.( pt) You ll need to use formatted text mode in order to do this problem: click the formatted text button at the bottom of the page and then click submit answer. If then A "# A "# ( pt) Find the maximum value of the objective function z x 4y subject to the constraint, x 0 y 0 x 4y3 0 x y3 8 x y3 y z 5.( pt) Find the maximum value of the objective function z 5x y subject to the constraint, x 0 y 0 3x y3 5 4x 3y3 30

9 y z

10 Young-Seon Lee WeBWorK problems..( pt) Let Q represent a mass of radioactive radium, where half-life is 70. The quantity of radium present after t years is Q 500 t4 70 (a) Determine the initial quantity ( when t 0 ). Q 0 = (b) Determine the quantity present after 000 years Q 000 =.( pt) Find x such that 5 log 9 3.( pt) Find the domain, x-intercept, and vertical asymptote of y log 5 x 7 6 WW Prob Lib Math course-section, semester year a WeBWorK assignment 7 due 4703 at :00 PM. Domain is x 5 a, where a x-intercept is x int Vertical asymptote, x asy 4.( pt) Find numbers a b c so that log xy 4 z 4 alog x blog y clog z b c 5.( pt) Find the exact value of log 4 log 4 3 3ln e 4 ln 4 e 3

11 Young-Seon Lee WeBWorK problems..( pt) Solve for x exactly.( pt) Solve for x ln x ln x 6 ln x 3.( pt) The population of a city is P 40057e 07 06t WW Prob Lib Math course-section, semester year WeBWorK assignment 8 due 4403 at :00 PM.,where t 0 represents the year 000. According to this model, when will the population reach 7599? t 4.( pt) The half-life of radioactive radium is 60 years. What percent of a present amount of radioactive radium will remain after 80 years? % 5.( pt) Determine the principal P that must be invested at a rate of %, compounded monthly, so that dollars will be available for retirement in 3 years. P

12 Young-Seon Lee WeBWorK problems. WW Prob Lib Math course-section, semester year WeBWorK assignment 9 due 403 at :00 PM..( pt) What is the seventh term ( n starting with ) of the sequence a n n 8 n n 9 Answer:.( pt) If a 3 9 and a 5 7 and a n is arithmetic, then find a 00 a 00 3.( pt) If a n is geometric, a 5 and r find a then Answer= 4.( pt) Evaluate the following expressions. (a) lne 5 (b) e ln5 (c) e ln: (d) ln e 4 5.( pt) If 5000 dollars is invested in a bank account at an interest rate of 4 percent per year, Find the amount in the bank after 4 years if interest is compounded continuously: How long will it take for 5000 dollars to increase by a factor of two if interest is compounded continuously?

Peter Alfeld. WeBWorK assignment number 1. Math 1090, Fall 2006, Section 3 Professor Margalit

Peter Alfeld. WeBWorK assignment number 1. Math 1090, Fall 2006, Section 3 Professor Margalit Math 1090, Fall 2006, Section 3 Professor Margalit Peter Alfeld WeBWorK assignment number 1 due 9/11/06 at 5:00 PM The main purpose of this first WeBWorK set is to review some prerequisites for this class