MATH College Algebra Review for Test 4

Transcription

1 MATH College Algebra Review for Test 4 Section Solve exactly: log 3 2x +11) = 4 2. Solve, rounded to the nearest thousandth: 4 x 1 = 3 x 3. Solve exactly: 25.7) x 7 =15 4. Solve exactly: log 2 3x 4) log 2 2x 5) = 3 5. Solve exactly: log 3 x + 4) + log 3 x 2) = 3 6. Suppose 5,000 is deposited in a saving account that earns 8 interest compounded quarterly. How many years will it take for the account to double in value? The formula for compounded savings is A = P 1+ r nt. Round your answer to the nearest hundredth of a year. n& 7. The concentration of a drug in a patient s bloodstream after t hours is modeled by the formula Ct) = ) t, where C is measured in milligrams per liter. How long rounded to the nearest hundredth of an hour) does it take for the concentration to reach 10 milligrams per liter? Section If f x, y) = 2x 2 3xy, determine f 2,3). In Problems 9-11, solve the systems exactly. 9. y = x 2 2x + y = 8 x 2 + y 2 = x y = x 2 + y 2 = 25 x 2 + 2y = A jet airliner travels 1200 miles in 4 hours with a tail wind. The return trip, into the wind, takes 5 hours. Find both the speed of the jet with no wind and the speed of the wind. 13. The electrical power P generated by a windmill varies jointly as the square of the diameter d of the area swept out by the blades and the cube of the wind velocity v. If a windmill with a 10 foot diameter and a 20 mile per hour wind generates 8000 watts, how much power would be generated if the blades swept out an area 20 feet in diameter and the wind was 10 miles per hour? Section A total of 10,000 is invested in three mutual funds. In one year the first fund grew by 4, the second by 5, and the third by 8. Total earnings for the year were 595. The amount invested in the third fund was 1000 more than the amount invested in the first fund. DEFINE YOUR VARIABLES AND SET UP THE SYSTEM OF EQUATIONS NEEDED TO DETERMINE THE AMOUNT INVESTED AT EACH RATE. YOU DO NOT NEED TO SOLVE THE SYSTEM.

2 MATH College Algebra - Review for Test 4 Thomason) - p. 2 of Four hundred tickets were sold for a play, generating total sales of The prices of the tickets were 3 for children, 5 for students, and 8 for adults. The number of student tickets sold was 110 more than the number of adult tickets sold. DEFINE YOUR VARIABLES AND SET UP THE SYSTEM OF EQUATIONS NEEDED TO DETERMINE THE NUMBER OF EACH TYPE OF TICKET SOLD. YOU DO NOT NEED TO SOLVE THE SYSTEM. 16. Solve the system exactly by any method: x 2z = 5 2x + y = 2 & 3x + 4y z = 5 Section a) Represent the following linear system of equations by an augmented matrix. YOU DO NOT NEED TO SOLVE THE SYSTEM OF EQUATIONS. 5x + 3y + 7z = 0 2x + 4y z = 9 & 3x + 6z = 8 b) State the dimension of the matrix you wrote for Part a). 18. Each of the following augmented matrices represents a system of linear equations involving the variables x, y, and z. In each case, if there is exactly one solution, give it; if there is no solution, so state; and if there are infinitely many solutions, give the solution in parametric form a) Section 6.5 2& b) & If A = 2 3 & and B = 1 5 &, determine 3A 2B If A = & & and B = , determine AB, if possible & 21. If A = 0 1 and B = &, determine AB, if possible c) & 5 2

3 MATH College Algebra - Review for Test 4 Thomason) - p. 3 of a) The tables below concern three students who are co-enrolled at ACC and U.T. Austin. The table on the left gives the number of semester hours each student is taking at each institution. The table on the right gives the cost per semester hour at each institution. Write a matrix A and a column matrix B based on these following tables. ACC U.T. Austin Student Student Student Cost per Semester Hour ACC 30 U.T. Austin 50 b) Determine the matrix product AB. c) Interpret the 3rd row, 1st column entry in the product A Section Let A = 1 2. Determine A & x 2y 3z = a) Write the system x + y z = 2 & x y + 2z = 0 in the form AX = B. b) Use your calculator to determine A 1. c) Solve the system by computing X = A 1 B. 25. Solve the system exactly by any method: 2x + 6y 2z = 2 3x + 4 y + 5z = 10 & 4x + 3y 4z = 5 Variation Handout 26. According to Hookes Law, the amount s that a spring is stretched varies directly with the amount of force F that is applied to the spring. For a particular spring, a force of 12 pounds stretches the spring 8 inches. How much force must be applied to the spring to stretch it 10 inches? 27. Suppose that y is inversely proportional to x and that y = 9 when x = 5. What is the value of y when x =15? 28. The data shown in the table at the right satisfy the equation y = kx n, where n is a positive integer. Determine k and n. 29. The data shown in the table at the right satisfy the equation y = k, where n is a positive integer. n x Determine k and n. x 4 12 y x 9 27 y 324 4

4 MATH College Algebra - Review for Test 4 Thomason) - p. 4 of The electrical resistance R of a wire varies inversely as the square of its diameter d. If a wire with a diameter of 3 millimeters has a resistance of 0.4 ohm, what is the resistance of a wire of the same length if its diameter is 2 millimeters? 31. The variable z varies directly with the third power of x and inversely with the second power of y. When x is 5 and y is 4, z is Determine the formula for z in terms of x and y. 32. According to a law of physics, the load L that a beam can support varies jointly with its width w and the square of it height h and inversely with it length. A beam made of a certain material is 12 feet long, 4 inches wide, and 5 inches high and supports 1200 pounds. How much could a beam of the same material support if it were 6 feet long, 2 inches wide, and 10 inches high? Answers log11 log5.7 or ln11 ln5.7 etc. The base of the logarithm used doesnt matter.) yr hr ,16), 2,4) , 3 10), 10,3 10 ) 11. 0,5), 4, 3), 4, 3) 12. plane: 270 mph, wind: 30 mph watts 14. Let x, y, and z be the invested amounts that grew by 4, 5, and 8, respectively. x + y + z =10, x y z = 595 z = x Let c be the number of children tickets sold, let s be the number of student tickets sold, and let a be the number of adult tickets sold. c + s + a = 400 3c + 5s + 8a = 2260 s = a ,0, 2) 17. a) a) One solution: x = 2, y = 3, z = 7 0& 9 8 b) 3 4 b) Infinite number of solutions: 1 2z,3 4z, z), where z is any real number c) No solution

5 MATH College Algebra - Review for Test 4 Thomason) - p. 5 of & & & a) A = 9 6, B = b) AB = & & 640& c) 640 is the total amount Student 3 spent on tuition at ACC and U.T. Austin, combined & x& 10& 5 2 & 24. a) y = z & b) A 1 = c) 4,0, 2) 25. 2, 1,0) pounds k =1.25, n = k = 2,125,764, n = ohm 31. z = 512 x3 y pounds