# Trigonometry and Analytical Geometry

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Vovevabyn

Mathematics

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A local buffet charges \$7.50 per person for the lunch buffet and \$9.25 for the dinner buffet. If 27 people went out to eat and the total bill was \$227.00 before taxes, how many went to lunch and how many went to dinner?

A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1white, and 2 red. They used 95 black, 100 white and 90 red wires. How many of each cable were made?

On an 18-hole golf course, there are par-3 holes, par-4 holes, and par-5 holes. A golfer who shoots par on every hole has a score of 73. The sum of the number of par-3 holes and the number of par-5 holes is 11. How many of each type of hole are there on the golf course?

Michael's bank contains only nickels, dimes, and quarters. There are 58 coins in all, valued at \$ 4.40. The number of nickels is 2 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

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MATH 108 Trig 1. (10 pts) Identify which matrices are in row echelon or in reduced row echelon form. Subsequently write the system of equations corresponding to the matrices in question. , 2. (10 pts) Represent the system of equations in the matrix representation and solve it by deriving row echelon and reduced row echelon form of these matrices. Show all intermediate steps with their explanation. -5x+y = 17 x+y = 5 3. (10 pts) Solve equations. 3x - 6y = -39 4x + 6y = 74 4. (10 pts) Solve equations. -6x + 12y = -12 3x + 6y = 6 5. (10 pts) Solve equations. 2x + 2y + z = 14 2x - 3y - z = 3 3x + y + 4z = 10 6. (10 pts) Solve equations. 8x + 5y - z = 89 x + 6y + 8z = 65 -2x + y + z = -5 7. (10 pts) Solve a problem. A local buffet charges \$7.50 per person for the lunch buffet and \$9.25 for the dinner buffet. If 27 people went out to eat and the total bill was \$227.00 before taxes, how many went to lunch and how many went to dinner? 8. (10 pts) Solve a problem. A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1white, and 2 red. They used 95 black, 100 white and 90 red wires. How many of each cable were made? 9. (10 pts) Solve a problem. On an 18-hole golf course, there are par-3 holes, par-4 holes, and par-5 holes. A golfer who shoots par on every hole has a score of 73. The sum of the number of par-3 holes and the number of par-5 holes is 11. How many of each type of hole are there on the golf course? 10. (10 pts) Solve a problem. Michael's bank contains only nickels, dimes, and quarters. There are 58 coins in all, valued at \$ 4.40. The number of nickels is 2 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank? MATH 108 Trig 1. Identify which matrices are in row echelon or in reduced row echelon form. Subsequently write the system of equations corresponding to the matrices in question. , 2. Represent the system of equations in the matrix representation and solve it by deriving row echelon and reduced row echelon form of these matrices. Show all intermediate steps with their explanation. -5x+y = 17 x+y = 5 3. Solve equations. 3x - 6y = -39 4x + 6y = 74 4. Solve equations. -6x + 12y = -12 3x + 6y = 6 5. Solve equations. 2x + 2y + z = 14 2x - 3y - z = 3 3x + y + 4z = 10 6. Solve equations. 8x + 5y - z = 89 x + 6y + 8z = 65 -2x + y + z = -5 7. Solve a problem. A local buffet charges \$7.50 per person for the lunch buffet and \$9.25 for the dinner buffet. If 27 people went out to eat and the total bill was \$227.00 before taxes, how many went to lunch and how many went to dinner? 8. Solve a problem. A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1white, and 2 red. They used 95 black, 100 white and 90 red wires. How many of each cable were made? 9. Solve a problem. On an 18-hole golf course, there are par-3 holes, par-4 holes, and par-5 holes. A golfer who shoots par on every hole has a score of 73. The sum of the number of par-3 holes and the number of par-5 holes is 11. How many of each type of hole are there on the golf course? 10. Solve a problem. Michael's bank contains only nickels, dimes, and quarters. There are 58 coins in all, valued at \$ 4.40. The number of nickels is 2 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?
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