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A. Determine whether each of the following arguments is an example of inductive reasoning or deductive reasoning. 1. All home improvements cost more than the estimate. The engineer estimated that a home improvement will cost P100,000. Thus, it will cost more than P100,000. 2. All students in ADMU are smart. Mary Ann is a ADMU student. Therefore, Mary Ann is smart. 3. All passenger Jeepneys in Metro Manila are at least 10 years old. This jeepney is from Metro Manila. Therefore, this is at least 10 years old.

A. Determine whether each of the following arguments is an example of inductive reasoning or deductive reasoning. 1. All home improvements cost more than the estimate. The engineer estimated that a home improvement will cost P100,000. Thus, it will cost more than P100,000. 2. All students in ADMU are smart. Mary Ann is a ADMU student. Therefore, Mary Ann is smart. 3. All passenger Jeepneys in Metro Manila are at least 10 years old. This jeepney is from Metro Manila. Therefore, this is at least 10 years old.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4G u 8:42 O 0.00 KB/s 94 Chapter III - Rev.. Chapter 3 Review Problems A. Determine whether each of the following arguments is an example of inductive reasoning or deductive reasoning. 1. All home improvements cost more than the estimate. The engineer estimated that a home improvement will cost P100,000. Thus, it will cost more than P100,000. 2. All students in ADMU are smart. Mary Ann is a ADMU student. Therefore, Mary Ann is smart. 3. All passenger Jeepneys in Metro Manila are at least 10 years old. This jeepney is from Metro Manila. Therefore, this is at least 10 years old. 4. All engineers are men. My sister is an engineer. Therefore, my sister is a man. 5. Squares have four sides. Rectangles have four sides. Therefore, squares are rectangles. 6. Obtuse angles are greater than 180°. This angle is 190°. Therefore, this angle is obtuse. 7. It takes 2 hours to get to the school. If Peter leaves at 12 noon, he will reach the school by 2 o'clock in the afternoon. 8. All men are good-looking. Some teachers are good looking. Therefore, some teachers are men. B. Use Polya's four-step problem-solving strategy to solve each of the following exercises. 1. Find two consecutive positive integers whose product is 240. 2. The denominator of each fraction exceeds its numerator by 4. If 6 is added to the numerator and 2 is subtracted from the denominator, the resulting fraction equals to 5. Find the fraction. (Hint: Use rational expression) 3. Soledad is going to buy 30 multi-vitamin capsules, some P10 and some P18. If she has P340, what is the maximum number of P18 multi-vitamin capsules she can buy? (Use inequality) 4. How many different ways can a manager and supervisor select from an IT company branch in Manila if there are 8 employees available? (Hint: Use permutation) 5. The population of a small island is growing continuously at the rate of 2% per year. Estimate to the nearest thousand the population of the island after 20 years, given that the population is now 70,000. (Hint: Use continuous growth formula) 6. Find the sum of the first ten terms of the arithmetic sequence in which the first is 3 and the difference of each term is 4. C. Write the first five terms of the sequence whose nth term is given by the formula 1. an = 1 –2n 4. an - (n + 1)² 1 a, - 2. an = n³ – 1 5. n+1 3. a.- 6. an = n² + 2n 11 D. Use the difference table to predict the next term in the sequence. 1. 3, 10, 17, 24, 31, ... 2. 1,4, 9, 16, 25, 36, ... 3. 3,6, 11, 18, 27, ... 4. 15, 36, 77, 144, 243, 5. 12, 45, 98, 171, 264, ... 6. 13, 20, 27, 34, 41, 48, ... 7. 1, 12, 23, 34, 45, 56, ... 8. 0,7, 26, 63, 124, ... 9. 8, 11, 14, 17, 20, ... 10. 2, 5, 10, 17, 26, ... E. Write down a sequence for the number of shapes/dots in each pattern. Explain how to obtain the next number, 1.
Transcribed Image Text:4G u 8:42 O 0.00 KB/s 94 Chapter III - Rev.. Chapter 3 Review Problems A. Determine whether each of the following arguments is an example of inductive reasoning or deductive reasoning. 1. All home improvements cost more than the estimate. The engineer estimated that a home improvement will cost P100,000. Thus, it will cost more than P100,000. 2. All students in ADMU are smart. Mary Ann is a ADMU student. Therefore, Mary Ann is smart. 3. All passenger Jeepneys in Metro Manila are at least 10 years old. This jeepney is from Metro Manila. Therefore, this is at least 10 years old. 4. All engineers are men. My sister is an engineer. Therefore, my sister is a man. 5. Squares have four sides. Rectangles have four sides. Therefore, squares are rectangles. 6. Obtuse angles are greater than 180°. This angle is 190°. Therefore, this angle is obtuse. 7. It takes 2 hours to get to the school. If Peter leaves at 12 noon, he will reach the school by 2 o'clock in the afternoon. 8. All men are good-looking. Some teachers are good looking. Therefore, some teachers are men. B. Use Polya's four-step problem-solving strategy to solve each of the following exercises. 1. Find two consecutive positive integers whose product is 240. 2. The denominator of each fraction exceeds its numerator by 4. If 6 is added to the numerator and 2 is subtracted from the denominator, the resulting fraction equals to 5. Find the fraction. (Hint: Use rational expression) 3. Soledad is going to buy 30 multi-vitamin capsules, some P10 and some P18. If she has P340, what is the maximum number of P18 multi-vitamin capsules she can buy? (Use inequality) 4. How many different ways can a manager and supervisor select from an IT company branch in Manila if there are 8 employees available? (Hint: Use permutation) 5. The population of a small island is growing continuously at the rate of 2% per year. Estimate to the nearest thousand the population of the island after 20 years, given that the population is now 70,000. (Hint: Use continuous growth formula) 6. Find the sum of the first ten terms of the arithmetic sequence in which the first is 3 and the difference of each term is 4. C. Write the first five terms of the sequence whose nth term is given by the formula 1. an = 1 –2n 4. an - (n + 1)² 1 a, - 2. an = n³ – 1 5. n+1 3. a.- 6. an = n² + 2n 11 D. Use the difference table to predict the next term in the sequence. 1. 3, 10, 17, 24, 31, ... 2. 1,4, 9, 16, 25, 36, ... 3. 3,6, 11, 18, 27, ... 4. 15, 36, 77, 144, 243, 5. 12, 45, 98, 171, 264, ... 6. 13, 20, 27, 34, 41, 48, ... 7. 1, 12, 23, 34, 45, 56, ... 8. 0,7, 26, 63, 124, ... 9. 8, 11, 14, 17, 20, ... 10. 2, 5, 10, 17, 26, ... E. Write down a sequence for the number of shapes/dots in each pattern. Explain how to obtain the next number, 1.
4G n 8:53 C 15.8 KB/s 93 Chapter III - Rev.. Dut berore tne Science major. L English major. The Science major and Emelita leave for school at the same time. The Filipino major lives next door to Gina. 3. In a game of chess, a queen can travel any number of squares in a straight line - horizontally, vertically, or diagonally. Moving the queen from Queen (Q) to King (K) visiting each square exactly once with the minimum number of moves possible. 6. A snail is at the foot of a flight of ten steps. Everyday it will climb up three steps and clins back down two steps. When will it reach the top? 7. Given a symmetrical Greek cross from which has been cut a square piece. The area is exactly equal to the area of one of the arms of the cross. Cut the mutilated cross into four pieces and then rearranged them to form a square. 8. Arranged all twelve (12) numbers from 1 – 12 in the box below without being close to the numbers that follow or precede them. 9. Suppose we need to measure exactly 1 liter of water. All that we have are two containers. The smaller container holds 3 liters and the larger holds 5 liters. How can we use these two containers to measure exactly 1 liter of water? 5 liters 3 liters 10. Show how to move 3 matches to make 3 squares all the same size. 3/3
Transcribed Image Text:4G n 8:53 C 15.8 KB/s 93 Chapter III - Rev.. Dut berore tne Science major. L English major. The Science major and Emelita leave for school at the same time. The Filipino major lives next door to Gina. 3. In a game of chess, a queen can travel any number of squares in a straight line - horizontally, vertically, or diagonally. Moving the queen from Queen (Q) to King (K) visiting each square exactly once with the minimum number of moves possible. 6. A snail is at the foot of a flight of ten steps. Everyday it will climb up three steps and clins back down two steps. When will it reach the top? 7. Given a symmetrical Greek cross from which has been cut a square piece. The area is exactly equal to the area of one of the arms of the cross. Cut the mutilated cross into four pieces and then rearranged them to form a square. 8. Arranged all twelve (12) numbers from 1 – 12 in the box below without being close to the numbers that follow or precede them. 9. Suppose we need to measure exactly 1 liter of water. All that we have are two containers. The smaller container holds 3 liters and the larger holds 5 liters. How can we use these two containers to measure exactly 1 liter of water? 5 liters 3 liters 10. Show how to move 3 matches to make 3 squares all the same size. 3/3
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