Pearson eText Algebra and Trigonometry -- Instant Access (Pearson+)
11th Edition
ISBN: 9780136872689
Author: Michael Sullivan
Publisher: PEARSON+
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 1, Problem 1RE
To determine
To solve: The equation
Expert Solution & Answer
Answer to Problem 1RE
The solution of the equation
Explanation of Solution
Consider the given equation
Obtain the solution as follows.
Thus, the solution of the equation
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Use the graph to solve 3x2-3x-8=0
Într-un bloc sunt apartamente cu 2 camere și apartamente cu 3 camere , în total 20 de apartamente și 45 de camere.Calculați câte apartamente sunt cu 2 camere și câte apartamente sunt cu 3 camere.
1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k
components, where k is the greatest common divisor of {n, r,s}.
Chapter 1 Solutions
Pearson eText Algebra and Trigonometry -- Instant Access (Pearson+)
Ch. 1.1 - Prob. 1AYUCh. 1.1 - Prob. 2AYUCh. 1.1 - Prob. 3AYUCh. 1.1 - Prob. 4AYUCh. 1.1 - Prob. 5AYUCh. 1.1 - Prob. 6AYUCh. 1.1 - Prob. 7AYUCh. 1.1 - Prob. 8AYUCh. 1.1 - Prob. 9AYUCh. 1.1 - Prob. 10AYU
Ch. 1.1 - In Problems 11–18, mentally solve each...Ch. 1.1 - In Problems 11–18, mentally solve each...Ch. 1.1 - In Problems 11–18, mentally solve each...Ch. 1.1 - Prob. 14AYUCh. 1.1 - In Problems 11–18, mentally solve each...Ch. 1.1 - Prob. 16AYUCh. 1.1 - In Problems 11–18, mentally solve each...Ch. 1.1 - Prob. 18AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 20AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 22AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 24AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 26AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 28AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 30AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 32AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 34AYUCh. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - In Problems 19–68, solve each equation, if...Ch. 1.1 - Prob. 38AYUCh. 1.1 - Prob. 39AYUCh. 1.1 - Prob. 40AYUCh. 1.1 - Prob. 41AYUCh. 1.1 - Prob. 42AYUCh. 1.1 - Prob. 43AYUCh. 1.1 - Prob. 44AYUCh. 1.1 - Prob. 45AYUCh. 1.1 - Prob. 46AYUCh. 1.1 - Prob. 47AYUCh. 1.1 - Prob. 48AYUCh. 1.1 - Prob. 49AYUCh. 1.1 - Prob. 50AYUCh. 1.1 - Prob. 51AYUCh. 1.1 - Prob. 52AYUCh. 1.1 - Prob. 53AYUCh. 1.1 - Prob. 54AYUCh. 1.1 - Prob. 55AYUCh. 1.1 - Prob. 56AYUCh. 1.1 - Prob. 57AYUCh. 1.1 - Prob. 58AYUCh. 1.1 - Prob. 59AYUCh. 1.1 - Prob. 60AYUCh. 1.1 - Prob. 61AYUCh. 1.1 - Prob. 62AYUCh. 1.1 - Prob. 63AYUCh. 1.1 - Prob. 64AYUCh. 1.1 - Prob. 65AYUCh. 1.1 - Prob. 66AYUCh. 1.1 - Prob. 67AYUCh. 1.1 - Prob. 68AYUCh. 1.1 - Prob. 69AYUCh. 1.1 - Prob. 70AYUCh. 1.1 - Prob. 71AYUCh. 1.1 - Prob. 72AYUCh. 1.1 - In Problems 73–76, solve each equation. The...Ch. 1.1 - Prob. 74AYUCh. 1.1 - Prob. 75AYUCh. 1.1 - Prob. 76AYUCh. 1.1 - Find the number a for which x = 4 is a solution of...Ch. 1.1 - Prob. 78AYUCh. 1.1 - Problems 79–84 list some formulas that occur in...Ch. 1.1 - Problems 79–84 list some formulas that occur in...Ch. 1.1 - Problems 79–84 list some formulas that occur in...Ch. 1.1 - Prob. 82AYUCh. 1.1 - Problems 79–84 list some formulas that occur in...Ch. 1.1 - Prob. 84AYUCh. 1.1 - Prob. 85AYUCh. 1.1 - Prob. 86AYUCh. 1.1 - Prob. 87AYUCh. 1.1 - Computing Hourly Wages Leigh is paid...Ch. 1.1 - Computing Grades Going into the final exam, which...Ch. 1.1 - Prob. 90AYUCh. 1.1 - Prob. 91AYUCh. 1.1 - Prob. 92AYUCh. 1.1 - Prob. 93AYUCh. 1.1 - Prob. 94AYUCh. 1.1 - Prob. 95AYUCh. 1.1 - Prob. 96AYUCh. 1.1 - Prob. 97AYUCh. 1.1 - Geometry The perimeter of a rectangle is 42...Ch. 1.1 - Prob. 99AYUCh. 1.1 - Prob. 100AYUCh. 1.1 - Prob. 101AYUCh. 1.1 - Prob. 102AYUCh. 1.1 - Prob. 103AYUCh. 1.1 - Prob. 104AYUCh. 1.1 - Prob. 105AYUCh. 1.1 - Prob. 106AYUCh. 1.1 - Prob. 107AYUCh. 1.2 - Factor:
Ch. 1.2 - Factor:
Ch. 1.2 - The solution set of the equation (x – 3) (3x + 5)...Ch. 1.2 - True or False .
Ch. 1.2 - Complete the square of x2 + 5x. Factor the new...Ch. 1.2 - The quantity b2 – 4ac is called the _____ of a...Ch. 1.2 - Prob. 7AYUCh. 1.2 - Prob. 8AYUCh. 1.2 - Prob. 9AYUCh. 1.2 - Prob. 10AYUCh. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - Prob. 12AYUCh. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - Prob. 16AYUCh. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - Prob. 20AYUCh. 1.2 - Prob. 21AYUCh. 1.2 - Prob. 22AYUCh. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - Prob. 24AYUCh. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - Prob. 26AYUCh. 1.2 - Prob. 27AYUCh. 1.2 - Prob. 28AYUCh. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - In Problems 11–30, solve each equation by...Ch. 1.2 - In Problems 31–36, solve each equation by the...Ch. 1.2 - Prob. 32AYUCh. 1.2 - In Problems 31–36, solve each equation by the...Ch. 1.2 - Prob. 34AYUCh. 1.2 - In Problems 31–36, solve each equation by the...Ch. 1.2 - In Problems 31–36, solve each equation by the...Ch. 1.2 - In Problems 37–42, solve each equation by...Ch. 1.2 - In Problems 37–42, solve each equation by...Ch. 1.2 - In Problems 37–42, solve each equation by...Ch. 1.2 - Prob. 40AYUCh. 1.2 - In Problems 37–42, solve each equation by...Ch. 1.2 - In Problems 37–42, solve each equation by...Ch. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 44AYUCh. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 46AYUCh. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 48AYUCh. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 50AYUCh. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 52AYUCh. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 54AYUCh. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 56AYUCh. 1.2 - Prob. 57AYUCh. 1.2 - Prob. 58AYUCh. 1.2 - Prob. 59AYUCh. 1.2 - Prob. 60AYUCh. 1.2 - Prob. 61AYUCh. 1.2 - Prob. 62AYUCh. 1.2 - In Problems 43–66, find the real solutions, if...Ch. 1.2 - Prob. 64AYUCh. 1.2 - Prob. 65AYUCh. 1.2 - Prob. 66AYUCh. 1.2 - In Problems 67–72, find the real solutions, if...Ch. 1.2 - Prob. 68AYUCh. 1.2 - Prob. 69AYUCh. 1.2 - Prob. 70AYUCh. 1.2 - Prob. 71AYUCh. 1.2 - Prob. 72AYUCh. 1.2 - Prob. 73AYUCh. 1.2 - In Problems 73–78, use the discriminant to...Ch. 1.2 - Prob. 75AYUCh. 1.2 - Prob. 76AYUCh. 1.2 - Prob. 77AYUCh. 1.2 - Prob. 78AYUCh. 1.2 - Prob. 79AYUCh. 1.2 - Prob. 80AYUCh. 1.2 - Prob. 81AYUCh. 1.2 - Prob. 82AYUCh. 1.2 - Prob. 83AYUCh. 1.2 - Prob. 84AYUCh. 1.2 - Prob. 85AYUCh. 1.2 - Prob. 86AYUCh. 1.2 - Prob. 87AYUCh. 1.2 - Prob. 88AYUCh. 1.2 - Prob. 89AYUCh. 1.2 - Prob. 90AYUCh. 1.2 - Prob. 91AYUCh. 1.2 - Prob. 92AYUCh. 1.2 - Prob. 93AYUCh. 1.2 - Prob. 94AYUCh. 1.2 - Prob. 95AYUCh. 1.2 - Prob. 96AYUCh. 1.2 - Prob. 97AYUCh. 1.2 - Prob. 98AYUCh. 1.2 - Prob. 99AYUCh. 1.2 - Prob. 100AYUCh. 1.2 - Prob. 101AYUCh. 1.2 - Prob. 102AYUCh. 1.2 - Prob. 103AYUCh. 1.2 - Prob. 104AYUCh. 1.2 - Prob. 105AYUCh. 1.2 - Prob. 106AYUCh. 1.2 - Prob. 107AYUCh. 1.2 - Prob. 108AYUCh. 1.2 - Prob. 109AYUCh. 1.2 - Prob. 110AYUCh. 1.2 - Prob. 111AYUCh. 1.2 - Prob. 112AYUCh. 1.2 - Prob. 113AYUCh. 1.2 - Prob. 114AYUCh. 1.2 - Prob. 115AYUCh. 1.2 - Prob. 116AYUCh. 1.2 - Prob. 117AYUCh. 1.2 - Prob. 118AYUCh. 1.2 - Prob. 119AYUCh. 1.2 - Prob. 120AYUCh. 1.2 - Prob. 121AYUCh. 1.2 - Prob. 122AYUCh. 1.2 - Prob. 123AYUCh. 1.2 - Prob. 124AYUCh. 1.2 - Prob. 125AYUCh. 1.2 - Prob. 126AYUCh. 1.2 - Prob. 127AYUCh. 1.2 - Prob. 128AYUCh. 1.2 - Create three quadratic equations: one having two...Ch. 1.2 - Prob. 130AYUCh. 1.3 - Name the integers and the rational numbers in the...Ch. 1.3 - Prob. 2AYUCh. 1.3 - Rationalize the denominator of .
Ch. 1.3 - In the complex number 5 + 2i, the number 5 is...Ch. 1.3 - True or False The conjugate of 2 + 5i is –2 – 5i.
Ch. 1.3 - True or False All real numbers are complex...Ch. 1.3 - True or False If 2 – 3i is a solution of a...Ch. 1.3 - Prob. 8AYUCh. 1.3 - Prob. 9AYUCh. 1.3 - Prob. 10AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 14AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 16AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 18AYUCh. 1.3 - Prob. 19AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 22AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 26AYUCh. 1.3 - Prob. 27AYUCh. 1.3 - Prob. 28AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 31AYUCh. 1.3 - Prob. 32AYUCh. 1.3 - Prob. 33AYUCh. 1.3 - Prob. 34AYUCh. 1.3 - Prob. 35AYUCh. 1.3 - Prob. 36AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 38AYUCh. 1.3 - In Problems 11–58, perform the indicated...Ch. 1.3 - Prob. 40AYUCh. 1.3 - Prob. 41AYUCh. 1.3 - Prob. 42AYUCh. 1.3 - Prob. 43AYUCh. 1.3 - Prob. 44AYUCh. 1.3 - Prob. 45AYUCh. 1.3 - Prob. 46AYUCh. 1.3 - Prob. 47AYUCh. 1.3 - Prob. 48AYUCh. 1.3 - Prob. 49AYUCh. 1.3 - Prob. 50AYUCh. 1.3 - Prob. 51AYUCh. 1.3 - Prob. 52AYUCh. 1.3 - Prob. 53AYUCh. 1.3 - Prob. 54AYUCh. 1.3 - Prob. 55AYUCh. 1.3 - Prob. 56AYUCh. 1.3 - Prob. 57AYUCh. 1.3 - Prob. 58AYUCh. 1.3 - Prob. 59AYUCh. 1.3 - Prob. 60AYUCh. 1.3 - Prob. 61AYUCh. 1.3 - Prob. 62AYUCh. 1.3 - Prob. 63AYUCh. 1.3 - Prob. 64AYUCh. 1.3 - Prob. 65AYUCh. 1.3 - Prob. 66AYUCh. 1.3 - Prob. 67AYUCh. 1.3 - Prob. 68AYUCh. 1.3 - Prob. 69AYUCh. 1.3 - Prob. 70AYUCh. 1.3 - Prob. 71AYUCh. 1.3 - Prob. 72AYUCh. 1.3 - Prob. 73AYUCh. 1.3 - Prob. 74AYUCh. 1.3 - Prob. 75AYUCh. 1.3 - Prob. 76AYUCh. 1.3 - Prob. 77AYUCh. 1.3 - Prob. 78AYUCh. 1.3 - Prob. 79AYUCh. 1.3 - Prob. 80AYUCh. 1.3 - Prob. 81AYUCh. 1.3 - Prob. 82AYUCh. 1.3 - Prob. 83AYUCh. 1.3 - Prob. 84AYUCh. 1.3 - Prob. 85AYUCh. 1.3 - Prob. 86AYUCh. 1.3 - Prob. 87AYUCh. 1.3 - Prob. 88AYUCh. 1.3 - Prob. 89AYUCh. 1.3 - Prob. 90AYUCh. 1.3 - Prob. 91AYUCh. 1.3 - Prob. 92AYUCh. 1.3 - Prob. 93AYUCh. 1.3 - Prob. 94AYUCh. 1.3 - Prob. 95AYUCh. 1.3 - Prob. 96AYUCh. 1.3 - Prob. 97AYUCh. 1.3 - Prob. 98AYUCh. 1.3 - Prob. 99AYUCh. 1.3 - Prob. 100AYUCh. 1.3 - Prob. 101AYUCh. 1.3 - Prob. 103AYUCh. 1.3 - Prob. 104AYUCh. 1.4 - Prob. 1AYUCh. 1.4 - Prob. 2AYUCh. 1.4 - Prob. 3AYUCh. 1.4 - Prob. 4AYUCh. 1.4 - Prob. 5AYUCh. 1.4 - Prob. 6AYUCh. 1.4 - Prob. 7AYUCh. 1.4 - Prob. 8AYUCh. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - Prob. 14AYUCh. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - Prob. 17AYUCh. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - Prob. 20AYUCh. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - In Problems 9–42, find the real solutions, if any,...Ch. 1.4 - Prob. 40AYUCh. 1.4 - Prob. 41AYUCh. 1.4 - Prob. 42AYUCh. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - Prob. 45AYUCh. 1.4 - Prob. 46AYUCh. 1.4 - Prob. 47AYUCh. 1.4 - Prob. 48AYUCh. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - Prob. 50AYUCh. 1.4 - Prob. 51AYUCh. 1.4 - Prob. 52AYUCh. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - Prob. 68AYUCh. 1.4 - In Problems 43–74, find the real solutions of each...Ch. 1.4 - Prob. 70AYUCh. 1.4 - Prob. 71AYUCh. 1.4 - Prob. 72AYUCh. 1.4 - Prob. 73AYUCh. 1.4 - Prob. 74AYUCh. 1.4 - Prob. 75AYUCh. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - Prob. 77AYUCh. 1.4 - Prob. 78AYUCh. 1.4 - Prob. 79AYUCh. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - In Problems 75–90, find the real solutions of each...Ch. 1.4 - Prob. 89AYUCh. 1.4 - Prob. 90AYUCh. 1.4 - Prob. 91AYUCh. 1.4 - Prob. 92AYUCh. 1.4 - Prob. 93AYUCh. 1.4 - Prob. 94AYUCh. 1.4 - Prob. 95AYUCh. 1.4 - Prob. 96AYUCh. 1.4 - Prob. 97AYUCh. 1.4 - Prob. 98AYUCh. 1.4 - Prob. 99AYUCh. 1.4 - Prob. 100AYUCh. 1.4 - Prob. 101AYUCh. 1.4 - Prob. 102AYUCh. 1.4 - Prob. 103AYUCh. 1.4 - Prob. 104AYUCh. 1.4 - Prob. 105AYUCh. 1.4 - Prob. 106AYUCh. 1.4 - Prob. 107AYUCh. 1.4 - Prob. 108AYUCh. 1.4 - Prob. 109AYUCh. 1.4 - Prob. 110AYUCh. 1.4 - Prob. 111AYUCh. 1.4 - Prob. 112AYUCh. 1.4 - Prob. 113AYUCh. 1.4 - Prob. 114AYUCh. 1.4 - Prob. 115AYUCh. 1.4 - Prob. 116AYUCh. 1.4 - Prob. 117AYUCh. 1.4 - Prob. 118AYUCh. 1.4 - Prob. 119AYUCh. 1.4 - Prob. 120AYUCh. 1.4 - Prob. 121AYUCh. 1.4 - Prob. 122AYUCh. 1.4 - Prob. 123AYUCh. 1.5 - ‘Are You Prepared?’ Answers are given at the end...Ch. 1.5 - ‘Are You Prepared?’ Answers are given at the end...Ch. 1.5 - A(n) _____ ______, denoted [a, b], consists of all...Ch. 1.5 - The _____ _____ state that the sense, or...Ch. 1.5 - In Problems 5–8, assume that a < b and c <...Ch. 1.5 - In Problems 5–8, assume that a < b and c <...Ch. 1.5 - Prob. 7AYUCh. 1.5 - Prob. 8AYUCh. 1.5 - Prob. 9AYUCh. 1.5 - True or False A half-closed interval must have an...Ch. 1.5 - Multiple Choice Which of the following will not...Ch. 1.5 - Prob. 12AYUCh. 1.5 - In Problems 13–18, express the graph shown in blue...Ch. 1.5 - In Problems 13–18, express the graph shown in blue...Ch. 1.5 - In Problems 13–18, express the graph shown in blue...Ch. 1.5 - Prob. 16AYUCh. 1.5 - In Problems 13–18, express the graph shown in blue...Ch. 1.5 - Prob. 18AYUCh. 1.5 - Prob. 19AYUCh. 1.5 - Prob. 20AYUCh. 1.5 - In Problems 19–24, an inequality is given. Write...Ch. 1.5 - Prob. 22AYUCh. 1.5 - Prob. 23AYUCh. 1.5 - Prob. 24AYUCh. 1.5 - In Problems 25–32, write each inequality using...Ch. 1.5 - In Problems 25–32, write each inequality using...Ch. 1.5 - In Problems 25–32, write each inequality using...Ch. 1.5 - Prob. 28AYUCh. 1.5 - In Problems 25–32, write each inequality using...Ch. 1.5 - In Problems 25–32, write each inequality using...Ch. 1.5 - In Problems 25–32, write each inequality using...Ch. 1.5 - In Problems 25–32, write each inequality using...Ch. 1.5 - In Problems 33–40, write each interval as an...Ch. 1.5 - Prob. 34AYUCh. 1.5 - In Problems 33–40, write each interval as an...Ch. 1.5 - Prob. 36AYUCh. 1.5 - In Problems 33–40, write each interval as an...Ch. 1.5 - Prob. 38AYUCh. 1.5 - Prob. 39AYUCh. 1.5 - Prob. 40AYUCh. 1.5 - Prob. 41AYUCh. 1.5 - Prob. 42AYUCh. 1.5 - Prob. 43AYUCh. 1.5 - Prob. 44AYUCh. 1.5 - Prob. 45AYUCh. 1.5 - Prob. 46AYUCh. 1.5 - Prob. 47AYUCh. 1.5 - Prob. 48AYUCh. 1.5 - Prob. 49AYUCh. 1.5 - Prob. 50AYUCh. 1.5 - In Problems 41–58, fill in the blank to form a...Ch. 1.5 - Prob. 52AYUCh. 1.5 - In Problems 41–58, fill in the blank to form a...Ch. 1.5 - Prob. 54AYUCh. 1.5 - In Problems 41–58, fill in the blank to form a...Ch. 1.5 - Prob. 56AYUCh. 1.5 - In Problems 41–58, fill in the blank to form a...Ch. 1.5 - Prob. 58AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 60AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 62AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 64AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 66AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 68AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 72AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 74AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 76AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 78AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 80AYUCh. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - In Problems 59–96, solve each inequality Express...Ch. 1.5 - Prob. 83AYUCh. 1.5 - Prob. 84AYUCh. 1.5 - Prob. 85AYUCh. 1.5 - Prob. 86AYUCh. 1.5 - Prob. 87AYUCh. 1.5 - Prob. 88AYUCh. 1.5 - Prob. 89AYUCh. 1.5 - Prob. 90AYUCh. 1.5 - Prob. 91AYUCh. 1.5 - Prob. 92AYUCh. 1.5 - Prob. 93AYUCh. 1.5 - Prob. 94AYUCh. 1.5 - Prob. 95AYUCh. 1.5 - Prob. 96AYUCh. 1.5 - Prob. 97AYUCh. 1.5 - Prob. 98AYUCh. 1.5 - Prob. 99AYUCh. 1.5 - Prob. 100AYUCh. 1.5 - Prob. 101AYUCh. 1.5 - Prob. 102AYUCh. 1.5 - Prob. 103AYUCh. 1.5 - Prob. 104AYUCh. 1.5 - Prob. 105AYUCh. 1.5 - Prob. 106AYUCh. 1.5 - Prob. 107AYUCh. 1.5 - Prob. 108AYUCh. 1.5 - Prob. 109AYUCh. 1.5 - Prob. 110AYUCh. 1.5 - Prob. 111AYUCh. 1.5 - Prob. 112AYUCh. 1.5 - Prob. 113AYUCh. 1.5 - Prob. 114AYUCh. 1.5 - Prob. 115AYUCh. 1.5 - Prob. 116AYUCh. 1.5 - Prob. 117AYUCh. 1.5 - Prob. 118AYUCh. 1.5 - Prob. 119AYUCh. 1.5 - Prob. 120AYUCh. 1.5 - Prob. 121AYUCh. 1.5 - Prob. 122AYUCh. 1.5 - Prob. 123AYUCh. 1.5 - Prob. 124AYUCh. 1.5 - Prob. 125AYUCh. 1.5 - Prob. 126AYUCh. 1.5 - Prob. 127AYUCh. 1.5 - Prob. 128AYUCh. 1.5 - Prob. 129AYUCh. 1.5 - Prob. 130AYUCh. 1.5 - Prob. 131AYUCh. 1.5 - Prob. 132AYUCh. 1.5 - Prob. 133AYUCh. 1.5 - Prob. 134AYUCh. 1.6 - Prob. 1AYUCh. 1.6 - Prob. 2AYUCh. 1.6 - Prob. 3AYUCh. 1.6 - Prob. 4AYUCh. 1.6 - Prob. 5AYUCh. 1.6 - Prob. 6AYUCh. 1.6 - Prob. 7AYUCh. 1.6 - Prob. 8AYUCh. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - Prob. 23AYUCh. 1.6 - Prob. 24AYUCh. 1.6 - Prob. 25AYUCh. 1.6 - Prob. 26AYUCh. 1.6 - Prob. 27AYUCh. 1.6 - Prob. 28AYUCh. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - In Problems 9–36, find the real solutions, if any,...Ch. 1.6 - Prob. 31AYUCh. 1.6 - Prob. 32AYUCh. 1.6 - Prob. 33AYUCh. 1.6 - Prob. 34AYUCh. 1.6 - Prob. 35AYUCh. 1.6 - Prob. 36AYUCh. 1.6 - Prob. 37AYUCh. 1.6 - Prob. 38AYUCh. 1.6 - Prob. 39AYUCh. 1.6 - Prob. 40AYUCh. 1.6 - Prob. 41AYUCh. 1.6 - In Problems 37–70, solve each inequality. Express...Ch. 1.6 - In Problems 37–70, solve each inequality. Express...Ch. 1.6 - In Problems 37–70, solve each inequality. Express...Ch. 1.6 - In Problems 37–70, solve each inequality. Express...Ch. 1.6 - In Problems 37–70, solve each inequality. Express...Ch. 1.6 - Prob. 47AYUCh. 1.6 - Prob. 48AYUCh. 1.6 - Prob. 49AYUCh. 1.6 - Prob. 50AYUCh. 1.6 - In Problems 37–70, solve each inequality. Express...Ch. 1.6 - Prob. 52AYUCh. 1.6 - Prob. 53AYUCh. 1.6 - Prob. 54AYUCh. 1.6 - Prob. 55AYUCh. 1.6 - Prob. 56AYUCh. 1.6 - Prob. 57AYUCh. 1.6 - Prob. 58AYUCh. 1.6 - Prob. 59AYUCh. 1.6 - Prob. 60AYUCh. 1.6 - Prob. 61AYUCh. 1.6 - Prob. 62AYUCh. 1.6 - Prob. 63AYUCh. 1.6 - Prob. 64AYUCh. 1.6 - Prob. 65AYUCh. 1.6 - Prob. 66AYUCh. 1.6 - Prob. 67AYUCh. 1.6 - Prob. 68AYUCh. 1.6 - Prob. 69AYUCh. 1.6 - Prob. 70AYUCh. 1.6 - Prob. 71AYUCh. 1.6 - Prob. 72AYUCh. 1.6 - Prob. 73AYUCh. 1.6 - Prob. 74AYUCh. 1.6 - Prob. 75AYUCh. 1.6 - Prob. 76AYUCh. 1.6 - Prob. 77AYUCh. 1.6 - Prob. 78AYUCh. 1.6 - Prob. 79AYUCh. 1.6 - Prob. 80AYUCh. 1.6 - Prob. 81AYUCh. 1.6 - Prob. 82AYUCh. 1.6 - Prob. 83AYUCh. 1.6 - Prob. 84AYUCh. 1.6 - Prob. 85AYUCh. 1.6 - Prob. 86AYUCh. 1.6 - Prob. 87AYUCh. 1.6 - Prob. 88AYUCh. 1.6 - Prob. 89AYUCh. 1.6 - Prob. 90AYUCh. 1.6 - Prob. 91AYUCh. 1.6 - Prob. 92AYUCh. 1.6 - Prob. 93AYUCh. 1.6 - Prob. 94AYUCh. 1.6 - Prob. 95AYUCh. 1.6 - Prob. 96AYUCh. 1.6 - Prob. 97AYUCh. 1.6 - Prob. 98AYUCh. 1.6 - Prob. 99AYUCh. 1.6 - Prob. 100AYUCh. 1.6 - Prob. 101AYUCh. 1.6 - Prob. 102AYUCh. 1.7 - The process of using variables to represent...Ch. 1.7 - The money paid for the use of money is _____
Ch. 1.7 - Objects that move at a constant speed are said to...Ch. 1.7 - True or False The amount charged for the use of...Ch. 1.7 - True or False If an object moves at an average...Ch. 1.7 - Multiple Choice Suppose that you want to mix two...Ch. 1.7 - Multiple Choice Which of the following is the...Ch. 1.7 - Multiple Choice If it takes 5 hours to complete a...Ch. 1.7 - In Problems 9–18, translate each sentence into a...Ch. 1.7 - In Problems 9–18, translate each sentence into a...Ch. 1.7 - In Problems 9–18, translate each sentence into a...Ch. 1.7 - In Problems 9–18, translate each sentence into a...Ch. 1.7 - In Problems 9–18, translate each sentence into a...Ch. 1.7 - In Problems 9–18, translate each sentence into a...Ch. 1.7 - Prob. 15AYUCh. 1.7 - Prob. 16AYUCh. 1.7 - Prob. 17AYUCh. 1.7 - Prob. 18AYUCh. 1.7 - Financial Planning Betsy, a recent retiree,...Ch. 1.7 - Prob. 20AYUCh. 1.7 - Banking A bank loaned out $12,000, part of it at...Ch. 1.7 - Prob. 22AYUCh. 1.7 - Prob. 23AYUCh. 1.7 - Prob. 24AYUCh. 1.7 - Prob. 25AYUCh. 1.7 - Prob. 26AYUCh. 1.7 - Physics: Uniform Motion A motorboat can maintain a...Ch. 1.7 - Prob. 28AYUCh. 1.7 - Physics: Uniform Motion A motorboat maintained a...Ch. 1.7 - Prob. 30AYUCh. 1.7 - Prob. 31AYUCh. 1.7 - Prob. 32AYUCh. 1.7 - Prob. 33AYUCh. 1.7 - Prob. 34AYUCh. 1.7 - Working Together on a Job Trent can deliver his...Ch. 1.7 - Working Together on a Job Patrice, by himself, can...Ch. 1.7 - Prob. 37AYUCh. 1.7 - Prob. 38AYUCh. 1.7 - Football A tight end can run the 100-yard dash in...Ch. 1.7 - Prob. 40AYUCh. 1.7 - Prob. 41AYUCh. 1.7 - Prob. 42AYUCh. 1.7 - Prob. 43AYUCh. 1.7 - Prob. 44AYUCh. 1.7 - Prob. 45AYUCh. 1.7 - Prob. 46AYUCh. 1.7 - Prob. 47AYUCh. 1.7 - Prob. 48AYUCh. 1.7 - Emptying Oil Tankers An oil tanker can be emptied...Ch. 1.7 - Prob. 50AYUCh. 1.7 - Prob. 51AYUCh. 1.7 - Prob. 52AYUCh. 1.7 - Prob. 53AYUCh. 1.7 - Prob. 54AYUCh. 1.7 - Prob. 55AYUCh. 1.7 - Prob. 56AYUCh. 1.7 - Prob. 57AYUCh. 1.7 - Prob. 58AYUCh. 1.7 - Prob. 59AYUCh. 1.7 - Prob. 61AYUCh. 1.7 - Prob. 62AYUCh. 1.7 - Prob. 63AYUCh. 1.7 - Prob. 64AYUCh. 1 - Prob. 1RECh. 1 - In Problems 1–27, find the real solutions, if any,...Ch. 1 - In Problems 1–27, find the real solutions, if any,...Ch. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Prob. 52RECh. 1 - Prob. 53RECh. 1 - Prob. 54RECh. 1 - Prob. 55RECh. 1 - Prob. 56RECh. 1 - Prob. 57RECh. 1 - Prob. 58RECh. 1 - Prob. 59RECh. 1 - Prob. 60RECh. 1 - Prob. 1CTCh. 1 - Prob. 2CTCh. 1 - Prob. 3CTCh. 1 - Prob. 4CTCh. 1 - Prob. 5CTCh. 1 - Prob. 6CTCh. 1 - Prob. 7CTCh. 1 - Prob. 8CTCh. 1 - Prob. 9CTCh. 1 - Prob. 10CTCh. 1 - Prob. 11CTCh. 1 - Prob. 12CTCh. 1 - Prob. 13CT
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]arrow_forwardR denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]arrow_forwardQuestion 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]arrow_forward
- part b pleasearrow_forwardQuestion 5 (a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the matrix a cl |df equals 3 and the determinant of determinant of the matrix a+3b cl d+3e f ГЪ e [ c ] equals 2. Compute the [5] (b) Calculate the adjugate Adj (A) of the 2 × 2 matrix [1 2 A = over R. (c) Working over the field F3 with 3 elements, use row and column operations to put the matrix [6] 0123] A = 3210 into canonical form for equivalence and write down the canonical form. What is the rank of A as a matrix over F3? 4arrow_forwardQuestion 2 In this question, V = Q4 and - U = {(x, y, z, w) EV | x+y2w+ z = 0}, W = {(x, y, z, w) € V | x − 2y + w − z = 0}, Z = {(x, y, z, w) € V | xyzw = 0}. (a) Determine which of U, W, Z are subspaces of V. Justify your answers. (b) Show that UW is a subspace of V and determine its dimension. (c) Is VU+W? Is V = UW? Justify your answers. [10] [7] '00'arrow_forward
- Tools Sign in Different masses and Indicated velocities Rotational inert > C C Chegg 39. The balls shown have different masses and speeds. Rank the following from greatest to least: 2.0 m/s 8.5 m/s 9.0 m/s 12.0 m/s 1.0 kg A 1.2 kg B 0.8 kg C 5.0 kg D C a. The momenta b. The impulses needed to stop the balls Solved 39. The balls shown have different masses and speeds. | Chegg.com Images may be subject to copyright. Learn More Share H Save Visit > quizlet.com%2FBoyE3qwOAUqXvw95Fgh5Rw.jpg&imgrefurl=https%3A%2F%2Fquizlet.com%2F529359992%2Fc. Xarrow_forwardSimplify the below expression. 3 - (-7)arrow_forward(6) ≤ a) Determine the following groups: Homz(Q, Z), Homz(Q, Q), Homz(Q/Z, Z) for n E N. Homz(Z/nZ, Q) b) Show for ME MR: HomR (R, M) = M.arrow_forward
- 1. If f(x² + 1) = x + 5x² + 3, what is f(x² - 1)?arrow_forward2. What is the total length of the shortest path that goes from (0,4) to a point on the x-axis, then to a point on the line y = 6, then to (18.4)?arrow_forwardموضوع الدرس Prove that Determine the following groups Homz(QZ) Hom = (Q13,Z) Homz(Q), Hom/z/nZ, Qt for neN- (2) Every factor group of adivisible group is divisble. • If R is a Skew ficald (aring with identity and each non Zero element is invertible then every R-module is free.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSON
Contemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSON
Introduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY