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This guide presents a series of algebraic and mathematical problems relevant to real-world applications, ranging from calculating distances on hills and event attendance costs to analyzing population growth and statistics. It covers essential concepts such as trigonometry, discriminants, and standard deviations, providing step-by-step solutions for each problem. By understanding these concepts, students will enhance their mathematical skills and application in everyday situations, paving the way for success in both academics and life.
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Algebra Upward Bound Math and Science RahulRaghunathan
Problem 1 You are walking up a 500. meter high hill. The trail has an incline of 12 degrees. How far will you walk to get to the top?
Solution 1 • We know angle A (12 degrees) and the length of the opposite side (500. m). We want to know the length of the hypotenuse (H), so we will use the formula • Sine = • Substituting in the appropriate values,
Solution 1 Sine 12 = 0.21
Problem 3 • A member on speak series allows people to join for 11$ then pay 1$ for every event attended. What is the maximum events one can attend for a total of 46$?
Solution 3 • We write the equation that shows the cost of speaker series related to number of events attended ( a) 46 = 1. a + 11 46 = a + 11 35 = a
Problem 4 • Find the Discriminant of V + 4V + 9 = 0
Solution 4 • Discriminant formula is b2 – 4 (a)(c) Where a = 1, b = 4 and C = 9 Substituting we get = 42-4(1)(9) = 16-36 = -20
Problem 5 • Add (4j+8) and (8j+3)
Solution 5 • Add the like terms from the quantities above • (4j+8) + (8j+3) = ( 4j+8j) + ( 8+3) = 12j+ 11
Problem 6 • The population of an industrial town is increasing by 5% every year. If the present population is 1 million, estimate the population five years hence.
Solution 6 • C. I = A-P =
Solution 6 • Present population, P = 1 million, rate of increase = 5% per annumHence population after 5 years = = 1000000 (1·05)5 = 1276280
Problem 7 • What is the center of the circle x2 + y2 -144 = 0 ?
Solution 7 • The standard equation of a circle is ( x-h)2 + (y-k)2 = r2 Now comparing with given equation we get ( x-0)2 + (y-0)2 = (12)2 The Center of the circle is (0,0)
Problem 8 • A wedding planner placed orders with a florist five times in the last year . What is the standard deviaton of the number of flowers needed • 70 Flowers , 90 Flowers , 21 Flowers , 63 Flowers , 91 Flowers
Solution 8 • Mean = = 67.12 Variance = (70-67.12)2 + (91-67.12)2+ (21-67.12)2+ (63-67.12)2+ (91-67.12)2 =3292.8 Varience =
Solution 8 • Variance = 658.56 • Standard Deviation =
