Math 2010 Week 4: Assignment 4 Please Answer The Following Q

Question

Math 2010 Week 4: Assignment 4 Please answer the following questions. 1. An airplane reaches an altitude of 3 mi above the earth. Assuming a clear day and that a passenger has binoculars, how far can that passenger see? (Hint: The radius of the earth is approximately 4000 miles) 2. State the measure of the angle formed by the minute hand and the hour hand of a clock when the time is a) 1:30 pm and b) 2:20 am. 3. Suppose that a circle is divided into three congruent arcs by points A, B, and C. What is the measure of each arc? What type of figure results when A, B, and C are joined by segments? 4. Answer the following problem from your textbook: Problem 29, Section 6.2. 5. The lengths of the legs of a right triangle are consecutive even integers. The numerical value of the area is three times that of the longer leg. Find the lengths of the legs of the triangle. 6. Answer the following problem from your textbook: Problem 18, Section 6.1. 7. Answer the following questions from your textbook: Problem 39, Section 6.1. 8. The radius of a Ferris wheel’s circular path is 40 ft. If a “ride” of 12 revolutions is made in 3 minutes, at what rate in feet per second is the passenger in a cart moving during the ride?

Dr. Jack HW Helper · Accepted Answer

This assignment encompasses various mathematical problems that involve geometry, trigonometry, and algebra, each contributing to a comprehensive understanding of the fundamentals in a Math 2010 course. The problems will be broken down, analyzed, and solved using appropriate mathematical principles and formulas. Problem 1: Altitude and Viewing Distance To calculate how far a passenger can see when the airplane is at an altitude of 3 miles, we can use the formula for the distance to the horizon: D = √(2 h R) Where: D = distance to the horizon h = height above the Earth's surface (in miles) R = radius of the Earth (approximately 4000 miles) Substituting the values: D = √(2 3 4000) = √24000 ≈ 154.92 miles Thus, the passenger can see approximately 154.92 miles away under clear conditions. Problem 2: Clock Angle Calculation To find the angle between the hour and minute hands of the clock, we use the formula: Angle = |(30H - (11/2)M)| Where: H = hour M = minutes a) For 1:30 pm (H = 1, M = 30): Angle = |(301 - (11/2)30)| = |30 - 165| = 135 degrees b) For 2:20 am (H = 2, M = 20): Angle = |(302 - (11/2)20)| = |60 - 110| = 50 degrees The angles formed are 135 degrees for 1:30 pm and 50 degrees for 2:20 am. Problem 3: Congruent Arcs in a Circle If a circle is divided into three congruent arcs, each arc measures: Arc Measure = 360 degrees / 3 = 120 degrees When points A, B, and C are connected, they form an equilateral triangle because all sides (or arcs) are equal in measure. Problem 4: Area and Length of Triangle Legs Let the lengths of the legs of the right triangle be represented as 2n and 2n + 2, where n is a positive integer. The area A of a right triangle is given by: A = 1/2 base height Setting the area equal to three times the longer leg: 1/2 2n (2n + 2) = 3 * (2n + 2) Simplifying the equation: n(n + 1) = 3(n + 1) This implies: n^2 - 2n = 0 Factoring yields: n(n - 2) = 0 Thus, n = 2, meaning the lengths of the legs are 4 and 6. Problem 5: Textbook Problem 18 For this pr

Math 2010 Week 4: Assignment 4 Please Answer The Following Q ✓ Solved

Math 2010 Week 4: Assignment 4 Please answer the following questions.

Paper For Above Instructions

Problem 1: Altitude and Viewing Distance

Problem 2: Clock Angle Calculation

Problem 3: Congruent Arcs in a Circle

Problem 4: Area and Length of Triangle Legs

Problem 5: Textbook Problem 18

Problem 6: Textbook Problem 39

Problem 7: Ferris Wheel Speed

Conclusion

References