Unit Activity Essays (1035 words) - Mathematics, Formula

Unit Activity Unit: Single-Variable Expressions This activity will help you meet these educational goals: Mathematical Practices- You will make sense of problems and solve them, use mathematics to model real-world situations, and use appropriate tools strategically. Introduction Have you ever made a mistake when trying to solve a math problem? It can be pretty easy to do, and often will result in losing points on an exam. In the real world, such mistakes can have more serious effects: Miscalculating how much gas you have left in your car will leave you stranded. Miscalculating how much money you have left in your bank account might cost you an overdraft fee. Even more serious, miscalculations have resulted in serious accidents happening many times. Once, as a result of not using the correct units, a satellite sent to Mars burned up in the atmosphere, wasting over $300 million dollars. Fortunately, there are steps you can take to help avoid making errors along the way. One of these strategies is manipulating formulas so they are solving for the variable you want before you substitute values for the variables in the formula. This technique is especially useful when working with large, unwieldy numbers. __________________________________________________________________________ Directions and Analysis Task 1: A Journey to Earth Every moment of every day, light pours out from the Sun at the center of our solar system and travels to Earth. It does not arrive at Earth instantaneously though; it takes time to get here. Your task is to figure out how long it takes for light to travel from the Sun to Earth. a. The formula for the velocity of an object is [pic], where v is the velocity of the object, d is the distance traveled, and t is the time elapsed while that distance is traveled. If you had only this formula to work with, what should your first step be in determining how long it takes for light to reach Earth from the Sun? What additional information do you need to calculate this? Type your response here: b. Solve for the variable you are looking for. Show your work. Type your response here: c. Now search the Internet for the values of the variables you do not know. What are they? Type your response here: d. Using the formula you derived and the values you researched, calculate the time it takes for light to travel from the Sun to Earth. Type your response here: e. Felix Baumgartner is a daredevil famous for breaking the sound barrier during a freefall on October 14, 2012. Aided by a weather balloon, he climbed to a height of 128,100 feet. More than 24 miles in the air, he was so high up that he could see Earth's curvature. He then jumped out of the capsule that carried him. On the way down, he traveled at an average of 335.92 miles per hour, at one point even going as fast as 720 miles per hour, breaking the record for the highest skydive ever attempted and breaking the sound barrier in the process. Using the formula you derived in part b, how long did it take Baumgartner to reach the ground, in minutes? Be careful about unit conversions, and show your work. Type your response here: Task 2: Interest in Finance Interest is a concept familiar to most people: every credit card in existence has a term called annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a credit card that has a minimum payment each month equal to the interest owed. Can you figure out how much the interest rate is based on this amount? The formula for simple interest is [pic]where I is the amount you will pay in interest, r is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the number of times the interest is applied. a. To solve for the interest rate of your credit card, you need to understand which variables in the above formula you have. If your minimum monthly payment is $22 on the $1,000 credit card bill, which variables do you know the values of? Type your response here: b. Manipulate the formula so it will calculate the interest rate you are paying instead of the amount of money you are paying. Type your response here: c. Now that you have a formula that will give you the interest rate, plug in the values for