2.2: Solving Equations Through Various Methods Page 87 3) 3 7) {≈–2.4265} 11) {≈–1.4751, ≈1.2372} 15) {≈–1.3794, ≈1.6030} 19) {≈–2.1149, ≈0.2541, ≈1.8608} 23) {≈–1.7521} 27) {0, ≈2.2074} 31) {≈–0.6514, ≈1.1513} 33) {≈7.0334} 11/20/2018 5:34 AM 2.2: Solving Equations Through Various Methods

Pre-Calculus AB Pre-AP/Dual, Revised ©2015 Applications Section 2.3 Pre-Calculus AB Pre-AP/Dual, Revised ©2015 viet.dang@humble.k12.tx.us 11/20/2018 5:34 AM 2.3: Applications

Steps Read the problem 2 times. Once to read it, a second time to note all critical information, and lastly to determine the equation needed and what is being asked for. Determine the variables Draw a picture if applicable. Translate from English to Math. Solve for at least one variable. Find any remaining information. Interpret your answer. 11/20/2018 5:34 AM 2.3: Applications

Example 1 The average of two real numbers is 39.625. One number is 1500 times the reciprocal of the other. Find the two numbers. 11/20/2018 5:34 AM 2.3: Applications

Example 1 The average of two real numbers is 39.625. One number is 1500 times the reciprocal of the other. Find the two numbers. 11/20/2018 5:34 AM 2.3: Applications

Example 2 The sum of two numbers is 15 and the difference of the squares is 5. What are the numbers? 11/20/2018 5:34 AM 2.3: Applications

Example 3 The width of a rectangle is three times its height. If it has an area of 60.75 square feet, what are the dimensions? 11/20/2018 5:34 AM 2.3: Applications

Your Turn A rectangle is twice as wide as it is high. If it has an area of 24.5 in2, what are its dimensions? What are the numbers? 11/20/2018 5:34 AM 2.3: Applications

Example 4 A real estate investment yields a return of 10% per year and a certificate of deposit (CD) which paus 6% per year. How much of $7,500 should be put in the real estate investment and how much should be put into the CD to obtain a return of 7% on the entire $7,500? 11/20/2018 5:34 AM 2.3: Applications

Example 4 A real estate investment yields a return of 10% per year and a certificate of deposit (CD) which paus 6% per year. How much of $7,500 should be put in the real estate investment and how much should be put into the CD to obtain a return of 7% on the entire $7,500? 11/20/2018 5:34 AM 2.3: Applications

Example 5 You have already invested $550 in a stock with an annual return of 11%. How much of an additional $1100 should be invested at 12% and how much at 6% so that the total return on the entire $1,650 is 9%? 11/20/2018 5:34 AM 2.3: Applications

Example 5 You have already invested $550 in a stock with an annual return of 11%. How much of an additional $1100 should be invested at 12% and how much at 6% so that the total return on the entire $1,650 is 9%? 11/20/2018 5:34 AM 2.3: Applications

Your Turn A high risk stock pays dividends at a rate of 12% per year and a savings account which pays 6% interest per year. How much of the $9,000 investment should be put in the stock and how much should be put in savings to obtain a return of 8% per year on the total investment? 11/20/2018 5:34 AM 2.3: Applications

Your Turn A high risk stock pays dividends at a rate of 12% per year and a savings account which pays 6% interest per year. How much of the $9,000 investment should be put in the stock and how much should be put in savings to obtain a return of 8% per year on the total investment? 11/20/2018 5:34 AM 2.3: Applications

Example 6 A chemist has 30 ml of a 40% acid solution in a test tube. How much of the solution should be poured off and replaced with pure acid so that the new mix is 70% acid? 11/20/2018 5:34 AM 2.3: Applications

Example 7 A canoeist paddled a total of 11 hours on a 48 km round trip to Bear Lake. The upstream trip followed a period of heavy rain and the current he paddled against was 3 km/h. For the downstream return trip, he paddled with the current that slowed to 2 km/hr. At what speed would he paddle the canoe in still water? Distance Rate Time Downstream Upstream 11/20/2018 5:34 AM 2.3: Applications

Example 7 A canoeist paddled a total of 11 hours on a 48 km round trip to Bear Lake. The upstream trip followed a period of heavy rain and the current he paddled against was 3 km/h. For the downstream return trip, he paddled with the current that slowed to 2 km/hr. At what speed would he paddle the canoe in still water? Distance Rate Time Downstream Upstream 11/20/2018 5:34 AM 2.3: Applications

Example 7 A canoeist paddled a total of 11 hours on a 48km round trip to Bear Lake. The upstream trip followed a period of heavy rain and the current he paddled against was 3 km/h. For the downstream return trip, he paddled with the current that slowed to 2 km/hr. At what speed would he paddle the canoe in still water? 11/20/2018 5:34 AM 2.3: Applications

Austin to Colorado Springs Colorado Springs to Austin Your Turn A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown? Distance Rate Time Austin to Colorado Springs Colorado Springs to Austin 11/20/2018 5:34 AM 2.3: Applications

Austin to Colorado Springs Colorado Springs to Austin Your Turn A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown? Distance Rate Time Austin to Colorado Springs Colorado Springs to Austin 11/20/2018 5:34 AM 2.3: Applications

Your Turn A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown? 11/20/2018 5:34 AM 2.3: Applications

Assignment Worksheet 11/20/2018 5:34 AM 2.3: Applications