If you didn’t complete your quiz corrections in class today, here is the format I would like you to use as you complete them tonight:
These are all considered “classic” story problems. Please create equations and solve 3 of the problems below:
1. During the spring and summer, you do a spring yard cleanup for households and you also paint houses. You earn $8 an hour doing cleanups and $12 an hour painting. Last spring and summer, you worked a total of 400 hours and earned $3800. How many hours did you spend doing yard cleanups? How many hours did you spend painting?
2. A total of $45,000 is invested into two funds paying %5.5 and 6.5% annual interest. The combined annual interest is $2725. How much of the $45,000 is invested in each type of fund?
3. Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many of each kind of ticket were sold?
4. Two swimming teams are competing in a 400 meter relay. Each leg of the relay is 100 meters. During the last leg of the race, the swimmer in lane 1 has a 1.2 second head start on the swimmer in lane 2 as shown. After how many seconds into the leg will the swimmer in lane 2 catch up to the swimmer in lane 1.
5. In your chemistry lab, you have a bottle of 1% hydrochloric acid solution and a bottle of 5% hydrochloric acid solution. You need 100 milliliters of a 3% hydrochloric acid solution for an experiment. How many milliliters of each solution do you need to mix together?
6. A rectangle has a perimeter of 14 feet, and twice its length l is equal to 1 less than 4 times its width w. Find the length and width of the rectangle
Please pick 3 of the problems below.
- Create equations to represent the situation.
- Explain in words how the equation fits each part of the problem.
- Solve the system of equations.
1. A total of $12,000 is invested in two funds paying 9% and 11% simple interest. If the yearly interest is $1,180, how much of the $12,000 is invested at 9% and how much is invested at 11%?
2. Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many of each kind of ticket were sold?
3. Larry wants 50 pounds of tea that ha can sell for $5.14 per pound. If he has tea that costs $7.80 per pound and tea that costs $4.30 per pound, how much of each should he use?
4. Kerry’s motorboat takes 3 hours to make a downstream trip with a 3-mph current. The return trip against the same current takes 5 hours. Find the speed of the boat in still water.
5. The Hare knows he can run faster than the Tortoise, so he gave the Tortoise a 2 mile head start. The Hare usually runs about 6 miles per hour while the Tortoise can hold a sustained 3 miles per hour all day long.” Find and explain the meaning of the solution to this linear system.
6. There are 2 times as many quarters as dimes in Eric’s pocket. He has $1.20 in coins totally. How many coins of each type does Eric have?
Challenge Problem (Optional): In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have? (Try solving this problem without guess and check.)
Put a post here RIGHT NOW!
Today we wrapped up our initial study of transformations, and moved into real world applications of piecewise functions.
Please come to class tomorrow with your ONE parking function complete.
A few of observations from class today:
- y = x – 2 does not create a horizontal line where y is always -2.
- When creating inequalities for piecewise functions, be sure that you don’t have overlapping x-values.
- Always use proper notation for piecewise functions. Start with f(x). Then draw the brace, then an expression. The domain goes last. A comma separates the function and the domain.
Please complete the Problem Set tonight for homework. If you get stuck on problem 4, post a question on the blog, or come to class with a written question tomorrow.
Today in class we made a VERY IMPORTANT DOCUMENT summarizing what we’ve learned about transformations of functions.
Please complete the exercises and examples on page 132 and 133 tonight for homework.
Today in class we really worked towards formalizing the differences between horizontal (stretch/shrink) and vertical (stretch/shrink). Please be sure to keep those things straight as you complete the PROBLEM SET for homework on Monday.
Today in class we (finally) got to start our study of Horizontal Stretch/Shrink.
Please come to class on Monday with Examples 1 and 2 complete. Be sure to carefully look at which x-values have the same y-values!
Today in class we focused on Horizontal Transformations of functions.
Pleases complete the Problem Set tonight for homework.