Aplicaciones de las membranas a la industria láctea

1. INTRODUCCIÓN

2.3. PROCESOS CON MEMBRANAS

2.3.2. Aplicaciones de las membranas a la industria láctea

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 144

M.1. What is the slope of the line below? _____

M. 2. What is the slope of the line below? ______

Solve the problems below. Show all of your work.

M.3 Jeremiah runs at a pace of 3 miles per hour. Jeremiah has already run 6 miles this week. Jeremiah plans to run for 4 more hours this week. At this rate, how many total miles will Jeremiah run this week? _________

W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.2. Explain how you know your answer makes sense. Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

M.4 Joey earns tips at a rate of ½ dollars per root beer float he makes. At this rate, how many floats does he need to make to earn $12 in tips? ________

! 145 M.5. Joe is filling an Olympic size swimming pool with a hose

that doesn’t have good water pressure. Joe fills the pool for three hours at a rate of 60 gallons per hour, then for two hours at a rate of 30 gallons per hour. Joe shuts off the hose for an hour to see if he can make the water pressure return to normal. He then fills the pool at a rate of 40 gallons per hour for four hours. Make a table and graph showing the times and gallons at each stage of the filling process.

Show all of your work, and number and label the graph.

Table:

M.6. What is the average rate of the filling process?______

W.3. Explain the steps you used to determine the average gallons per hour.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 146

M.1. What is the slope of the line below? _____

M. 2. What is the slope of the line below? ______

Solve the problems below. Show all of your work.

M.3 Carrie works at a coffee shop. She earns tips at a rate of ¾ dollars per drink she makes. At this rate, how many drinks would she need to make to earn $6 in tips? _________

W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________ M.4 Andrew can mow 2 lawns per hour. He has already mowed 4 lawns this week. He plans to mow lawns for 5 more hours this week. At this rate, how many total lawns will Andrew mow this week? _______

! 147 M.5. A car leaves Moab at 7 am and travels for three hours at 70

miles per hour, then for an hour at 50 miles per hour. The car stops for two hours, then continues for four hours at 75 miles per hour.

Make a table and graph showing the times and distances traveled at each stage of the journey. Show all of your work, and number and label the graph.

Table:

M.6. What is the average speed for the whole journey?______

W.3. Explain the steps you used to determine the average speed for the whole journey.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 148

M.1. What is the slope of the line below? _____

M. 2. What is the slope of the line below? ______

Solve the problems below. Show all of your work.

M.3 Andrea makes soap to sell at the farmers market. She sells each bar of soap for $5. She has already made $20 today. If she sells 7 more bars of soap today at this price, how much total money will she have made today?_________

W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________ M.4 Sarah has a credit card debt of $40. She pays off the credit card at a rate of 4/5 dollars per week. At this rate, how many weeks will it take her to pay off the full $40 she owes on her credit card? ______

! 149 M.5. Tina has a job picking berries. She gets to work at 7 am and

picks berries for 2 hours at a rate of 6 baskets per hour. She then picks berries at a rate of 8 baskets per hour for 3 hours. She takes a lunch break for 1 hour. Then she picks berries at a rate of 5 baskets per hour for 1 hour.

Make a table and graph showing the times and number of berry baskets picked for each stage of Tina’s workday. Show all of your work, and number and label the graph.

Table:

M.6. What is the average rate of berry picking for Tina’s workday? _____

W.3. Explain the steps you used to determine the average number of baskets picked for the workday.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 150

M.1. What is the slope of the line below? _____

M. 2. What is the slope of the line below? ______

Solve the problems below. Show all of your work.

M.3 A tree grows ¼ inch per year. At this rate, how many years will it take for the tree to be 12 inches tall? _________

W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________ M.4 Harriet earns $8 per hour for baby-sitting. She has already earned $16 this week for baby-sitting. She plans to baby-sit for 6 more hours this week. How much total money will she earn for baby-sitting this week? _______

! 151 M.5. A bicyclist left Ogden at 8 AM and traveled at a rate of 20

miles per hour for 3 hours, then took a break for 1 hour. The bicyclist then traveled for 2 hours at a rate of 30 miles per hour, and then 1 hour at a rate of 35 miles per hour.

Make a table and graph showing the times and distances traveled at each stage of the bike ride. Show all of your work, and number and label the graph.

Table:

M.6. What is the average speed for the whole bike ride?______

W.3. Explain the steps you used to determine the average speed for the whole bike ride.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 152

M.1. What is the slope of the line below? _____

M. 2. What is the slope of t he line below? ______

Solve the problems below. Show all of your work.

M.3 Sam earns $3 for every dog she walks. She already earned $9 this week. She plans to walk 8 more dogs this week. At this rate, how much total money would she earn this week? _________ W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________ M.4 Jordy reads at a rate of 2/3 pages per minute. At this rate, how many minutes will it take her to read 18 pages?________

! 153 M.5. Steven wants to take a hot bath, but doesn’t have a very

good water heater. Steven fills his bathtub for 8 minutes at a rate of 2 gallons per minute, and then turns off the water for 5 minutes to let it get hot. He turns the water back on and fills the bathtub at a rate of 3 gallons per minute for 5 minutes, and then at a rate of 2 gallons per minute for 4 minutes.

Make a table and graph showing the times and gallons at each stage of filling process. Show all of your work, and number and label the graph.

Table:

M.6. What is the average rate for the filling process?______

W.3. Explain the steps you used to determine the average gallons per minute.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 154

M.1. What is the slope of the line below? _____

M. 2. What is the slope of the line below? ______

Solve the problems below. Show all of your work.

M.3 A tree grows at a rate of 1/3 inches per month. At this rate, how many months will it take for the tree to be 12 inches tall? _____

W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.2. Explain how you know your answer makes sense. Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________ M.4 James can bike at a rate of 6 miles per hour. James has already biked 12 miles of a trail. At this rate, James needs to bike for 4 more hours to finish the trail. How many total miles long is the trail?_________

! 155 M.5. Mike works at a juice bottling factory. He arrives at work at

10 am and fills bottles of juice at a rate of 80 bottles per hour for the first 3 hours of his shift. He then takes a 1 hour lunch break. When he returns from break, he fills bottles at a rate of 60 bottles per hour for 2 hours, and then at a rate of 90 bottles per hour for 1 hour.

Make a table and graph showing the times and bottles filled at each stage of Mike’s workday. Show all of your work, and number and label the graph.

Table:

M.6. What is the average rate Mike fills bottles at for the workday?______

W.3. Explain the steps you used to determine the average rate for the workday.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 156

M.1. What is the slope of the line below? _____

M. 2. What is the slope of the line below? ______

Solve the problems below. Show all of your work.

M.3 Samantha can run at a rate of 6 miles per hour. She has already run 3 miles this week. She plans to run for 3 more hours this week. At this rate, how many total miles will she run this week?_________

W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.2. Explain how you know your answer makes sense. Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

M.4 The water level in a dog’s water dish decreases by ½ inch per hour on a hot day. How many hours will it take for the dog’s dish to be empty if it is 6 inches deep at the start of the day?_______

! 157 M.5. Heidi invests $60 in a savings account. Heidi earns $2 per

month in interest for the first 6 months, no interest for the next 4 months, $3 per month in interest for the following 3 months, and $5 per month in interest for 9 months.

Make a table and graph showing the times and amount of interest earned at each stage of the account.

Show all of your work, and number and label the graph.

Table:

M.6. What is the average rate of interest earned during the whole time period described?_____

W.3. Explain the steps you used to determine the average amount of interest earned.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.4. How do you know your answer is correct? Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________

! 158

M.1. What is the slope of the line below? _____

M. 2. What is the slope of the line below? ______

Solve the problems below. Show all of your work.

M.3 A drone descends at a rate of 4/5 feet per minute when preparing for landing. How many minutes will it take a drone to descend a total of 20 feet? ______

W.1. Describe in writing the process you used to solve the problem above.

___________________________________________________ ___________________________________________________ ___________________________________________________

W.2. Explain how you know your answer makes sense. Provide an example to support your reasoning.

___________________________________________________ ___________________________________________________ ___________________________________________________ M.4 Mark can skateboard at a pace of 9 miles per hour. He has already skateboarded for 5 miles this week. He plans to

skateboard for 2 more hours this week. At this rate, how many total miles will he skateboard this week?_________

! 159 M.5. Jami is filling a swimming pool with water. She fills the pool

for 3 hours at a rate of 30 gallons per hour. She then turns off the water when she goes to lunch for 1 hour. When she gets back, she fills the pool for 4 hours at a rate of 50 gallons per hour, and then for 1 hour at a rate of 40 gallons per hour.

Make a table and graph showing the times and gallons at each stage of filling process. Show all of your work, and number and label the graph.

Table:

M.6. What is the average rate for the filling process?______

W.3. Explain the steps you used to determine the average

In document Producción de leche de larga duración (ESL) mediante membranas cerámicas de microfiltración (página 64-71)