Algebra 2 8-1 Guided Practice: Inverse Variation

Last updated almost 3 years ago

21 questions

3

5

A.CED.2

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10

A.CED.2

3

14

A.CED.2

A.CED.4

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9

3

10

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Algebra 2 8-1 Guided Practice: Inverse Variation

Last updated almost 3 years ago

21 questions

3

5

A.CED.2

3

10

Take Note: Identify the common forms representing inverse variation between x and y, with a constant of variation k.

y=\frac{k}{x}
y=kx
x=\frac{k}{y}
xy=k
k=\frac{y}{x}

10

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Direct variation
Inverse variation
Neither

A.CED.2

3

10

Take Note: Summarize the process used in Problem 2 to determine a function that models inverse variation.

14

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

-56

A.CED.2

A.CED.4

3

10

Take Note: Summarize the process used in Problem 3 to model the given inverse variation using a table.

10

A.CED.2

A.CED.4

10

A.CED.2

A.CED.4

3

10

Take Note: Define combined variation.

10

Take Note: Define joint variation.

9

Take Note: Match each equation form on the left with the combined variation it represents on the right.

Draggable item		Corresponding Item
c=kab		c varies jointly with a and b
c=\frac{kab}{d}		c varies jointly with a and b and inversely with d
c=\frac{ka}{db}

10

A.CED.2

3

10

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

Recall the formula for potential energy used in Problem 5, PE=gmh, as well as the gravitational constant, 9.8.

A.CED.2

12

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

Recall the formula for potential energy used in Problem 5, PE=gmh.

6 m
9 m
10 m
12 m

A.CED.2

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick.

How many square feet can you cover?
If l and w represent the length and width of the rectangle in feet, what equation relates l and w?
Justify your reasoning.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Identify the common forms representing inverse variation between x and y, with a constant of variation k.

y=\frac{k}{x}
y=kx
x=\frac{k}{y}
xy=k
k=\frac{y}{x}

Common forms of inverse variation

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Direct variation
Inverse variation
Neither

Video Check: Select all that apply with regards to the video embedded directly above this item.

10

Take Note: Summarize the process used in Problem 2 to determine a function that models inverse variation.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

-56
26
-28

What is the function that models the inverse variation?
What does the graph of this function look like?
What is y when x = 2?

Video Check: Select all that apply with regards to the video embedded directly above this item.

10

Take Note: Summarize the process used in Problem 3 to model the given inverse variation using a table.

10

Problem 3 Got It? After a major storm, your math class volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard.

What function models the time needed to clear the debris from an average-sized yard relative to the number of students who do the work?

A.CED.2

A.CED.4

10

Problem 3 Got It? After a major storm, your math calss volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard?

How many students should there be to clear debris from an average-sized yard in at most 25 minutes?

A.CED.2

A.CED.4

Video Check: Select all that apply with regards to the video embedded directly above this item.

10

Take Note: Define combined variation.

10

Take Note: Define joint variation.

Take Note: Match each equation form on the left with the combined variation it represents on the right.

Draggable item		Corresponding Item
c=kab		c varies jointly with a and b
c=\frac{kab}{d}		c varies jointly with a and b and inversely with d
c=\frac{ka}{db}		c varies directly with a and inversely with the product db

10

Problem 4 Got It? The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120 ft2 to a depth of 3 in., how many bags do you need to mulch 200 ft2 to a depth of 4 in.?

A.CED.2

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

Recall the formula for potential energy used in Problem 5, PE=gmh, as well as the gravitational constant, 9.8.

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

Recall the formula for potential energy used in Problem 5, PE=gmh.

6 m
9 m
10 m
12 m
Yes. You must calculate the potential energy of both divers in order to determine at what height of the second diver their PE will be equivalent.
No. You don't need to calculate the potential energy of either diver in order to determine at what height of the second diver the PE will be equivalent.

At what height should a 40-kg diver stand to have equal potential energy?
Do you need to find the potential energy of either diver to solve this?

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick. 


How many square feet can you cover? 
If l and w represent the length and width of the rectangle in feet, what equation relates l and w? 
Justify your reasoning.

You can cover a square foot with a 3-in. layer 6 times with each bag. So with each bag, you can cover 6 ft2 with a 3-in. layer, and with 20 bags, you can cover 120 ft2 with a 3-in. layer. 
  

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Common forms of inverse variation

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

26

-28

What is the function that models the inverse variation?

What does the graph of this function look like?

What is y when x = 2?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 3 Got It? After a major storm, your math class volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard.

What function models the time needed to clear the debris from an average-sized yard relative to the number of students who do the work?

B

C

D

Problem 3 Got It? After a major storm, your math calss volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard?

How many students should there be to clear debris from an average-sized yard in at most 25 minutes?

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

c varies directly with a and inversely with the product db

Problem 4 Got It? The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120 ft2 to a depth of 3 in., how many bags do you need to mulch 200 ft2 to a depth of 4 in.?

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Yes. You must calculate the potential energy of both divers in order to determine at what height of the second diver their PE will be equivalent.

No. You don't need to calculate the potential energy of either diver in order to determine at what height of the second diver the PE will be equivalent. 

At what height should a 40-kg diver stand to have equal potential energy?

Do you need to find the potential energy of either diver to solve this?

Algebra 2 8-1 Guided Practice: Inverse Variation

Algebra 2 8-1 Guided Practice: Inverse Variation

Take Note: Identify the common forms representing inverse variation between x and y, with a constant of variation k.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations. NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Take Note: Summarize the process used in Problem 2 to determine a function that models inverse variation.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7. Drag the appropriate item from the left to respond to each question on the right.

Take Note: Summarize the process used in Problem 3 to model the given inverse variation using a table.

Take Note: Define combined variation.

Take Note: Define joint variation.

Take Note: Match each equation form on the left with the combined variation it represents on the right.

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?Recall the formula for potential energy used in Problem 5, PE=gmh, as well as the gravitational constant, 9.8.

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.Recall the formula for potential energy used in Problem 5, PE=gmh.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick. How many square feet can you cover? If l and w represent the length and width of the rectangle in feet, what equation relates l and w? Justify your reasoning.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Identify the common forms representing inverse variation between x and y, with a constant of variation k.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations. NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process used in Problem 2 to determine a function that models inverse variation.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7. Drag the appropriate item from the left to respond to each question on the right.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process used in Problem 3 to model the given inverse variation using a table.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define combined variation.

Take Note: Define joint variation.

Take Note: Match each equation form on the left with the combined variation it represents on the right.

Problem 4 Got It? The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120 ft2 to a depth of 3 in., how many bags do you need to mulch 200 ft2 to a depth of 4 in.?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?Recall the formula for potential energy used in Problem 5, PE=gmh, as well as the gravitational constant, 9.8.

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.Recall the formula for potential energy used in Problem 5, PE=gmh.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

Recall the formula for potential energy used in Problem 5, PE=gmh, as well as the gravitational constant, 9.8.

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

Recall the formula for potential energy used in Problem 5, PE=gmh.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick.

How many square feet can you cover?
If l and w represent the length and width of the rectangle in feet, what equation relates l and w?
Justify your reasoning.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

Recall the formula for potential energy used in Problem 5, PE=gmh, as well as the gravitational constant, 9.8.

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

Recall the formula for potential energy used in Problem 5, PE=gmh.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?