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Questions and Answers
What is joint variation?
What is joint variation?
It occurs when one quantity varies directly as the product of two or more other quantities.
The statement y varies jointly as x and z if there exists a nonzero number k such that y = ______, where x≠0 and z≠0, represents joint variation.
The statement y varies jointly as x and z if there exists a nonzero number k such that y = ______, where x≠0 and z≠0, represents joint variation.
kxz
If a rectangle has a length of 2 meters and a width of 5 meters, what is the area of the rectangle?
If a rectangle has a length of 2 meters and a width of 5 meters, what is the area of the rectangle?
10 square meters
What is the value of the constant of variation, k, if the area of a rectangle is 60 square feet, its length is 15 feet, and its width is 4 feet?
What is the value of the constant of variation, k, if the area of a rectangle is 60 square feet, its length is 15 feet, and its width is 4 feet?
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If y varies directly as x and inversely as z, and y = 22 when x = 4 and z = 6, what is the value of the constant of variation, k?
If y varies directly as x and inversely as z, and y = 22 when x = 4 and z = 6, what is the value of the constant of variation, k?
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What is y equal to when x = 10 and z = 25, given the information from the previous question?
What is y equal to when x = 10 and z = 25, given the information from the previous question?
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What is the name for a situation where one quantity varies directly as the product of two or more other quantities?
What is the name for a situation where one quantity varies directly as the product of two or more other quantities?
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What is the formula for joint variation, where y varies jointly as x and z
What is the formula for joint variation, where y varies jointly as x and z
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What does the k represent in the equation for joint variation?
What does the k represent in the equation for joint variation?
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In joint variation, what constraint is placed on the values of x and z?
In joint variation, what constraint is placed on the values of x and z?
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The area of a rectangle varies jointly as its length and width.
The area of a rectangle varies jointly as its length and width.
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If the area of a rectangle is represented by A, its length by l, and its width by w, what is the equation for joint variation?
If the area of a rectangle is represented by A, its length by l, and its width by w, what is the equation for joint variation?
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When describing joint variation, is the term "varies inversely" ever used?
When describing joint variation, is the term "varies inversely" ever used?
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What does combined variation describe?
What does combined variation describe?
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In combined variation, if y varies directly as x and inversely as z, what is the general equation that represents this?
In combined variation, if y varies directly as x and inversely as z, what is the general equation that represents this?
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How do you determine the value of the constant of variation (k) in combined variation?
How do you determine the value of the constant of variation (k) in combined variation?
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Combined variation is a situation where a variable depends on ______ other variables.
Combined variation is a situation where a variable depends on ______ other variables.
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Study Notes
Joint Variation
- Joint variation occurs when one quantity varies directly as the product of two or more other quantities
- If y varies jointly as x and z, then y = kxz, where k is a nonzero constant and x ≠ 0, z ≠ 0
- Example: The area of a rectangle varies jointly as its length and width. If A = 60 sq ft, I = 15 ft, and w = 4 ft, the equation for joint variation is A = klw. Solving for k gives k = 1.
Combined Variation
- Combined variation describes a situation where a variable depends on two or more other variables
- It involves direct and inverse variation
- If y varies directly as x and inversely as z, then y = kx/z, where k is a nonzero constant
- Example: if y varies directly as x and inversely as z, and y = 22 when x = 4 and z = 6, find y when x = 10 and z = 25.
- First, find the constant of variation (k). Using the given values, 22 = k(4/6). Solving for k gives k= 33
- Then, use the constant of variation to find y when x = 10 and z = 25. Y = 33(10/25) = 13.2
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Description
This quiz delves into the concepts of joint and combined variation in algebra. You'll explore how one quantity can vary directly as a product of others and how to handle scenarios involving both direct and inverse variations. Test your understanding with examples and practical problems.
