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Questions and Answers
If y varies directly as x and y=25 when x=15, find x when y=40.
If y varies directly as x and y=25 when x=15, find x when y=40.
If a is directly proportional to b^3 and a=10 when b=2, find a when b=4.
If a is directly proportional to b^3 and a=10 when b=2, find a when b=4.
80
If y varies inversely as x and y=22 when x=6, find x when y=15.
If y varies inversely as x and y=22 when x=6, find x when y=15.
8.8
Joint variation involves the variable mentioned first in the problem being isolated on the left of the equal sign.
Joint variation involves the variable mentioned first in the problem being isolated on the left of the equal sign.
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If z varies jointly as x and the square root of y and z=6 when x=3 and y=16, find z when x=7 and y=4.
If z varies jointly as x and the square root of y and z=6 when x=3 and y=16, find z when x=7 and y=4.
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Given that the surface area of a cylinder varies jointly as the radius and the sum of radius and height, find the surface area of a cylinder with a radius of 3 and height 10.
Given that the surface area of a cylinder varies jointly as the radius and the sum of radius and height, find the surface area of a cylinder with a radius of 3 and height 10.
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Study Notes
Direct Variation
- Direct variation occurs when two variables, y and x, change in such a way that the ratio y/x is constant.
- Example problem: If y = 25 when x = 15, calculate x when y = 40 using the proportion relationship.
Inverse Variation
- Inverse variation expresses a relationship where one variable increases as the other decreases, maintaining a constant product xy = k.
- Example calculation: If y = 22 when x = 6, find x when y = 15, resulting in x = 8.8 through calculated steps.
Joint Variation
- Joint variation involves relationships where a variable directly depends on the product of two or more variables.
- Example definition includes setting one variable equal to the product of others with a constant k.
Compound Variation
- A combination of direct and inverse variation, where one variable is affected by changes in multiple others.
- Example problem: If z varies jointly with x and the square root of y, use initial conditions to solve for different values.
Surface Area of a Cylinder
- The formula for the surface area (SA) of a cylinder is affected by both the radius and height.
- Example: For a cylinder with height 8 and radius 4, calculation yields a surface area of 96π. In a second scenario with a radius of 3 and height of 10, use the established relationship to determine SA.
Proportions and Constants
- Key in all types of variations is the identification and use of constant k to maintain equations during calculations.
- Always plug values into the established formula to solve for unknowns effectively.
Studying That Suits You
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Description
Test your understanding of direct and inverse variations with these algebra flashcards. Each card presents a unique problem along with its definition related to proportionality. Perfect for students looking to reinforce their knowledge of algebraic relationships.
