Questions and Answers
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.
80
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.
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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.
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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.
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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.
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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.
