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Questions and Answers
Which of the following represents an inverse variation?
Which of the following represents an inverse variation?
What is the mathematical translation of 'The volume (V) of a cylinder varies jointly as the square of radius (r) and height (h)'?
What is the mathematical translation of 'The volume (V) of a cylinder varies jointly as the square of radius (r) and height (h)'?
What is the simplest form of $x^{10}x^{5}$?
What is the simplest form of $x^{10}x^{5}$?
If y varies inversely as x, what is x when y = 5 and k = 60?
If y varies inversely as x, what is x when y = 5 and k = 60?
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Which of the following describes the situation of the amount of rain and the level of water on a dam?
Which of the following describes the situation of the amount of rain and the level of water on a dam?
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What is the evaluated value of $(x^{5})(x^{1})^{3}$?
What is the evaluated value of $(x^{5})(x^{1})^{3}$?
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If the mass of a certain object is 4 kg when its weight is 24 N, what is the mass of another object that weighs 18 N?
If the mass of a certain object is 4 kg when its weight is 24 N, what is the mass of another object that weighs 18 N?
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How many men were needed to finish constructing a well in 4 hours if it takes 10 hours for 2 men?
How many men were needed to finish constructing a well in 4 hours if it takes 10 hours for 2 men?
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Which of the following laws of exponents describes the rule 'add the exponents of the same base'?
Which of the following laws of exponents describes the rule 'add the exponents of the same base'?
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Which of the following is equivalent to $\sqrt{8a^3}$?
Which of the following is equivalent to $\sqrt{8a^3}$?
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Study Notes
Inverse Variation
- A relation where one variable increases as another decreases proportionally.
- Represented by an equation of the form y = k/x, where k is a constant.
Direct Variation
- A relation where one variable increases as another increases proportionally.
- Represented by an equation of the form y = kx, where k is a constant.
Combined Variation
- A relationship involving more than one variable. The variables may be related in ways that are direct or inverse.
Joint Variation
- A type of combined variation where one variable is directly proportional to two or more other variables.
- If z varies directly with x and y, it is represented as z = kxy where k is the constant of variation.
Mathematical Translation
- "The volume (V) of a cylinder varies jointly as the square of radius (r) and height (h)" translates to V = kr²h.
Direct Variation Problems
- If y varies directly with x, and y = 15 when x = 5, find y when x = 7.
- y = 21
Inverse Variation Problems
- If y varies inversely as x, what is x when y = 5 and k = 60?
- x = 12
Combined Variation Problems
- On a given planet, the weight (W) of an object varies directly with the mass (M) of the object. If the mass of a certain object is 4 kg when its weight is 24 N, what is the mass of another object that weights 18 N?
- 3 kg
Inverse Variation Problems
- The number of hours constructing a deep well is inversely proportional to the number of men doing it. It takes 10 hours for 2 men to construct the well. How many men were needed to finish in 4 hours?
- 5
Joint Variation Problems
- The area A of a triangle varies jointly as the base b and the height h. If A = 12m² when b = 6 and h = 4m, what is the new area when b increases by 2m and h increases by 4m? -32m²
Laws of Exponents
- The rule "add the exponents of the same base" describes the product of powers rule (e.g., xm * xn = xm+n).
Simplifying Expressions
- Simplify (a6b3c3)2/ (a15b20c5)
- a-3b-17c1
Evaluating Expressions
- What is the evaluated value of (x4/ 5)2?
- x8/ 25
Other Problems
- What is the simplest form of 8a4bc2d2/ 4a2c4d3e−3?
- 2a2b/ c2d
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Description
Test your understanding of direct, inverse, combined, and joint variation concepts in mathematics. This quiz covers the equations, definitions, and problem-solving techniques related to these types of variation. Brush up on your skills and see how well you can apply these principles.
