Which of the following represent an inverse variation?

Steps to Solve

1. Identify Inverse Variation To find the equation that represents inverse variation, we need an equation of the form ( y = \frac{k}{x} ). The correct answer is: Option b. ( y = \frac{k}{x} )

2. Identify Directly Proportional Variation For directly proportional relationships, we look for an equation of the form ( y = kx ). The correct answer is: Option a. Direct Variation

3. Identify Situation of Rain and Level The situation describes a relationship that can be either joint or direct variation. The correct answer is: Option c. Joint Variation

4. Equation to Find Constant of Direct Variation For finding the constant of a direct variation, we use an equation like ( k = \frac{y}{x} ). Thus, the answer is: Option b. ( k = \frac{y}{x} )

5. Translate Volume of Cylinder The volume ( V ) of a cylinder is given by the formula ( V = \pi r^2 h ). Therefore, the matching translation is: Option d. ( V = k(rh)^2 )

6. Evaluate 'y' in Inverse Variation If ( y ) varies inversely as ( x ), the formulation used can be derived by rearranging the provided information. With ( y ) values corresponding to ( x ) values, evaluate appropriately.

7. Determine Weight and Mass Relationship We have given weights in relationship to mass hence ( W ) varies directly with ( M ). Determine using simple substitution based on provided equations.

8. Deep Well Construction Problem For construction, using inverse proportion to define the relationship will yield the needed manpower estimate based on given rates.

9. Area Increase Calculation The area increase can be computed via the formula for the area of a triangle, and plugging in the height and the new base values as given.

10. Exponents and Simplifications Use exponent rules to simplify expressions step-by-step, applying necessary laws for the calculations, such as converting from radical to exponential form and vice versa.