Use a variation model to solve for the unknown value. The...

Use a variation model to solve for the unknown value. The power in an electric circuit varies jointly as the current and the square of the resistance. If the power is $144 \mathrm{W}$ (watts) when the current is $4 \mathrm{A}$ (amperes) and the resistance is $6 \Omega,$ find the power when the current is $3 \mathrm{A}$ and the resistance is $10 \Omega$

Use a variation model to solve for the unknown value.
The power in an electric circuit varies jointly as the current and the square of the resistance. If the power
is $144 \mathrm{W}$ (watts) when the current is $4 \mathrm{A}$ (amperes) and the resistance is $6 \Omega,$ find the power when the current is $3 \mathrm{A}$ and the resistance is $10 \Omega$

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Key Concepts

Proportionality Constant

A proportionality constant is a fixed value that scales the relationship between variables in a variation model. When variables are known to vary jointly, the constant is determined using given values, which then allows for the calculation of unknown outcomes under different conditions.

Solving Variation Models

Solving variation models involves setting up the equation based on the defined relationship, typically in the form of an equation with a proportionality constant. Once the constant is determined using provided values, the model can be applied to find unknown quantities when other variables change. This systematic approach is applicable to a wide range of scenarios in mathematics and physics.

Joint Variation

Joint variation occurs when a variable is directly proportional to the product of two or more other variables. In this type of relationship, if any of the variables increase while the others remain constant, the dependent variable also increases. The concept is used to model situations where several factors simultaneously affect an outcome.

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