Manipulating Equations and Dimensional Analysis

Front

Define dimensional analysis.

Back

Dimensional analysis is a mathematical technique used to convert one set of units to another, ensuring that equations are dimensionally consistent.

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What is the formula to solve for a variable in a linear equation of the form ax + b = c?

Back

To solve for x, rearrange the equation to x = (c - b) / a.

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Convert 1256 seconds to hours.

Back

0.35 h.

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Convert 27 picoseconds to femtoseconds.

Back

27,000 fs.

Front

Solve for y in the equation: 3x + y = 12.

Back

y = -3x + 12.

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What is the principle of isolating a variable in an equation?

Back

The principle involves rearranging the equation to get the desired variable on one side and all other terms on the opposite side.

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What does it mean for an equation to be dimensionally consistent?

Back

An equation is dimensionally consistent if all terms on both sides of the equation have the same dimensions.

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