Dimensional Analysis and Variable Isolation

This video tutorial covers lesson 2.8 on literal equations and dimensional analysis. It teaches how to solve equations for specific variables, apply formulas to real-world problems, and use dimensional analysis for unit conversion. The lesson includes solving equations with variables in multiple places and applying these concepts to word problems, such as calculating fuel economy and converting units of measurement.

What is the primary focus of dimensional analysis?

• Converting units from one form to another

• Finding the average of a set of numbers

• Solving equations for a specific variable

• Calculating the area of geometric shapes

When solving for a variable, what is the first step if the variable is being added to another term?

• Add the term to both sides

• Divide both sides by the term

• Subtract the term from both sides

• Multiply both sides by the term

In the equation 5B + 12C = 9, what operation would you perform to isolate B?

• Multiply both sides by 5

• Subtract 12C from both sides

• Add 12C to both sides

• Divide both sides by 5

How do you handle variables that appear on both sides of an equation?

• Add them together

• Subtract one from the other

• Ignore one of the variables

• Move them to one side of the equation

What is the result of isolating X in the equation 7X + YX = 4 + 2Z?

• X = (4 + 2Z) * (7 + Y)

• X = (4 - 2Z) / (7 - Y)

• X = (4 - 2Z) * (7 - Y)

• X = (4 + 2Z) / (7 + Y)

In the formula E = M/G, what operation is needed to solve for M?

• Add G to both sides

• Divide both sides by G

• Subtract G from both sides

• Multiply both sides by G

What does the variable E represent in the context of a car's fuel economy?

• Energy used

• Efficiency of the engine

• Miles per gallon

• Gallons of fuel used

What is the first step in converting kilograms to pounds using dimensional analysis?

• Convert pounds to kilograms

• Convert ounces to pounds

• Convert grams to ounces

• Convert kilograms to grams

If 1 gram is approximately 0.0353 ounces, how many ounces are in 52 kilograms?

• 1835.6 grams

• 1835.6 ounces

• 1835.6 kilograms

• 1835.6 pounds

What is the final step in converting ounces to pounds?

• Divide by 16

• Add 16

• Multiply by 16

• Subtract 16