MAT 171 7.1, 7.2, 8.1, 7.3

Front

What is partial fraction decomposition?

Back

Partial fraction decomposition is a method used to express a rational function as the sum of simpler fractions, making it easier to integrate or manipulate.

Front

How do you perform partial fraction decomposition for a rational expression?

Back

To perform partial fraction decomposition, factor the denominator into linear or irreducible quadratic factors, then express the rational function as a sum of fractions with unknown coefficients, and solve for those coefficients.

Front

What is the formula for the average velocity of a current in a river or stream?

Back

The average velocity of the current can be calculated using the formula: Current Velocity = (Distance Downstream / Time Downstream) - (Boat Speed).

Front

What is the addition method for solving systems of equations?

Back

The addition method, also known as the elimination method, involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to solve for the remaining variable.

Front

What is the significance of the roots of a polynomial in partial fraction decomposition?

Back

The roots of a polynomial determine the linear factors in the denominator, which are essential for setting up the partial fraction decomposition.

Front

What is the relationship between distance, rate, and time in motion problems?

Back

The relationship is given by the formula: Distance = Rate × Time. This can be rearranged to find any of the three variables.

Front

How do you check the correctness of a partial fraction decomposition?

Back

To check the correctness, combine the fractions on the right side back into a single fraction and see if it equals the original rational expression.

Front

What are the steps to solve a system of equations using the addition method?

Back

1. Align the equations. 2. Multiply one or both equations to obtain opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable. 4. Solve for the remaining variable.

Front

What are the steps to solve a system of equations using the substitution method?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.