College Algebra Unit 4 - Milestone 4 with answers and rationale

College Algebra Unit 4 - Milestone 4 with answers and rationale 18 questions were answered correctly. 2 questions were answered incorrectly. 1 Angela is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. She uses the following formula to calculate voltage: The circuit she tests has a current of amps and a resistance of ohms. What is the voltage of the circuit? • • • • RATIONALE The voltage of the circuit is the product of the current and resistance. Recall that we can write as and as . Once we have expressed voltage in terms of , we need to multiply these two complex numbers by using FOIL. Multiply the first terms , the outside terms , the inside terms , and the last terms . Next, evaluate each multiplication. The expression multiplies to Next, combine like terms. and can combine to . Now we can simplify the last term, , which contains the imaginary unit squared. Recall that the is equivalent to , which can be substituted in our expression. . CONCEPT Complex Numbers in Electrical Engineering 2 Perform the multiplication and combine like terms. • • correct • • RATIONALE To multiply a set of three binomials, we can choose any two binomials to multiply using FOIL, and then distribute the remaining binomial to get a final product. Here, we will use FOIL to multiply , but you can choose any two binomials to start. Once the binomials have been multiplied together, evaluate the multiplication. . and combined is . can be expressed as . We still need to distribute the third binomial, . When multiplying these two terms, we will start The will need to be multiplied by everything inside the parentheses. times equals . This is one part of the final product. We will distribute into as well. When multiplying these two terms, we will start by distributing into . times equals . This is another part of the final product. The final step is to add these two parts together. This is the final product of the three binomials, found by adding the two parts: and . CONCEPT Multiplying Polynomials 3 Divide the following expression. • • • • correct RATIONALE Start by rewriting the expression into multiple fractions with as the denominator. Remember to use the correct signs (addition or subtraction) between the fractions. Now that we have individual fractions, we can simplify each fraction. To do this, cancel out common factors in the numerator and denominator. Let's consider the first set, . simplifies to because we can factor out from both terms. Next, consider the second set, . simplifies to because we can factor out from both terms. Next, consider the third set, . simplifies to because we can factor out from both terms. The expression can be simplified to . CONCEPT Polynomials Divided by Monomials 4 Select the quadratic equation that has no real solution. • • • correct • RATIONALE We can tell if a quadratic has no real solutions by using the quadratic formula. We can use the discriminant, or the value underneath the square root. Because the discriminant is underneath a square root sign, it must not have a negative value. If it is greater than or equal to zero, it will have real solutions. If it is negative, it will have non-real solutions. This is the expression for the discriminant. For each quadratic equation, we can substitute the appropriate values into this expression and determine if it will have real or non-real solutions. For this answer choice, plug the coefficients into the expression for the discriminant, and determine if the discriminant is negative. In the equation , , , and . Now that the appropriate values are plugged in, evaluate the discriminant. squared is and times times is . Next, find the difference between and .