College Algebra Unit 4 - Milestone 4 with answers!!
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?
•
volts
•
volts. correct
•
volts
•
volts
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.
is replaced by . Next, evaluate
.
, times is equal to . Finally,
combine like terms and .
The voltage is equivalent to , or
.
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.
When FOILing, multiply the first terms, outside
terms, inside terms, and last terms together.
Once the binomials have been multiplied
together, evaluate the multiplication.
is equivalent to .
The next step is to combine like terms, and
.
and combined is . can
be expressed as . We still need to
distribute the third binomial, .
When multiplying these two terms, we will start
by distributing into .
The will need to be multiplied by everything
inside the parentheses.
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