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?
•
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,
.
, 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.
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?
•
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,
.
, 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.
