College Algebra Unit 4 - Milestone 4 with answers!!
18 questions were answered correctly.
2 questions were answered incorrectly.
1
Angela is an
... [Show More] 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?
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volts
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volts. correct
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volts
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volts
RATIONALE
The voltage of the circuit is the product of
the current and resistance. Recall that we
can
write as and as .
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.
The expression multiplies
to Next, combine like
terms.
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.
is replaced by . Next, evaluate
.
CONCEPT
Complex Numbers in Electrical Engineering
2
Perform the multiplication and combine like terms.
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correct
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RATIONALE
The voltage is equivalent to , or
.
times is equal to . Finally,
combine like terms and .
When FOILing, multiply the first terms, outside
terms, inside terms, and last terms together.
Once the binomials have been multiplied
together, evaluate the multiplication.
The will need to be multiplied by everything
inside the parentheses.
When multiplying these two terms, we will start
by distributing into .
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.
and combined is . can
be expressed as . We still need to
distribute the third binomial, .
is equivalent to .
The next step is to combine like terms, and
.
CONCEPT
Multiplying Polynomials
3
Divide the following expression.
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times equals .
This is one part of the final product. We will
distribute into as well.
times equals . This
is another part of the final product. The final step
is to add these two parts together.
When multiplying these two terms, we will start
by distributing into .
This is the final product of the three binomials,
found by adding the two parts:
and .
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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, .
CONCEPT
Polynomials Divided by Monomials
4
Select the quadratic equation that has no real solution.
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correct [Show Less]