WEBVTT
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Hi, and welcome.
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My name is Anthony Varela.
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And today we're going to
talk about literal equations.
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So we'll see examples of
different literal equations.
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And then we're going to practice
rewriting the literal equation
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for the other variables
in that equation.
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So let's start off by talking
about what an equation is.
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Well, it's a statement that two
quantities are equal in value.
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So this equation tells us that
3x is the same value as 6.
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Now let's compare this
then to 3x equals 6y.
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This is still an equation.
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It relates two quantities as
being equal to each other.
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3x is the same value as 6y.
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But this is an example
of a literal equation.
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It's an equation with
more than one variable.
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And we actually encounter
literal equations all the time
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in mathematics.
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For example, y equals mx
plus b is a literal equation.
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This is the equation to a
line in slope intercept form.
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Literal equations are
oftentimes formulas.
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And we use formulas to
calculate certain quantities
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and measurements.
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And depending on what we know
and what we need to solve,
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it might be helpful to
rewrite the literal equation.
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So for example, the
area of a rectangle
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has the formula A equals
L times W. Area equals
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the length times the width.
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Now depending on what
dimensions I know,
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I might know the
measurement for area.
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I might want to
rewrite this equation
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and write this as L equals
something or W equals something
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instead of A equals something.
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So to do this, what
I'm going to do
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is divide both sides by
L to have an equation
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for W. W equals the area
divided by the length.
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Similarly, I can take the
area and divide by the width.
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And that would give me an
equation for the length.
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Length equals area
divided by the width.
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So we're going to go over some
other common formulas that
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are literal equations
and rewrite for all
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of the different variables.
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We're going to use
distance equals rate times
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time, the area of
a circle as being
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pi times the radius squared,
and our Pythagorean theorem.
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So a distance rate
in time is actually
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very similar to our
area of a rectangle.
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We have distance
equals rate times time.
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So if I wanted to write
an equation for rate,
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I would divide distance by time.
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So r equals d over t.
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If I wanted to write
an equation for time,
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I would divide distance by
the rate. t equals d over r.
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So now let's go on to
our area of a circle.
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And so the area of
a circle is pi times
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r squared, where r is
the radius to the circle.
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And that's our
only variable here.
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Remember, pi is a number.
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So I'd like to
rewrite this equation
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to say r equals something.
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Well, I see that r
is being squared.
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And then we're
multiplying it by pi.
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So what we're going
to do is we're
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going to divide by pi first.
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So we're going to
divide the area by pi
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because this exponent of 2
is applied to the radius,
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not to pi.
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So now we have
the radius squared
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equals the area divided by pi.
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So to isolate r,
we're going to take
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the square root of both sides.
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And the radius is the square
root of the area divided by pi.
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The last equation is
the Pythagorean theorem.
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And this relates the
legs of a right triangle
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to its hypotenuse.
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So a and b are the legs,
and c is the hypotenuse.
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a squared plus b squared
equals c squared.
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And I'd like to rewrite
this equation so that I
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have a equals something,
b equals something,
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and c equals something.
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Well, then almost to my c
equals something equation,
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all you need to do is take
the square root of both sides.
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So c equals the square root
of a squared plus b squared.
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Well, now let's begin with
our Pythagorean theorem.
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And let's rewrite this
so that our equation says
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a equals something.
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So first, I need to
move that b squared term
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to the other side
of the equal sign.
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So I'm going to subtract it out.
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So I have a squared equals
c squared minus b squared.
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Well, then I'll take
the square root.
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And I have my equation
a equals the square root
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of c squared minus b squared.
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Similarly, we're going to begin
with our Pythagorean theorem.
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We've already written for
c equals and a equals,
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so we want to isolate b on
one side of the equal sign.
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So I'm going to move
my a squared term over
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through subtraction.
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So b squared equals c
squared minus a squared.
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And I'll finish this up
by taking the square root.
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So now we have an
equation that has b
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on one side of the equals sign.
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So let's review our lesson
on a literal equations.
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Well, a literal equation
contains more than one
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variable.
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And they're very
common in mathematics.
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We looked at some formulas
that are all literal equations.
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And we practiced rewriting
them for each variable.
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And this involved applying
inverse operations
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in the reverse
order of operations
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to isolate a variable.
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So thanks for watching this
tutorial on literal equations.
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Hope to see you next time.