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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example

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# Isolating quantities — Basic example

Watch Sal work through a basic Isolating quantities problem.

## Want to join the conversation?

- I moved pgh to the left instead and solved from there and I got a different answer. Is my answer totally wrong ?(5 votes)
- why isnt the answer c?(3 votes)
- In this question we're given an equation and asked to solve for something other than the variable that it's normally solved for. We just do our algebra in order to get the result that we want.

P = P_0 + pgh

pgh = P - P_0

h = (P - P_0) / pg

The answer isn't C here because we have to first isolate the pgh term before dividing by pg. Whenever multiplying/dividing, we have to do it to every single term, and C) assumes we did order of operations wrong.(3 votes)

- At0:03, Sal mentions the Greek letter rho. What does rho mean?(2 votes)
- Rho is just a letter, so it doesn't have any special meaning. In science, you may come across it used to talk about densities.(3 votes)

- why is it so complex and complicated(0 votes)
- because the ancient math guys wanted to make us suffer(7 votes)

- So, we basically try to cancel out both sides of the equations that are equal, and then we isolate the necessary variable, and finally we simplify down to get our answer.(2 votes)
- i didnt think i was going to get it but i get it now(2 votes)
- In practice it was p= l+h*2, you first divide 2 to both sides and it becomes p divided 2, and then minus l separately but here you write p-po over pg combined?(2 votes)
- What is sub zero... is it like a variable or an equation?(0 votes)
- Well,
`sub zero`

is an example of keeping different quantities that have the same variable separate using a subscript. In this case we have two kinds of pressure:

P which is absolute pressure and P₀ which is atmospheric pressure.

We use this method of naming or distinguishing otherwise identical variables a lot in algebra and geometry to calculate slope and distance--subscripts allow us to use multiple values for x or y

The famous slope equation is Δy/Δx = m = (y₂ - y₁ ) / (x₂ - x₁ )

and, of course, we use it to tell apart the y-value for the second point (y₂ ) from the y-value for the first point (y₁ ) , not to mention the x-value for the second point (x₂ ) from the x-value of the first point (x₁ )

Same with distance formula D = √( (x₂ - x₁ )² + (y₂ - y₁ )²)

So subscripts are an old friend. Here we have to make sure we**do not combine**the variables by merging them into 2 P because they are NOT the same.(4 votes)

## Video transcript

- [Instructor] The absolute
pressure P in a fluid of density rho, I know this
looks like a lowercase p but this is the Greek letter rho, which we typically use for density, at a given depth h can be
found with the above equation where capital P with the
little subscript of this, I guess P sub zero, or
maybe it's just an O but it looks like a zero, P sub
zero is atmospheric pressure and g is gravitational acceleration. Which of the following
is the correct expression for the depth in terms
of the absolute pressure, atmospheric pressure, fluid density, and gravitational acceleration? So essentially what we
wanna do is we wanna solve for depth, we wanna solve for h. So let's see if we can do that. So we have P is equal to P
sub, I'll call this P sub zero, plus rho times g times h. Now to solve for h, I would
at least wanna isolate this term that contains
h on the right-hand side and so let me subtract P
sub zero from both sides. So subtract P sub zero,
subtract P sub zero, and then on the left-hand side, I have capital P minus capital P sub zero is equal to, those are
going to cancel out. You're gonna have rho times g time h and now to solve for h
I can divide both sides by rho times g, so let's do that. Let's divide this side by rho times g and let's divide this side by rho times g. Rho times g divided by rho times g is just going to be one
and we get h is equal to this thing right over here. We could say h is equal to capital P minus capital P sub zero over rho times g, and that is the first
choice right over there.