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Course: Digital SAT Math > Unit 4
Lesson 6: Isolating quantities: foundationsIsolating quantities — Basic example
Watch Sal work through a basic Isolating quantities problem.
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- why is it so complex and complicated(1 vote)
- because the ancient math guys wanted to make us suffer(44 votes)
- 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?(4 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.(7 votes)
- That's what the Oldie Mathematicians would say.(0 votes)
- i didnt think i was going to get it but i get it now(5 votes)
- At0:03, Sal mentions the Greek letter rho. What does rho mean?(3 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.(5 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.(3 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?(3 votes)
- I signed up for a Math SAT, not a Physics class. This genuinely confused me when I read it, but then I realized that the focus of the problem was not on physics. LOL(0 votes)
- I hope all math questions on test day will be 100% isolating quantities(0 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.