Translate each statement into an equation using k as the constant of proportionality. Q varies j

Translate each statement into an equation using k as the...

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Key Concepts

Direct Variation

Direct variation is the relationship where one variable increases or decreases in direct proportion to another. The equation for direct variation is typically expressed as y = kx, where k is the constant of proportionality.

Inverse Variation

Inverse variation describes the relationship between two variables such that when one variable increases, the other decreases in a way that their product remains constant. This relationship is represented by the equation y = k/x, where k is the constant of proportionality.

Joint Variation

Joint variation occurs when a variable depends directly on two or more other variables. It is modeled by an equation where the variable is equal to a constant multiplied by the product of the other variables, such as y = kxz, indicating that y varies jointly as x and z.

Constant of Proportionality

The constant of proportionality, denoted as k, is the fixed number that relates the variables in any direct, inverse, or joint variation model. It is determined by substituting known values from the problem into the variation equation.

Transcript

00:01 Okay, so this question says that q very shortly with m, the square of n, but then inversely with the variable p.

00:08 And then it gives us some examples to use and says, here's, you know, q's 2, m's 3, n6, p is 12.

00:16 That's it all solved out, but now i'm going to give you one missing, and you kind of have to figure out what that missing value is.

00:21 So the first thing we're going to do is we're going to turn this sentence that it gave us into an equation.

00:26 And we're going to be using kind of the two general forms, which is y equals kx if it varies directly, and y equals k over x if it varies indirectly.

00:38 This one does both, so we're going to be combining them.

00:41 So since it's jointly with m and the square of n, that gives us that q is equal to k m and then n squared, right, because square of n is n squared, and then inversely with p, tell us we need to divide.

00:57 Divide by that p.

00:59 So this is the equation i'm going to be using to get basically everything.

01:04 Right.

01:05 So that's your first step.

01:05 You really need to know how to turn that sentence into an equation.

01:09 And now what i'm going to be doing is i'm going to be coming over here and i'm going to be using these values.

01:15 Oops.

01:16 Let's back up just a little bit.

01:17 There we go...