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You are given a pair of equations, one representing a supply curve and the other a demand curve, where $p$ is the per unit price for $x$ items. In each exercise (a) sketch their graphs on the same set of axes, (b) identify which is the supply and demand curve and the appropriate domain, (c) determine the coordinates of market equilibrium, (d) determine the revenue equation and (e) determine the revenue at market equilibrium.$$x^{2}+6 x-384+12 p=0 \quad x^{2}+8 x+220-11 p=0$$

(c) (5.491,26,742)(d) $R(x)-1 / 12\left(x^{3}+6 x^{2}-84 x\right)$(e) 146.84

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

Campbell University

Oregon State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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So we're given this pair of equations here and we want to solve it for P. So it's going to be um X squared minus Or actually my plus six acts -384, All divided by a Native 12. So that's one that's going to be our demand function clearly. And then the price function or the supply function is going to be X squared? Yeah plus eight x plus 2 20. Yeah. Okay. And that's all going to be divided by um 11. When we see that equilibrium is going to be reached at 5.493 20, 6.739. And then we can find the revenue function by multiplying X times this or this. That is.

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