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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.$$p=\sqrt{x+14}, \quad p=\sqrt{36-x}$$

(c) (11,5)(d) $R(x)=x \sqrt{36-x}$(e) 55

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

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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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given problem were given a pair of equations and they're already sell for peace. So we see that P equals could square effect plus 14. That's going to be our supply equation. And then the demand equation is going to be P equals route 36 minus X because this one is decreasing and we want to find the equilibrium point, that's going to be right here 11 5. Um And then lastly we want to find the revenue curve or the revenue equation. So we know that the revenue equation is always equal to X times P of X or P effective to demand function. So we're going to take this demand function being placed right here. So that's our revenue function right here. And we see that the revenue when the markets at equilibrium Is going to be when x equals 11. So if we go to x equals 11 um for the revenue curve, We see that 55 is the revenue at that specific point in time.

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