Answer to Question #24866 in Calculus for Denis

Question

Pair equations, one representing a supply curve and other demand curve.

a) Determine coordinates of the market equilibrium b) determine the revenue equation c) determine the revenue at market equilibrium.
Please explain how did you get the answer!!! Thanks
-7p+2x+7=0
p=sqrt(16-x)

Answer 1

a)p^2 = 16 - x,
x = 16 - p^2
-7p + 32 - 2p^2 + 7 = 0
2p^2 + 7p - 39 = 0
D = 49 - 4*2*(-39) = 361, sqrt(D) = 19
p1 = (-7 + 19)/4 = 3
p2 = -26/4 can't be used.
So, p = 3, x = 16 - 3^2 = 7

b) TR = P*Q = p*x

c) TR = 3*7 = 21