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Equilibrium price and quantity, Derivative

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Please help with the following problems.

1. You are in the market for oranges. The supply equation (in millions) for oranges is : S(P)= .3p^2 +11P - 40 The demand equation is D(P) = .7p^2 +P - 1

a. How many oranges are demanded at a price of $11.50?

b. Find the equilibrium price and quantity.

2. F(X)= x^2 +2, G(X)= 3(x-3)^2, H(X)= 5/2x-3

Calculate:
a. g(h(r))

b. f(g(5x))

3. Using the definition of a derivative, calculate f'(x) for the following:
a. f(x)=2/x^2

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This solution helps with problems involving equilibrium price and quantity derivative. Step by step calculations are provided in the solution.

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1. You are in the market for oranges. The supply equation (in millions) for oranges is : S(P)= .3p^2 +11P - 40 The demand equation is D(P) = .7p^2 +P - 1

a. How many oranges are demanded at a price of $11.50?

b. Find the equilibrium price and quantity.

(a) D(p) = 0.7p^2 + p - 1
Plug in p = 11.50
D(11.50) = 0.7(11.50)^2 + 11.50 - 1 = 103.08
103 oranges are demanded at a price of $11.50
(b) ...

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