A perfectly competitive industry consists of many identical firms, each with a long-run average total cost of LATC = 800 – 10Q + 0.1Q2 and long-run marginal cost of LMC = 800 – 20Q + 0.3Q2. In long-run equilibrium, each firm produces a quantity of .

Each firm produces a quantity of 50 in long run equilibrium.

Explanation:

If a perfectly competitive industry of many identical firms has a long-run average total cost of LATC = 800 – 10Q + 0.1Q² and long-run marginal cost of LMC = 800 – 20Q + 0.3Q², for long run equilibrium to occur, LATC must be equal to LMC i.e LATC = LMC.

Equating both cost equation to get quantity Q each firm produces gives;

800 – 10Q + 0.1Q² = 800 – 20Q + 0.3Q²

Bringing all the terms to one side of the equation, we will have;

800-800-10Q+20Q+0.10Q²-0.3Q² = 0

10Q-0.2Q² = 0

Factorizing out Q, the equation becomes;

Q(10-0.2Q) = 0

From the resulting equation;

10-0.2Q = 0

10 = 0.2Q

Q= 10/0.2

Q = 50

This shows that each firm produces a quantity of 50 in long run equilibrium.

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

our agriculture industry and our business industry