3. State thoroughly and precisely Euclids fifth postulate. According to Playfair, "Given a line l and...

3. State thoroughly and precisely Euclids fifth postulate.
According to Playfair, "Given a line l and a point P not on l, there is exactly one line through P that is parallel to l"
Are Euclids fifth postulate and Playfair's claim logically equivalent? If yes, justify your stance. If no, produce a counter example.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Using SAS (Side-angle-side postulate), find a point on a given line that is equally distant from...

Using SAS (Side-angle-side postulate), find a point on a given line that is equally distant from two given points. Find the midpoint using SAS.

The technology available allows to produce a good according to the production function F(L,K)=[(L-3)K]1/3 if L≥3...

The technology available allows to produce a good according to the production function F(L,K)=[(L-3)K]1/3 if L≥3 and K≥0, and F(L,K)=0 if L<3. The market demand for this good is D(p)=90/p. The prices of labor and capital are w=1 and r=9, respectively. A. (12 points) Describe the cost minimization problem of a firm with this technology, and calculate its conditional factor demands. Also, calculate the firm's total, average and marginal cost functions. B. (10 points) Calculate la supply of a competitive...

Consider n=3 state |3,l,j,?? 〉 of the hydrogen atom. Find the energy of each state under...

Consider n=3 state |3,l,j,?? 〉 of the hydrogen atom. Find the energy of each state under weak-field Zeeman splitting for n=3 level of the hydrogen and show them on a diagram. (no need to find the energy spectrum of the state with fine structure.)

According to the Solow model, in the steady state, both output per worker Y/L and the...

According to the Solow model, in the steady state, both output per worker Y/L and the capital stock per worker K/L grow at the rate of technological progress, and (choose one or both) A this is confirmed by U.S. data for the past half century—about 2 percent per year B this means that the capital-output ratio has remained approximately constant over time Technological progress also affects factor prices, and in the steady state, (choose two) A the real wage is...

Assume that a production function is given by y = AK^1/3 L^2/3. If A = 6 and L = 1, the depreciation rate is 0.15

Assume that a production function is given by y = AK^1/3 L^2/3. If A = 6 and L = 1, the depreciation rate is 0.15, and the savings rate is 0.4, the steady-state level of capital is?

Let L be the line passing through the point P=(−3, −4, 2) with direction vector →d=[−3,...

Let L be the line passing through the point P=(−3, −4, 2) with direction vector →d=[−3, 3, 0]T. Find the shortest distance d from the point P0=(1, −5, −1) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where needed to give an exact value for your answer. d = 0 Q = (0, 0, 0)

3. Frisbees are produced according to the production function q = 2K+L where q =output of...

3. Frisbees are produced according to the production function q = 2K+L where q =output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant deÖned in part a and part...

In the classic model given the following: Production function: Y=3 K^.5 L^.5 Labor (L) is 400...

In the classic model given the following: Production function: Y=3 K^.5 L^.5 Labor (L) is 400 units Capital (K) is 100 units Taxes (T) are 200 Government Spending (G) is 100 Marginal Propensity to Consume is .6 Investment is determined by the following function: I(r) = 1000- 100r where r is real interest rate. 1. a.) full formula, Y=c(Y-T)+I+G, What are the equilibrium values of C, I and r? b.) How much are Public savings, Private savings and National Savings?...

The production function of a certain country is given by Q = f(K,L) = 90K1/3,L2/3 where...

The production function of a certain country is given by Q = f(K,L) = 90K1/3,L2/3 where Q is the number of output produced in units of millions , K is the capital expenditures in units of $1 million and L is the size of labor force in thousands of worker – hours . Find the level of output if the capital expenditure is Tsh 27 million dollars and the labor level is 8,000 workers – hours. At the same level...

Consider a firm whose production is given by Q(K, L) = K^1/3L^1/3, where K and L...

Consider a firm whose production is given by Q(K, L) = K^1/3L^1/3, where K and L are, respectively, the quantities of capital and labour production inputs. Prices of capital and labour are both $1 per unit. (a) Derive and interpret the firm’s demand functions for capital and labour. (b) Derive and interpret the firm’s Long-Run Cost Function. (c) In the long-run, if the firm wished to produce 16 units of output, what quantities of capital and labour would it optimally...

Subjects