Homework Help for Mathematics
Mathematics is an exact and deductive science that studies abstract entities such as numbers, geometrical figures, symbols ans their relation.
10. Show by the substitution that
is a solution of the transport equation with velocity calculated in Q3. This would correspond to the spread of pollutant that was initially in a thin line along y = x. Hint: To reduce your writing, you may find it useful to write this as with .
Velocity in Q3 was calculated as 3.
3. Show by substitution that p = −x − 2y is a solution of the pressure equation above and calculate the
corresponding velocity v assuming λ = 1.
10. Show by substitution that
is a solution of the transport equation with the velocity calculated in Q3. This would correspond to the spread of pollutant that was initially in a thin line along y = x. Hint: To reduce your writing, you may find it useful to write this as with
1)The additional output obtained by adding another unit of labor to the production process is called _____. A. the marginal product of labor B. a variable cost C. the marginal cost of labor D. the average output of labor
2)The law of diminishing marginal returns states that: A. long-run average cost declines as output increases. B. if the marginal product is above the average product, the average will rise. C. as units of a variable input are added to a given amount of fixed inputs, the marginal product of the variable input eventually diminishes. D. if marginal product is positive, total product rises.
3)The short-run average variable cost curve: A. starts above the origin and always slopes upward. B. starts at the origin and always slopes upward. C. slopes downward at low rates of output and then slopes upward at higher rates of output. D. is always downward sloping.
4)If a firm shuts down in the short run and produces no output, its total cost will be: A. equal to the variable cost. B. equal to the fixed cost. C. equal to zero. D. equal to only explicit costs.
5)Which of the following is true of the MC curve? A. It intersects the AVC curve at its minimum, but it does not intersect the ATC curve at its minimum. B. It intersects both the ATC and the AVC curves at their minimums. C. It intersects the ATC curve at its minimum, but it does not intersect the AVC curve at its minimum. D. It intersects both the ATC and the AFC curves at their minimums.
6)The shape of the long-run average cost curve reflects _____. A. increasing and diminishing marginal returns B. market demand C. productivity of fixed inputs D. economies and diseconomies of scale
7)The price charged by a perfectly competitive firm is determined by: A. each individual firm. B. market demand and market supply. C. a group of firms acting together as a cartel. D. the firm's total costs.
8)The demand curve facing a perfectly competitive firm is: A. vertical at the equilibrium quantity. B. upward sloping. C. a horizontal straight line at the market price. D. a straight line through the origin.
9)The total revenue curve for a perfectly competitive firm_____. A. is a backward-bending curve B. is a vertical line intersecting the horizontal axis C. is a horizontal line intersecting the vertical axis D. is a straight line that starts from the origin and slopes upward
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