<span>The fact that Helen’s indifference curves touch the axes should immediately make you want to check for a corner point solution. To see the corner point optimum algebraically, notice if there was an interior solution, the tangency condition implies (S + 10)/(C +10) = 3, or S = 3C + 20. Combining this with the budget constraint, 9C + 3S = 30, we find that the optimal number of CDs would be given by 3018â’=Cwhich implies a negative number of CDs. Since it’s impossible to purchase a negative amount of something, our assumption that there was an interior solution must be false. Instead, the optimum will consist of C = 0 and Helen spending all her income on sandwiches: S = 10. Graphically, the corner optimum is reflected in the fact that the slope of the budget line is steeper than that of the indifference curve, even when C = 0. Specifically, note that at (C, S) = (0, 10) we have P C / P S = 3 > MRS C,S = 2. Thus, even at the corner point, the marginal utility per dollar spent on CDs is lower than on sandwiches. However, since she is already at a corner point with C = 0, she cannot give up any more CDs. Therefore the best Helen can do is to spend all her income on sandwiches: ( C , S ) = (0, 10). [Note: At the other corner with S = 0 and C = 3.3, P C / P S = 3 > MRS C,S = 0.75. Thus, Helen would prefer to buy more sandwiches and less CDs, which is of course entirely feasible at this corner point. Thus the S = 0 corner cannot be an optimum]</span>
Answer:..............................
Yes, what?
Question:
The quantities x and y are in proportion
x y
4 6
30 45
8 b
a 15
(a) Find the values of a and b.
(b) Find the constant of variation. Is it direct variation or inverse variation?
Answer:
and 
Constant of variation is 1.5
Direct Variation
Step-by-step explanation:
Solving (a): The values of a and b
First, we determine the equation that relates x and y
From the table, we have:
The slope (m) is:
The equation is then calculated using:
This gives:
Solving for the value of b
From the table: x = 8, y = b
Substitute these values in
Solving for the value of a
From the table: x = a, y = 15
Substitute these values in
Solve for a
Solving (b): The constant of variation.
This has been solved in (a) above as:
Direct or Inverse?
From the given table, we notice that y increases as x increases and y decreases as x decreases.
<em>This shows direct variation</em>
Answer:
5,8 or 8,5
Step-by-step explanation:
A arcade game gives 8 tickets this = y
For every 5 game played this = x
so we can make the assumption that every 5 games played he gets 8 tickets you can write this as 5,8 or. Every 5 game played is 8 tickets.
I would assume this to be equal to y⁴ ₓ y⁵
= y⁴ ⁺ ⁵, By law of indices.
= y⁹
I hope this helped.
