<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:
Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k). This makes sense, if you think about it.
Step-by-step explanation:
Answer:
x = 3
Step-by-step explanation:
subtract 7 from both sides, then subtract 4x from both sides after
6x +7 = 4x + 13
-7 -7
6x = 4x +6
-4x -4x
2x = 6
divide both sides by 2x
answer x =3
Let L = Length, and W = Width. We are given the fact that L = 2W, and also know that the area = L x W = 50 square feet. So, by substitution: 2W x W = 50 sq ft, or 2W^2 = 50 sq ft, so W = sq rt (50/2) = 5 ft. Now, L = 2W = 2(5) = 10 ft. The perimeter of the fence is given by: 2L + 2W = 2(10 ft) + 2(5 ft) =20 ft + 10 ft = 30 ft. So, Ben needs 30 ft of fencing.
<span>The first number = x
The </span>second number = 2x-3
x + 2x-3 = 36
3x = 36+3
3x = 39
x = 39/3
x = 13
The first number = x = 13
The second number = 2x-3 = 2*13 - 3 = 26 - 3 = 23
