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likoan [24]
3 years ago
12

Question 2.1: To draw the supply curve, the cost of inputs to production must be held constant. If the market price of oil decli

nes, which of the following statements are true? Select all correct answers.
a.The ceteris paribus assumption is violated.

b.The supply curve will move to a different place.

c.The quantity of gasoline supplied at each price will change.

d.The supply curve will become downward sloping.
Mathematics
1 answer:
Nookie1986 [14]3 years ago
6 0

Answer:

Option c. The quantity of gasoline supplied at each price will change.

Step-by-step explanation:

There is a close correlation between the demand and supply. In simple terms, the demand increases inversely to the supply. This causes the price of the goods and commodities to shift. The precise term is inflation - the increase in the price of goods due to the decrease in the supply and increase in demand.

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Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.​
Vedmedyk [2.9K]

Compute the gradient of f.

\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle

Set this equal to the zero vector and solve for the critical points.

3x^2-6y = 0 \implies x^2 = 2y

-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}

\implies x^2 = \pm2\sqrt{2x}

\implies x^4 = 8x

\implies x^4 - 8x = 0

\implies x (x-2) (x^2 + 2x + 4) = 0

\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0

\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0

The last case has no real solution, so we can ignore it.

Now,

x=0 \implies 0^2 = 2y \implies y=0

x=2 \implies 2^2 = 2y \implies y=2

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}

Check the sign of the determinant of the Hessian at each of the critical points.

\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0

which indicates a saddle point at (0, 0);

\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0

We also have f_{xx}(2,2) = 12 > 0, which together indicate a local minimum at (2, 2).

3 0
2 years ago
PLEASE HELP IM DESPERATE <br><br> If a1=9 and an=- 3an-1 – 5 then find the value of a5.
melomori [17]

Answer:

A5 is approximately 5.8 by 8.3 inches in size, and it's the closest in size to the U.S. paper size called the “half-letter” size, at 5.5 by 8.5 inches. But here's how all the A-series sizes break down: A0 paper is 841 by 1189 millimeters, approximately 33.1 by 46.8 inches.A5 measures 148 × 210 millimeters or 5.83 × 8.27 inches. In PostScript, its dimensions are rounded off to 420 × 595 points.A5148 x 210mm5.8 x 8.3 inch

3 0
3 years ago
Read 2 more answers
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inessss [21]

Answer:

a=7/36...............

8 0
3 years ago
Multiplicar:
oksian1 [2.3K]

Answer:

a. 42

b. -12x-5

c. -60

d. -75

e. 66

f. -90

g. 144

h. -135

4 0
3 years ago
The age of a woman is 4 times the age of her daughter. 5 yrs hence,the age of the woman will be 3 times the age of her daughter.
poizon [28]

Answer:

10

Step-by-step explanation:

If W is the present age of the woman and D is the present age of the daughter, then:

W = 4D

W + 5 = 3(D + 5)

Substituting the first equation into the second:

4D + 5 = 3(D + 5)

4D + 5 = 3D + 15

D = 10

The daughter is 10 years old.

8 0
4 years ago
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