If C = C(q) is a firm's total cost function, the quantity epsilon_{c} = q/C * (dC)/(dq) is called the elasticity of cost at the output q . Discuss the relationship between marginal cost and average cost for the intervals of being higher and lower than 1 (15 points). epsilon_{c}​

Answer:

I'm assuming the equation "Ax) = ax + bx² + cx+d" is really meant to read:

A(x) = ax^3 + bx² + cx+d

A(x) = x^3 + x^2 -4x -4

Step-by-step explanation:

(x+2)*(x+1)*(x-2)      [This reflect the fact that x= -2, x=-1, x=2 all result in a zero]

Multiply this out to get A(x) = x^3 + x^2 -4x -4

[tex]\\ \sf\longmapsto 2m+(-2m)+4m[/tex]

[tex]\\ \sf\longmapsto 2m-2m+4m[/tex]

[tex]\\ \sf\longmapsto (2-2)m+4m[/tex]

[tex]\\ \sf\longmapsto 0+4m[/tex]

[tex]\\ \sf\longmapsto 4m[/tex]

Answer:

4m

Step-by-step explanation:

2m+(-2m)+4m = 2m-2m+4m

                       = 4m

Hope it helps!!

Answer:

7 whole times, 7.2 decimal times

Step-by-step explanation:

Divide the numbers

Answer:

Two pieces of furniture.

Step-by-step explanation:

3 hours times 1 piece of furniture every 3/4 hours:

3 · [tex]\frac{3}{4}[/tex] = [tex]\frac{3*3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2.25

Assuming that pieces of furniture cannot be sold in parts, 2 whole pieces of furniture will be sold in 3 hours.

7y+10+7y+10+y-4

14y+20+y-4

15y+20-4

15y+16

answer= 15y+16

Answer:

7y+10+7y+10+y-4=

(7y+7y+y)+(10+10-4)=

15y+16=

Answer:

1,2,3,6,9,18,27,54

Step-by-step explanation:

1 x 54 = 54

2 x 27 = 54

3 x 18 = 54

6 x 9 = 54

9 x 6 = 54

18 x 3 = 54

27 x 2 = 54

54 x 1 = 54

Answer

44,005 + 5,001+ 100,009 + 93 + 3,000,007+ 7,000

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Meet at the middle of the two lines

Answer:

pretty sure it's c

Step-by-step explanation:

when we learned that, we're always supposed to start with x which in this occasion is 4 and y is 2

Answer

  595.005, 595.05,595.50 that's from least to greatest. please let me have brainliest

Step-by-step explanation:

595.005 , 595.50 595.05

Answer:

The slope is -4. The amount of money left goes down by 4 with each comic book.

Step-by-step explanation:

The answer is D

Answer:

4 better explanation inbox

Step-by-step explanation:

Answer:

[tex]t=-5[/tex]

Step-by-step explanation:

[tex]\frac{2t}{5} = \frac{t^{2} -5t}{5t}[/tex], [tex]t\neq 0[/tex]

[tex]\frac{2t}{5} = \frac{t(t-5)}{5t}[/tex]

[tex]\frac{2t}{5} = \frac{t-5}{5}[/tex]

[tex]2t = t-5[/tex]

[tex]t=-5[/tex]

Answer:

B

Step-by-step explanation:

In a function, every x-coordinate must be a different number.

If the same number appears more than once as an x-coordinate, it is not a function.

Answer: B

Answer:

K cool

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

Add 4 on both sides to get 2x = 14, then divide 2 on both sides to get x = 7.

Hope this helps :)

Answer:

6 tomatoes

Step-by-step explanation:

480/80=6

Answer:

6 tomatoes

Step-by-step explanation:

480 ÷ 80

=> 6 tomatoes

Hoped this helped.

Answer:

hello are you a Latina hola como estas soy niña

Answer:

616

Step-by-step explanation: hope it helps :)

Answer:665,830 my answer

Step-by-step explanation:

so. what have you got so far?

How can a digit have no value?

c=-9-8c

+8c

9c=-9

c=-1

Hope this helps:D!!

The letter C is equal to negative one.

c = -1

Hope this helps!

Answer:

16.3x

17. 8y

18.x+y

I thing these are the answers of these equations

It looks like given matrices are supposed to be

[tex]\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}[/tex]

You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:

• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues

• det(A) = determinant of A = product of eigenvalues

(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since

[tex]\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6[/tex]

[tex]\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5[/tex]

and

λ₁ + λ₂ = 6   ⇒   λ₁ λ₂ = λ₁ (6 - λ₁) = 5

⇒   6 λ₁ - λ₁² = 5

⇒   λ₁² - 6 λ₁ + 5 = 0

⇒   (λ₁ - 5) (λ₁ - 1) = 0

⇒   λ₁ = 5 or λ₁ = 1

To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.

• For λ = 1, we have

[tex]\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0[/tex]

With v = (v₁, v₂)ᵀ, this equation tells us that

2 v₁ + 2 v₂ = 0

so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.

• For λ = 5, we would end up with

[tex]\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0[/tex]

and this tells us

-2 v₁ + 2 v₂ = 0

and it follows that v = (1, 1)ᵀ.

Then the decomposition of A into PDP⁻¹ is obtained with

[tex]P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}[/tex]

where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.

(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if

[tex]P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}i&0\\0&i\end{bmatrix}[/tex]

(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:

[tex]\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0[/tex]

Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:

det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0

and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.

• For λ = 1,

[tex]\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0[/tex]

tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.

• For λ = 2,

[tex]\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0[/tex]

tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.

• For λ = 3,

[tex]\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0[/tex]

tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.

Then we have A = PDP⁻¹ for

[tex]P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}[/tex]

(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,

• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃   ⇒   λ₂ + λ₃ = 7

• det(A) = 20 = 2 λ₂ λ₃   ⇒   λ₂ λ₃ = 10

and we find λ₂ = 2 and λ₃ = 5.

I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.

• For λ = 2,

[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0[/tex]

tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.

• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.

[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0[/tex]

This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.

Then A = PDP⁻¹ if

[tex]P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}[/tex]

Answer:

AD=7,BE=6,AB=4,AC=3.

Answer:

The answer that you put is right

Answer:

[tex]\huge\boxed{x > 1}[/tex]

Step-by-step explanation:

-4(x - 2) + 5 < 9

Subtract 5.

-4(x - 2) < 4

Divide by -4 (Flip the sign when dividing by a negative number).

x - 2 > -1

Add 2.

x > 1

Hope it helps :) and let me know if you want me to elaborate.

Answer:

x>1

Step-by-step explanation:

I had that same question hope that helped

Answer:  54° or 40°, depending on my interpretation of the problem.

Step-by-step explanation:

I do not understand the drawing. I see a right angle with a line bisecting it at 36 degrees.  A right angle is 90°, so the other angle should be (90 - 36) or 54°.  But what's shown is (14 - 1)°, and I don't know how to interpret that.  Is the "1" supposed to be an "x"?  If so, x = 40°

Answer:

15 is the answer

Step-by-step explanation:

If it was designed as an alternate angle, then it would 63 degrees