Differentiate implicitly to find the first partial derivatives of z. 11x2 + 2y^2 + 5z^2 = 4 ϑz/ϑx =
ϑz/ϑy =

Answer:

fourth option

Step-by-step explanation:

Given

3x < - 9 ( divide both sides by 3 )

x < - 3

solution set is { x | x < - 3 }

Answer:

5,500

Step-by-step explanation:

2,500 + 3,000:

2000 + 3000 + 500

5000 + 500

5500

Easy!

Answer

A

Step-by-step explanation:

The linear function defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given series is -4, -1, 2, 5, 8. The common difference of the series is  calculated as,

d = -1 - ( -4 )

d = -1 + 4

d = 3

The equation will be written as,

an = a₁ + d(n - 1)

an = -4 + 3(n - 1)

Therefore, the linear function that defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.

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Answer:

Mean:5

Mode: 4

Range: 7

Median: 5

Step-by-step explanation:

A. There are 37 terms in the sum.

B. The sum of the given series is 7,696.

A. Using arithmetic sequences, We can observe that each term in the sum is obtained by adding 11 to the previous term. Therefore, the nth term can be expressed as:

\(a_n = 10 + 11(n-1)\)

We want to find the number of terms in the sum up to \(a_n\) = 406. Setting \(a_n\)= 406 and solving for n, we get:

406 = 10 + 11(n-1)

396 = 11(n-1)

n = 37

Therefore, there are 37 terms in the sum.

B. We can use the formula for the sum of an arithmetic series:

\(S_n = n/2 * (a_1 + a_n)\)

where \(S_n\) is the sum of the first n terms, \(a_1\) is the first term, and\(a_n\) is the nth term.

In this case, we have:

\(a_1\)= 10

\(a_n\)= 406

n = 37

Substituting these values, we get:

\(S_{37}\) = 37/2 * (10 + 406)

\(S_{37}\) = 18.5 * 416

\(S_{37}\) = 7,696

Therefore, the sum of the given series is 7,696.

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The half life period is the time in which only half of the given population remains. It can be represented through this equation:

\(f(t)=a\times(1/2)^{\frac{t}{h}}\)

We're given:

For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.

This can be calculated simply by multiplying the given half-life by 3:

28 million years x 3

= 84 million years

84 million years

Kiera's actions reveal a combination of options A, B, and D. Firstly, Kiera demonstrates her belief in her mother's abilities by taking charge and handling a problematic situation independently.

When her mother's campaign video fails to load, Kiera promptly steps in and manages to get the content loaded, exhibiting her resourcefulness and support for her mother's cause. Furthermore, Kiera attends the luncheon despite feeling uneasy and out of place, indicating her willingness to show up and support her mother's endeavors. However, Kiera's discomfort highlights her struggles with her mother's newfound political fame, and the changes that come with it, such as the exclusive event that she attends. Lastly, Kiera's decision to seek out friends and social connections suggests her recognition of the shifting dynamics in her household and her need for companionship amidst the family's political spotlight. Therefore, Kiera's actions in chapter 2 reveal her loyalty and support for her mother's campaign, but also her internal conflict and search for stability amidst the changes in her life.

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The third pattern because you can divide 12 by the number of shapes in the sequence and start counting from the remainder.

In this case choice C has 5 shapes. 12/5 is 2, with a remainder of 2.

The second term in choice C is Circle, so choice C is the answer.

Of course, you can also list them all out.

If there is no remainder when you divide then the 12th term is the last term in the sequence.

Answer:

yes

Step-by-step explanation:

What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%

annual interest, compounded monthly?

Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=$120,000

t=12 years

r=14%=14/100=0.14

n=12

substitute in the given formula

Solve for P

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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We can see here that the solutions to the triangles are:

1. 62.2°.

2. 35.9°

3. 61.9°

4. 53.1°

We can see here that using trigonometric ratio formula, we find the values of x.

We see the following:

1. Cos x = 7/15 = 0.4666

x = \(cos^{-1}\) 0.4666 = 62.2°.

2. Sin x = 27/46 = 0.5869

x° = \(sin^{-1}\)  0.5869  = 35.9°

3. Sin x = 30/34 = 0.8823

x° = \(sin^{-1}\) 0.8823 = 61.9°

4. Tan x = 8/6 = 1.3333

x° = 1.3333 = 53.1°

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The text discusses a production function and addresses various aspects of a firm's decision-making. It covers profit maximization, factor demand functions, supply function, profit function, Hotelling's lemma, cost minimization, conditional factor demand functions, and the cost function. These concepts are derived using mathematical calculations and formulas. Hotelling's lemma is verified, and the cost function is determined.

(a) The firm's profit maximization problem can be stated as follows: Maximize profits (π) by choosing the optimal levels of inputs (z and zo) that maximize the output (y) given the prices of output (p) and inputs (w, w₂).

(b) To derive the firm's factor demand functions, we need to find the conditions that maximize profits.

The first-order condition for input z is given by:

∂π/∂z = p * (∂f/∂z) - w = 0

Substituting the production function f(z) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/4 * z^(-3/4) / z^(1/2)) - w = 0

Simplifying, we get:

p * (1/4 * z^(-7/4)) - w = 0

Solving for z, we find:

z = (4w/p)^(4/7)

Similarly, for input zo, the first-order condition is:

∂π/∂zo = p * (∂f/∂zo) - w₂ = 0

Substituting the production function f(zo) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Simplifying, we get:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Solving for zo, we find:

zo = (2w₂ / (pz^(1/4)))^(2/3)

(c) To derive the firm's supply function, we need to find the level of output (y) that maximizes profits.

Using the production function f(z), we can express y as a function of z:

y = z^(1/4) / z^(1/2)

Given the factor demand functions for z and zo, we can substitute them into the production function to obtain the supply function for y:

y = (4w/p)^(4/7)^(1/4) / (4w/p)^(4/7)^(1/2)

Simplifying, we get:

y = (4w/p)^(1/7)

(d) The firm's profit function is given by:

π = p * y - w * z - w₂ * zo

Substituting the expressions for y, z, and zo derived earlier, we have:

π = p * ((4w/p)^(1/7)) - w * ((4w/p)^(4/7)) - w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

(e) To verify Hotelling's lemma, we need to calculate the partial derivatives of the profit function with respect to the prices of output (p), input z (z₁), and input zo (z₂).

Hotelling's lemma states that the partial derivatives of the profit function with respect to the prices are equal to the respective factor demands:

∂π/∂p = y - z * (∂y/∂z) - zo * (∂y/∂zo) = 0

∂π/∂z₁ = -w + p * (∂y/∂z₁) = 0

∂π/∂z₂ = -w₂ + p * (∂y/∂z₂) = 0

By calculating these partial derivatives and equating them to zero, we can verify Hotelling's lemma.

(f) The firm's cost minimization problem can be stated as follows: Minimize the cost of production (C) given the level of output (y), prices of inputs (w, w₂), and factor demand functions for inputs (z, zo).

(g) To derive the firm's conditional factor demand functions, we need to find the conditions that minimize costs. We can express the cost function as follows:

C = w * z + w₂ * zo

Taking the derivative of the cost function with respect to z and setting it to zero, we get:

∂C/∂z = w - p * (∂y/∂z) = 0

Simplifying, we have:

w = p * (1/4 * z^(-3/4) / z^(1/2))

Solving for z, we find the conditional factor demand for z.

Similarly, taking the derivative of the cost function with respect to zo and setting it to zero, we get:

∂C/∂zo = w₂ - p * (∂y/∂zo) = 0

Simplifying, we have:

w₂ = p * (1/2 * z^(1/4) * zo^(-3/2))

Solving for zo, we find the conditional factor demand for zo.

(h) The firm's cost function is given by:

C = w * z + w₂ * zo

Substituting the expressions for z and zo derived earlier, we have:

C = w * ((4w/p)^(4/7)) + w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

This represents the firm's cost function.

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Therefore, the solution to the given differential equation is: y = -cos(x)(x + C), where C is the constant of integration.

To solve the differential equation using separation of variables, we will separate the variables and integrate.

e^(-y) sec(x) - dy/dx cos(x) = 0

Rearranging the equation:

e^(-y) sec(x) = dy/dx cos(x)

Divide both sides by e^(-y) sec(x) to isolate the variables:

dy/dx = cos(x) / (e^(-y) sec(x))

Now, we can separate the variables by multiplying both sides by dx:

dy / (cos(x) e^(-y)) = dx

Next, integrate both sides with respect to their respective variables:

∫ dy / (cos(x) e^(-y)) = ∫ dx

The integral of the left side can be simplified using substitution. Let u = e^(-y), then du = -e^(-y) dy:

∫ -du / (cos(x) u) = ∫ dx

Applying the integral:

ln|u| / cos(x) = x + C

Substituting back u = e^(-y):

ln|e^(-y)| / cos(x) = x + C

Using the property ln(e^a) = a, we have:

(-y) / cos(x) = x + C

Simplifying further:

y = -cos(x)(x + C)

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The solution to the given differential equation is "y(t) = c1 e^(-2t) cos(2t√2) + c2 e^(-2t) sin(2t√2)".

To solve the differential equation y'' + 4y' + 12y = 0, we first find the characteristic equation by assuming that the solution is of the form y = e^(rt), where r is a constant:

r^2 e^(rt) + 4r e^(rt) + 12 e^(rt) = 0

Dividing both sides by e^(rt) gives:

r^2 + 4r + 12 = 0

We can solve for r using the quadratic formula:

r = [-4 ± sqrt(4^2 - 4(1)(12))] / (2(1))

r = [-4 ± sqrt(16 - 48)] / 2

r = [-4 ± sqrt(-32)] / 2

r = -2 ± 2i√2

So, the general solution to the differential equation is:

y(t) = c1 e^(-2t) cos(2t√2) + c2 e^(-2t) sin(2t√2)

where c1 and c2 are constants determined by initial conditions.

Therefore, the solution to the differential equation y'' + 4y' + 12y = 0 is:

y(t) = c1 e^(-2t) cos(2t√2) + c2 e^(-2t) sin(2t√2).

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Answer:

11t-5u

Step-by-step explanation:

combine like terms

3t-4u+8t-u

(3t+8t)+(-4u-u)

(11t)+(-5u)

11t-5u

Hopes this helps please mark brainliest

Answer:

11t - 5u

Step-by-step explanation:

Given expression,

→ 3t - 4u + 8t - u

Let's solve the given expression,

→ 3t - 4u + 8t - u

→ (3t + 8t) + (-4u - u)

→ 11t - 5u

Hence, the answer is 11t - 5u.

Answer:

5/72

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

divide 36 by 10 be sure it's the easiest part

Answer:

Unit rate per year is :---

\( \frac{(50.4 - 7.2)}{(14 - 2)} = \frac{43.2}{12} = \boxed{3.6 \: feet \: per \: year} \\\)

After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.

First, find the value of the investment when it is compounded periodically, 12 times a year.

The formula is:

= Amount invested x ( 1 + rate ) ^ number of periods

= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰

= $ 53, 678. 16

If compounded annually, the value would be :

= 9, 000 x ( 1 + 9 % ) ²⁰

= $ 50, 439. 69

The difference is :

= 53, 678. 16 - 50, 439. 69

= $ 3, 238. 47

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Answer:

Step-by-step explanation:

Total surface area = 2πr(r+h)

If the total area of the bigger cylinder is 400cm² and radius is 4cm, then;

400=2(3.14)(r)(r+4)

400= 6.26r(r+4)

400=100.48 + 25.12h

299.52 = 25.12h

H = 299.52/25.12

H = 11.92cm

For the smaller cylinder

The height is calculated as;

H/h = R/r

11/92/

Based on the AAS conrguence theorem, the congruence statement that is correct is: B. △MDQ ≅ △RBS.

According to the AAS conrguence theorem, when two consecutive angles and a non-included side of a triangle is congruent to the corresponding two consecutive angles and a non-included side of another triangle, both triangles are said to be congruent triangles.

The two pairs of consecutive congruent angles are: ∠M ≅ ∠R; and ∠D ≅ ∠B

The one pair of non-included congruent sides is: MQ ≅ RS

Therefore, the correct congruence statement is: B. △MDQ ≅ △RBS.

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Answer:  B) 115 pounds

Step-by-step explanation:

Because x is the number of days passed, after 21 days, x = 21.

\(y = -15(21)+430\\\\Multiply\\\\y = -315+430\\\\y=115\)

Hope it helps <3

Answer:

115

Step-by-step explanation:

got it correct on edge 2020

Using implicit differentiation dz/dt = -34

Differentiation is the process of finding the derivative of a function.

Since x² + y² + z² = 9, dx/dt = 8, and dy/dt = 9, we need to find dz/dt when (x, y, z) = (2, 2, 1).

So, differentiating implicitly and also applying the chain rule, we have that

x² + y² + z² = 9

d(x² + y² + z²)/dt = d9/dt

dx²/dx × dx/dt  + dy²/dy × dy/dt + dz²/dz × dz/dt = d9/dt

2xdx/dt  + 2ydy/dt + 2zdz/dt = 0

xdx/dt  + ydy/dt + zdz/dt = 0

Making dz/dt subject of the formula, we have that

zdz/dt = -(xdx/dt  + ydy/dt)

dz/dt =  -(xdx/dt  + ydy/dt)/z

Given that

Substituting the values of the variables into the equation, we have that

dz/dt =  -(xdx/dt  + ydy/dt)/z

dz/dt =  -(2 × 8  + 2 × 9)/1

= -(16 + 18)/1

= - 34

So, dz/dt = -34

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The question is incomplete. Here is the complete question

If  x² + y² + z²  = 9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x, y, z) = (2, 2, 1).

Answer:

325 centimeters

Step-by-step explanation:

Answer:

700mi cube

Step-by-step explanation:

10x7x10=700mi cube

The range of the function y = 2sin(x) is the set of all possible values that the function can take. The range of the function y = 2sin(x) is [-2, 2].

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function, sin(x), has a range between -1 and 1, inclusive. When we multiply the sine function by 2, as in the case of y = 2sin(x), the range is expanded.

Multiplying the range of sin(x) [-1, 1] by 2 gives us the range of 2sin(x), which is [-2, 2].

Therefore, the range of the function y = 2sin(x) is [-2, 2].

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Answer:

What's the full question? I'm not sure how to help with just this information :(

Answer:

A

Step-by-step explanation:

The parentheses are switched around, making the answer still the same. However, for Answer choice C, it is Commutative Property because the factors are switched around.

=====================================================

Explanation:

The equation shown for choice A is in the form p*(q*r) = (p*q)*r which is the general format for the associative property of multiplication.

In this case, p = 2.5, q = 1/5 and r = 2/3.

The order of p,q,r stays the same while the parenthesis shift around. The stuff in the parenthesis is done first before anything else. Though with multiplication, the order doesn't matter which is why we can freely shift the parenthesis like this.

Addition has a similar rule which says p+(q+r) = (p+q)+r.

Answer:

(x - 7)(x + 4)

Step-by-step explanation:

Note that 4 times 7 is 28, and that -7x + 4x = -3x.

Therefore, x^2 - 3x - 28 factors into (x - 7)(x + 4)

The factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Writing a number or any mathematical object as the result of several factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

The factorization will be done as below:-

x² – 3x – 28

Split the middle term as 7 and 4.

x² – 7x  +  4x – 28 = 0

x ( x - 7 ) + 4 ( x -7 ) = 0

Take x-7 common from the whole equation.

( x - 7 ) ( x + 4 ) = 0

Therefore, the factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).

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Answer: The question is not complete. the figure is attached below.

The polygon is a rectangle.

Step-by-step explanation:

Line 1 goes through (-2, 3)

hence the slope of line 1 = -3/2

Line 2 goes through (0, 3) (2, 0)

hence the slope of line 2 = -3/2

Line 3 goes through (0, 1) (-3, 1)

hence the slope of line 3 = 2/3

Line 4 goes through (3, 0) (0, -2)

Hence the slope of line 4 = 2/3

therefore -3/2 * 2/3 = -1

Line1 + Line3      Line1 + Line4       Line2 + Line3        Line2+Line4

because, the distance between Line1 and Line2 is not equal to that Line3 and Line4.

The polygon is a rectangle polygon.