filling in the missing numbers.
42, 57,?, 74,? ​

The work done by the force F(x, y) in moving the particle along the given path is ( A: 2).

The work done by the force vector field F(x, y) = 3xyi - j in moving a particle along the unit circle x = sin(t), y = cos(t) for 0 ≤ t ≤ π,  to evaluate the line integral of F along the given path.

The line integral of a vector field F along a curve C parameterized by r(t) = xi + yj, where a ≤ t ≤ b, is given by:

∫ F · dr = ∫ (F(x, y) · r'(t)) dt

where r'(t) = dx/dt i + dy/dt j is the derivative of the position vector with respect to t.

Let's calculate the line integral for the given scenario:

the vector field F(x, y) = 3xyi - j.

The parametric equations for the unit circle are x = sin(t) and y = cos(t).

Differentiating x and y with respect to t,

dx/dt = cos(t)

dy/dt = -sin(t)

Now, substituting these values into the expression for the line integral:

∫ F · dr = ∫ (3xyi - j) · (cos(t)i - sin(t)j) dt

= ∫ (3sin(t)cos(t) - (-sin(t))) dt

= ∫ (3sin(t)cos(t) + sin(t)) dt

= ∫ sin(t)(3cos(t) + 1) dt

Integrating this expression with respect to t from 0 to π:

∫ F · dr = [-3cos(t) - cos²(t)/2] evaluated from 0 to π

= [-3cos(π) - cos²(π)/2] - [-3cos(0) - cos²(0)/2]

= [3 - 1/2] - [3 - 1/2]

= 2

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Answer:

40 m/hr

Step-by-step explanation:

6 hours * 80 m/hr      +     6 hours * x m/hr  = 720 miles

6 * 80     +    6 * x   = 720

x = 40 m/hr

Answer:

I would say B

Step-by-step explanation:

it seems like the reasonable choice (it's sounds and looks like it make since)

The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

For new customers, there is an additional one-time $150 service fee.

Now, Let the number of months of service = x

And, the total amount paid in dollars by an customer = y

Hence, The correct linear equation is,

⇒ y = 150x

Thus, The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

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The number of simulation trials that would be likely to produce results that are  closest to the actual probability is 25. The correct option is C).

The following steps can be used  in order to determine the number of simulations:

Step 1 - Remember the maximum number of trials gives the maximum chance to produce results that are  closest to the actual probability.

Step 2 - Now, check all the options given in the question and choose the largest one.

From the above steps, it can be concluded that the correct option is C) 25.

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Full question :

Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.

A. 10

B. 15

C. 25

D. 20

Answer: -11

Step-by-step explanation:

First, since he has 125$, that is the total amount of the money he has. So since he bought a Chromebook for 136$. Meaning we have to subtract 125 by 136 which gives us the answer of -11.

Answer:

Sample response: Factor the GCF of five out of the total bill. Divide both terms of the expression by 5. The result is 5x – 23, which is the expression that can be used to find the amount each person pays.

i took the test.

Answer:

Factor the GCF of five out of the total bill. Divide both terms of the expression by 5. The result is 5x – 23, which is the expression that can be used to find the amount each person pays.

Step-by-step explanation:

I took the test, I got 100%

Option B, the savings account with 3.5% annual interest compounded monthly, would have a larger balance after 10 years.

Simple interest is calculated by multiplying the principal investment by the annual interest rate.

Compound interest is calculated by adding the interest earned in each compounding period (in this case, each month) to the principal balance, and then calculating the interest on the new balance for the next compounding period.

This means that compound interest earns interest on the interest earned in previous compounding periods, leading to a larger balance over time compared to simple interest.

To calculate the balance of the savings account with 3.5% annual interest compounded monthly after 10 years, we can use the formula:

A = P * (1 + r/n)^(nt)

where A is the balance after t years, P is the principal investment, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years.

For this savings account, n = 12 (since the interest is compounded monthly), t = 10, and r = 0.035.

Plugging these values into the formula, we get:

A = P * (1 + 0.035/12)^(12 * 10)

The balance of the savings account with simple interest after 10 years can be calculated by multiplying the principal investment by the annual interest rate and then multiplying by the number of years:

A = P * (1 + 0.035 * 10)

Comparing the two formulas,

it is clear that the balance with compound interest will be larger after 10 years, as the balance grows faster due to the interest earned on the interest in each compounding period.

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Answer:

it's blurry

Step-by-step explanation:

Answer:

x=NEGATIVE 1/2, POSITIVE 2

Step-by-step explanation:

Just use math.waycom

The non-negative zero of the function f(x) is x = 2.

The zero of the function is where the y-value is zero. The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

here, we have,

For a given function f(x), the "zeros" of the function are the values of x such that:

f(x) = 0

In this case, we have the function:

f(x) = 6*x^2 - 9*x - 6

If we want to find the zeros of this function, we need to solve:

f(x) = 0 =  6*x^2 - 9*x - 6

To solve this, we can use the Bhaskara's formula, which says that for a general quadratic equation:

0 = a*x^2 + b*x + c

The zeros are:

x = -b ±√b² - 4ac / 2a

In this case our equation is:

0 =  6*x^2 - 9*x - 6

then, in the above notation, we have:

a = 6

b = -9

c = -6

Replacing these in our general formula, we get:

x = 9±15 /12

Then we have two zeros:

x = (9 + 15)/12 = 24/12 = 2

x = (9 - 15)/12 = -6/12 = -1/2

But we want only the non-negative, so we can discard the second one.

Concluding, the non-negative zero of the function f(x) is x = 2.

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Answer:

\(10 x - 2y\)

Step-by-step explanation:

\(8x−2y+x+x \\ 9x−2y+x \\ 10x−2y\)

5

You just divide it normally

Answer:

5

Step-by-step explanation:

Answer:

(0, 0), (20, 1), (40, 2), (60, 3), (80, 4)

Step-by-step explanation:

Step-by-step explanation:

You cant because a=3

Answer:

a+2=5 is not equivalent to a=1

in this situation a must equal 3 for the equation to be true.

Step-by-step explanation:

There is Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x represent Watusi's speed,

y represent Ubangi's speed,

And z represents Pigmy's speed.

According to the given information, we can write the system of equations as

x + y + z = 30  .....(i)

z + 2x/3 = 22 - y  .....(ii)

4x + 3y - z = 12  .....(iii)

The above system of equations gives the values of x, y, and z when solving

x = 6, y = 3, z = 21

This means Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

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Hello!

Answer:

1 quart = 4 cups

7 quarts = 28 cups

1 guest needs 2 cups

12 guests need 24 cups

She has 28 and needs 24, yes there is enough

Hope this helps! Have a day <3

Answer:

There are 10 two point questions and 16 five point questions.

Step-by-step explanation:

The vertical velocity of the string at the origin at time t would be zero, as the origin is a fixed point.

The origin is a fixed point, so it does not move. This means that the vertical velocity of the string at the origin at time t would be zero.

The origin of the string is a fixed point, meaning that it does not move. This implies that the vertical velocity of the string at the origin at time t would be zero, as the origin does not move or change its position. Since the origin is a fixed point, the vertical velocity of the string at the origin at time t would remain constant, and would be equal to zero. Thus, the vertical velocity of the string at the origin at time t would be zero.

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Answer:

Before you get started, take this readiness quiz.

Write as an inequality: x is at least 30.

If you missed this problem, review (Figure).

Solve 8-3y<41.

If you missed this problem, review

Answer:

(D) r=−0.92. The linear relationship between lawn size and gas remaining is strong and negative.

Step-by-step explanation:

Answer:

1. rhombus

2. rectangle

3. parallelogram

Step-by-step explanation:

A pair (x, p) is an equilibrium, if and only if x and p are optimal solutions to the standard form problem and its dual, respectively.

To show that a pair (x, p) is an equilibrium if and only if x and p are optimal solutions to the standard form problem and its dual, we need to demonstrate both directions of the equivalence.
First, let's assume that (x, p) is an equilibrium. An equilibrium occurs when the primal problem and its dual problem satisfy certain conditions. In this case, we have:
1. Primal problem:
  - Objective function: maximize \(c^T * x\) (where c is the cost vector and x is the decision variable)
  - Subject to: Ax = b (where A is the constraint matrix and b is the right-hand side vector)
2. Dual problem:
  - Objective function: minimize \(b^T * p\) (where p is the dual variable)
  - Subject to: \(A^T * p \geq c\) (where \(A^T\) is the transpose of A)
Now, if (x, p) is an equilibrium, it means that both the primal and dual problems are feasible, and their objective functions are equal. This implies that x and p are optimal solutions to their respective problems.
Conversely, let's assume that x and p are optimal solutions to the standard form problem and its dual, respectively. This means that x and p satisfy the feasibility conditions and optimize the objective functions of their respective problems.
Since x and p are optimal solutions, the objective functions of the primal and dual problems are equal. This condition ensures that (x, p) is an equilibrium.

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A pair (x, p) is an equilibrium if and only if x is an optimal solution to the standard form problem and p is an optimal solution to its dual. Both conditions must be satisfied for equilibrium.

To show that a pair (x, p) is an equilibrium, we need to prove two conditions: (1) x is an optimal solution to the standard form problem, and (2) p is an optimal solution to its dual.

First, assume that (x, p) is an equilibrium. This means that x is feasible and satisfies the constraints of the standard form problem. We can also assume that p is feasible and satisfies the constraints of the dual problem.

To prove condition (1), we can use contradiction. Suppose x is not an optimal solution. Then there exists another feasible solution x' that yields a better objective function value. However, this contradicts the definition of an equilibrium, so x must be an optimal solution.

Similarly, to prove condition (2), we can assume that p is not an optimal solution. Then there exists another feasible solution p' to the dual problem that yields a better objective function value. Again, this contradicts the definition of an equilibrium, so p must be an optimal solution.

Conversely, if x is an optimal solution to the standard form problem and p is an optimal solution to its dual, we can conclude that (x, p) is an equilibrium. This is because both x and p satisfy the necessary conditions for optimality.

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Answer:

18

Step-by-step explanation:

18 ÷ 3 = 6

6 ⋅ 2 = 12

Therefore, 12 is 2/3 of 18.

The lengthof the rectangle is 23 cm and width of the rectangle is 25cm.

Consecutive odd integers are odd integers that follow each other and they differ by 2.

Given that Length and width are consecutive odd integers then

Let length be x so width will be x+2.

The \(Perimeter \ of \ Rectangle = 2 (Length \ + \ Width)\)

Perimeter of Rectangle= 96cm

\(96 = 2 (Length \ + \ Width)\\(Length \ + \ Width) = 48\\x + x + 2 = 48\\2x = 46\\x = 23\)

So, length = x = 23cm

therefore, width = x+2 = 25cm

Therefore, Length of the rectangle is 23 cm and the Width of the rectangle is 25 cm.

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Step-by-step explanation:

There are 60 * 60 * 24 =  86400 seconds in a day

if the light flashes 5 times every 10 seconds, that means it flashes once every 2 seconds.

It follows the flashes in a day are 86400 / 2 = 43200

Step-by-step explanation:

-3x+7y = -18 ...1

4x-4y = 8 ...2

...1 × 4

-12x + 28y = -72 ...3

...2 × 3

12x - 12y = 24 ...4

...3 + ...4

28y - 12y = -72 + 24

16y = -48

y = -3

Replace y = -3 in ...2

4x - 4(-3) = 8

4x + 12 = 8

4x = 8 - 12

4x = -4

x = -1

Answer:

\(\huge\boxed{\boxed{(x,y)=(-1,-3)}}\)

Step-by-step explanation:

multiply first equation by 4 and second by 3 respectively:

\( \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}\)

combine the equations:

\( \underline{ \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}} \\ \displaystyle16y = - 48\)

divide both sides by -48:

\( \displaystyle \: \frac{16y}{16} = \frac{ - 48}{16} \\ y = - 3\)

substitute the value of y to the second equation

\( \displaystyle \: 4x - 4. - 3 = 8\)

simplify multiplication:

\( \displaystyle \: 4x + 12 = 8\)

cancel 12 from both sides:

\( \displaystyle \: 4x = - 4\)

divide both sides by 4

\( \displaystyle \: \frac{4x}{4} = \frac{ - 4}{4} \\ x = - 1\)

therefore our solution is

\(\displaystyle (x,y)=(-1,-3)\)

Answer:

The mode would be

Step-by-step explanation:

To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.

15, 15, 17, 17, 17, 19, 22, 24, 29

If this is the rewritten version then we can conquer that the mode would be 17 since 17 is displayed the greatest amount of times. (out of the other numbers.)

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Answer:

x = A / ( 4y)

Step-by-step explanation:

A = 4xy

Divide each side by 4y

A/ ( 4y) = 4xy/4y

A / ( 4y) = x

Answer:

1

Step-by-step explanation:

h(-2)=-3(-2)-5

h(-2)=6-5

h(-2)=1

h(-2)=1

x=-2, but i'm assuming you want h(x)