Let F= 6(x+y)i + 8 sin(y)j,. Find the line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order.

line integral =

Answer:

Angle 10=74 deg

Alternate Interior angle theorem

Step-by-step explanation:

They are Alternate Interior angles.

The general solution of a linear second order homogeneous equation is represented as the combination of two particular solutions.

This is because the linear second order homogeneous equation is of the form ax2+bx+c=0 and has two distinct roots, i.e. x1 and x2. The general solution of the equation can be written as y=C1y1+C2y2, where C1 and C2 are constants and y1 and y2 are the two particular solutions. The particular solutions can be derived from the two distinct roots of the equation using the formula y1=e^(x1*t) and y2=e^(x2*t). The constants C1 and C2 can be found by solving the linear combination of the two particular solutions for the given initial conditions of the equation. This gives the general solution of the linear second order homogeneous equation as a combination of the two particular solutions.

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La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.

En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.

Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:

I = (1 + r / 36500)ⁿ

Donde:

La situación es descrita por la siguiente expresión matemática:

1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵

Donde R es la tasa efectiva de interés anual.

Finalmente, despejamos la variable correspondiente:

R = 21,375

La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.

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The sum of the first four classroom numbers in a row is 4d + 12

The classrooms are consecutive even integers

the first term would be x

the second would be x + 2

the third would be x + 4

the fourth term would be x + 6

we would have to simplify this

d + d + 2 + d + 4 + d + 6

= 4d + 12

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Answer:

Step-by-step explanation:

Given,

Dimensions of a cuboid = 3.6cm, 8.2cm and 11cm

As we know,

Volume of a cuboid = length × breadth × height

Therefore,

Volume of the given cuboid

= 3.6cm × 8.2cm × 11cm

\( = 3.6cm \: \times 90.2 {cm}^{2} \)

\( = 324.72 {cm}^{3} (ans)\)

Hello there! :)

V=lwh (length times width times height)

We are given that:

Length=3.6 cm

Width=8.2 cm

Height=11 cm

Plug the values into the formula for volume:

V=lwh

V=(3.6)(8.2)(11)

Multiply:

V=324.72 cm³ (cubic centimeters)

Remember, volume is measured in cubic centimeters.

Hope it helps. Please let me know if you have any questions.

~A smiley teen who adores helping others

\(MagicalNature :)\)

Answer:

42 Units :)

Step-by-step explanation:

Answer:

B.42 on EDGE2022

Step-by-step explanation:

Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.

A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.

The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).

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Answer:

JL = 78

Step-by-step explanation:

MN is a midsegment. Based on the midsegment theorem,

MN = ½(JL)

MN = 5x - 16

JL = 4x + 34

Plug in the value

5x - 16 = ½(4x + 34)

5x - 16 = ½*4x + ½*34

5x - 16 = 2x + 17

Collect like terms

5x - 2x = 16 + 17

3x = 33

Divide both sides by 3

x = 11

✔️JL = 4x + 34

Plug in the value of x

JL = 4(11) + 34

JL = 44 + 34

JL = 78

The rules would make this input-output pair true are Rule 3, Rule and Rule 6

An input-output pair is a set of related data that includes an input, or the information given to a system, and the corresponding output, or the result produced by the system based on that input. This is a common way to test and evaluate the performance of a machine learning model, by comparing the predicted output to the actual output.

Since the input is 36 and output is 9. Any rule that produces 9 will be true.

Rule 1: subtract  5

output = 36 - 5 = 31

This could not be a rule for this input-output

Rule 2: If odd, subtract 9. If even, write 3

36 is not odd

output = 36 - 3 = 33

This could not be a rule for this input-output

Rule 3: Subtract 9, then divide by 3

36 - 9 = 27

output = 27/3 = 9

This could be a rule for this input-output

Rule 4:  Divide by 4.

output = 36/4 = 9

This could be a rule for this input-output

Rule 5: Add 2, then divide by 2.

36 + 2 = 38

output = 38/2 = 19

This could not be a rule for this input-output

Rule 6: Write 9.

output = 9

This could be a rule for this input-output

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Answer:

80 months

Step-by-step explanation:

If the present monthly heating costs average $300, but the insulation is expected to reduce heating costs by 10%, then there will be a monthly saving of 10%:

\(\implies \rm Monthly\;saving=10\%\;of\;\$300 =\dfrac{10}{100} \times \$300=\$30\)

To calculate how many months it will take to recover the cost of the insulation, divide the cost of installing the insulation by the monthly saving:

\(\implies \rm Number\;of\;months=\dfrac{\$2400}{\$30}=80\)

Therefore, it will take 80 months to recover the cost of the insulation.

Answer:

80 months

Step-by-step explanation:

The expected monthly savings from the insulation are: $300 × 10% = $30.

So, the number of months required to recover the cost of the insulation, $2400, is $2400/$30 = 80 months.

Answer:

51 x 51 = 2601

Step-by-step explanation:

Answer:

2601

Step-by-step explanation:

hope it helps

Answer:

a. dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

b. y = 20000/(200 + t)

Step-by-step explanation:

a. Write an IVP to determine y, the number of grams of salt in the tank at time, t.

Let y be the mass of salt.

The net flow into the tank dy/dt = mass flow in - mass flow out

Since only water flows into the tank, the mass flow in = 0 g/min

Let m be the mass of salt in the tank at time t. Since the volume of the tank is 200 L and water flows in at a rate of 4 L/min and out at a rate of 2 L/min, the net rate of increase of the volume of the tank is rate in - rate out = 4 L/min - 2 L/min = 2L/min. So, in time, t, the volume of the water in the tank increases by  2t. So, the volume of the tank in time, t is V = 200 + 2t.

So, the concentration of salt in the tank at time t is mass/volume = m/(200 + 2t).

Since the well mixed solution leaves at a rate of 2 L/min, the mass flow out is concentration × volume flow out =  y/(200 + 2t) × 2 = 2y/(200 + 2t)

The net flow into the tank dy/dt = mass flow in - mass flow out

dy/dt = 0 - 2y/(200 + 2t)

dy/dt = - 2y/(200 + 2t)

Since the initial mass of salt in the tank is 100 g, y(0) = 100 g

So, the initial value problem IVP is

dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

b. Solve an IVP to determine, the number of grams of salt in the tank at time, t.

Solving the IVP, we have

dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

Separating the variables, we have

dy/y = - 2dt/(200 + 2t)

Integrating both sides, we have

∫dy/y = - ∫2dt/(200 + 2t)

㏑y = - ㏑(200 + t) + ㏑C

㏑y + ㏑(200 + t) = ㏑C

㏑[y(200 + t)] = ㏑C

y(200 + t)] = C

y = C/(200 + t) since y(0) = 100, we have

100 = C/(200 + 0)

100 = C/200

C = 100 × 200

C = 20000

So, y = C/(200 + t)

y = 20000/(200 + t)

Answer:

The walkway should be 2ft wide.

Step-by-step explanation:

Let x be the width of the walkway surrounding the pool.

The area including the pool is 560ft².

Let's solve for the value of x.

The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.

A = lw

560 = (24 + 2x)(16 + 2x)

560 = 384 + 48x + 32x + 4x²

4x² + 80x + 384 - 560 = 0

4x² + 80x - 176 = 0

Divide the whole equation by 4

x² + 20x - 44 = 0

(x + 22)(x -2) = 0

x = -22; x = 2

Since we are dealing with dimensions, take the one with the positive value.

x = 2ft

Let's check

560ft² = (24ft + 2x)(16ft + 2x)

560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))

560ft² = (24ft + 4ft)(16ft + 4ft)

560ft² = (28ft)(20ft)

560ft² = 560ft² ✔

Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

idk

Step-by-step explanation:

Answer:

w = 30

Step-by-step explanation:

a = lw

l = 2w

a = 2w × w

1800 = 2w × w

1800 ÷ 2 = w × w

900 = w × w

square root of 900 = square root of w^2

(I don't have the symbol for square root)

30 = w

check work:

a = lw

l = 2w

l = 2(30)

l = 60

1800 = 60 × 30

1800 = 1800

correct answer

Answer:

(C) 1

Step-by-step explanation:

In a function, a real zero is where the function is equal to zero, or:

\(f(x)=0\)

which can be rewritten as:

\(y=0\)

which is essentially the y-intercept.

Recall that the y-intercept of a graph is where the graph crosses the y-axis (the x-coordinate is equal to 0).

We can see that the graph only crosses the y-axis at one point, meaning it only has one y-intercept, meaning it has only one real zero.

Thus, the answer is (C), 1

Answer:

The first one

Step-by-step explanation:

I did this and got it right and I solved it

8×3 equal 24/1 so make it to a whole number 24

Answer:

Step-by-step explanation:

cosB = a/c = 4/5

so c = 5a/4 = 5*90/4 = 112.5

b² = c² - a² = 112.5² - 90² = 4556.25

b = 67.5

3 divided by sqrt8 + sqrt5=

3/(sqrt8+sqrt5)=

3(sqrt8-sqrt5)/(sqrt8+sqrt5)(sqrt8-sqrt5)=

(6sqrt2-3sqrt5)/3=

y=5x-46

below is proof

https://ibb.co/wJxjn9H

The medians are about the same.

Option C is the correct answer.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

Movie theater 1.

From the box plot given,

The median is 995.

Movie theater 2.

From the box plot given,

The median is 995.

Thus,

The median in both the box plot is the same.

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Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:

10 root 2

Step-by-step explanation:

root 200 = root 2 × root 100 = 10 root 2

Answer:

C x= 85°

Step-by-step explanation:

x+ 60° + 35° =180°

x= 180° - 60° - 35°

x= 85°

The second difference of the given number table is: Option A: -2

The second difference method can be used to determine a quadratic model.  In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.

Thus, Applying the second difference concept to our problem, we have:

First difference:

-4 - (-9) = 5

-1 - (-4) = 3

Thus, second difference is:

3 - 5 = -2

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Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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Answer:

A)

B) Yes, he has to add more chlorine.

Step-by-step explanation:

What is being said, in other words, is that the absolute difference between the chlorine levels of a sample x and 3.25 ppm has to be, at most, 1.75 ppm.

This situation can be described by the absolute value inequality:

We can solve this inequality as following:

Now, notice that the sample exctracted by the lifeguard is below this interval. Therefore, we has to add more chlorine.

So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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