Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. = = = F = (-2x + 10y) i +(6x -8y)}; C is the region bounded above by y=-3x 2 + 7 and below by y = 4x2 in the first quadrant O -3 64 4ဝ O 56 3 24

There is no value of t for which the exponential term is zero. Therefore, the solution A(t) remains physically feasible for all positive time values.

To derive the initial value problem (IVP) governing A(t), we start by setting up a differential equation based on the given information.

Let A(t) represent the number of pounds of salt in the tank at time t.

The rate of change of salt in the tank is given by the following equation:

dA/dt = (rate in) - (rate out)

The rate at which salt is being pumped into the tank is given by:

(rate in) = (concentration of salt in incoming water) * (rate of incoming water)

(rate in) = (3 lbs/gal) * (4 gal/min) = 12 lbs/min

The rate at which the saltwater solution is being pumped out of the tank is given by:

(rate out) = (concentration of salt in tank) * (rate of outgoing water)

(rate out) = (A(t)/400 lbs/gal) * (4 gal/min) = (A(t)/100) lbs/min

Substituting these values into the differential equation, we have:

dA/dt = 12 - (A(t)/100)

To solve this IVP, we also need an initial condition. Since initially there are 10 lbs of salt in the tank, we have A(0) = 10.

Now, let's consider the new condition where the solution is being pumped out at the rate of 5 gallons per minute.

The rate at which the saltwater solution is being pumped out of the tank is now given by:

(rate out) = (A(t)/100) * (5 gal/min) = (A(t)/20) lbs/min

Therefore, the new differential equation is:

dA/dt = 12 - (A(t)/20)

The initial condition remains the same, A(0) = 10.

To solve this new IVP, we can use various methods such as separation of variables or integrating factors. Let's use the integrating factor method.

We start by multiplying both sides of the equation by the integrating factor, which is the exponential of the integral of the coefficient of A(t) with respect to t. In this case, the coefficient is -1/20.

Multiplying the equation by the integrating factor, we have:

e^(∫(-1/20)dt) * dA/dt - (1/20)e^(∫(-1/20)dt) * A(t) = 12e^(∫(-1/20)dt)

Simplifying the equation, we get:

e^(-t/20) * dA/dt - (1/20)e^(-t/20) * A(t) = 12e^(-t/20)

This can be rewritten as:

(d/dt)(e^(-t/20) * A(t)) = 12e^(-t/20)

Integrating both sides with respect to t, we have:

e^(-t/20) * A(t) = -240e^(-t/20) + C

Solving for A(t), we get:

A(t) = -240 + Ce^(t/20)

Using the initial condition A(0) = 10, we can solve for C:

10 = -240 + Ce^(0/20)

10 = -240 + C

Therefore, C = 250, and the solution to the IVP is:

A(t) = -240 + 250e^(t/20)

To find the largest time value for which the solution is physically feasible, we need to ensure that A(t) remains non-negative. From the equation, we can see that A(t) will always be positive as long as the exponential term remains positive.

The largest time value for which

the solution is physically feasible is when the exponential term is equal to zero:

e^(t/20) = 0

However, there is no value of t for which the exponential term is zero. Therefore, the solution A(t) remains physically feasible for all positive time values.

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True.

A system of equations is a set of two or more equations that are to be solved simultaneously.

A system of equations is a set of two or more equations that are to be solved simultaneously. In linear algebra, a system of equations is typically represented as a set of linear equations in the form:

a11x1 + a12x2 + ... + a1nxn = b1
a21x1 + a22x2 + ... + a2nxn = b2
...
am1x1 + am2x2 + ... + amnxn = bm

where the variables x1, x2, ..., xn are the unknowns, the coefficients aij and the constants bi are given, and the goal is to find a solution vector (x1, x2, ..., xn) that satisfies all the equations in the system.

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Answer:

1, 3, 5, 7 and 19

Step-by-step explanation:

to find the first 4 terms, substitute n = 1, 2, 3, 4 into the rule, then

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 - 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

the first 4 terms are 1, 3, 5, 7

to find the 10th term , substitute n = 10 into the rule

a₁₀ = 2(20) - 1 = 20 - 1 = 19

The line integral R is equal to 4 units.  we evaluate the line integral by parameterizing the curve C. Let's let y = t and x = 4 - t^2, where t varies from -3 to 2.

We can calculate dx = -2t dt and dy = dt. Substituting these values into the integral expression, we get R = ∫(4t(−2t dt) + (4 − t^2)dt). Simplifying and evaluating the integral, we find R = 4 units. This represents the total "signed area" under the curve C.

To evaluate the line integral R, we start by parameterizing the curve C. In this case, the curve is defined by the equation x = 4 - y^2, which is the arc of a parabola. We need to find a suitable parameterization for this curve.

Let's choose y as our parameter and express x in terms of y. We have y = t, where t varies from -3 to 2. Plugging this into the equation x = 4 - y^2, we get x = 4 - t^2.

Next, we need to calculate the differentials dx and dy. Since y = t, dy = dt. For dx, we differentiate x = 4 - t^2 with respect to t, giving us dx = -2t dt.

Now we substitute these values into the line integral expression R = ∫(scy dx + x dy). We have R = ∫(4t(-2t dt) + (4 - t^2)dt).

\(Simplifying this expression, we get R = ∫(-8t^2 dt + 4t dt + (4 - t^2)dt).\)

\(Integrating each term separately, we find R = ∫(-8t^2 dt) + ∫(4t dt) + ∫(4 - t^2)dt.\)

Evaluating these integrals, we get R = (-8/3)t^3 + 2t^2 + 4t - (1/3)t^3 + 4t - t^3/3.

\(Simplifying further, we have R = (-8/3 - 1/3 - 1/3)t^3 + 2t^2 + 8t.Evaluating this expression at t = 2 and t = -3, we find R = 4 units.\)

Therefore, the line integral R, which represents the total "signed area" under the curve C, is equal to 4 units.

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Answer:

Mean: 3

Median: 2

Mode: 1

Range: 6

Step-by-step explanation:

1.) The mean is the average of all the numbers. To find it, you add up all the numbers and then divide that by the amount of numbers. So, you would do:   7 + 2 + 1 + 4 + 1 = 15

15 ÷ 5 = 3

The mean is 3.

2.) The median is the middle number. In order to find it, you must put all the numbers in order:

1, 1, 2, 4, 7

The middle number is 2, so the median is 2.

3.) Mode is the number that appears the most often. Because 1 appears twice and the rest only appear once, the mode is 1.

4.) The range is the difference between the biggest and smallest numbers. Since 7 is the biggest number and 1 is the smallest, you would subtract them. 7-1 is 6, so the range would be 6.

Answer:

90%

Step-by-step explanation:

cost price of both tv = 2500

sale price of undamaged = 3000

sale price of damaged = 2200

sale price of both tv = 5200

profit = sale price - cost price

profit = 5200 - 2500

profit = 2700

profit percentage = profit × 100 ÷ cost price

profit percentage = 2700 × 100 ÷ 2500

profit percentage = 90%

The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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Answer:

Step-by-step explanation:

The probability of a randomly selected person from this group visiting a physical therapist will be 68.

In a group of patients having injuries, 28% visit both a physical therapist and a chiropractor while 8% visit neither

A = Visiting a physical therapist

B = Visiting a chiropractor

The probability of visiting a physical therapist exceeds the probability of visiting a chiropractor by 16%.

Pr(A union B)' = .08

Pr(A union B) = 1 - .08 = .92

Pr(A intersect B) = .28

Pr(A) = Pr(B) + .16

Pr(A union B) = Pr(A) + Pr(B) - Pr(A intersect B)

.92 = [Pr(B) + .16] + Pr(B) - .28

.92 = 2Pr(B) - .12

1.04 = 2 Pr(B)

.52 = Pr(B)

Since, Pr(A) = Pr(B) + .16 then P(A) = .52 + .16 = .68.

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Answer:

x = -102

Step-by-step explanation:

Step 1: Multiply both sides by 10.

Step 2: Subtract 8 from both sides.

Step 3: Divide both sides by -1.

Step 4: Check if solution is correct.

Therefore, x = 11.

Have a lovely rest of your day/night.

Answer:

4000

Step-by-step explanation:

5000 * .8 is 4000

Answer:

4000 students

Step-by-step explanation:

Number of computer science majors = 80% of 5000

                                                              = 0.8 * 5000

                                                              = 4000

The probability that the man would have done at least this well by chance, assuming he has no ESP is 0.182

To determine the probability that the man would have gotten at least 22 out of 30 correct by chance, we can use a binomial probability distribution, where:

n = 30 (the number of trials, or coin flips)

p = 0.5 (the probability of getting a correct guess by chance, assuming the coin is fair)

The probability of getting exactly 22 correct guesses by chance can be calculated as:

P(X = 22) = (30 choose 22) × 0.5^22 × 0.5^8 = 0.128

where (30 choose 22) is the number of ways to choose 22 correct guesses out of 30.

The probability of getting 22 or more correct guesses by chance can be calculated as:

P(X >= 22) = P(X = 22) + P(X = 23) + ... + P(X = 30)

This can be calculated using a binomial probability calculator, which gives:

P(X >= 22) = 0.182

Therefore, the probability is 0.182

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The given question is incomplete, the complete question is :

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 30 times, and the man is asked to predict the outcome in advance. He gets 22 out of 30 correct. What is the probability that he would have done at least this well if he had no ESP?

The coefficient of x² in the Taylor series for sin²x about x=0 is 1

If a Taylor Series is centred at 0, then the series is known as the Maclaurin series.

Maclaurin series is given by f(x) = \(\text{\Large$ \Sigma$}\limits^{\infty}_{k=0} \frac{f^{(k)}(a)}{k!}x^k\)

f(x) = sin²x

We need coefficient of x², let us take n=5

f(x) = \(\text{\Large$ \Sigma$}\limits^{\infty}_{k=0} \frac{f^{(k)}(a)}{k!}x^k\)

f^0(x) = sin²x => f^0(0) = 0

f^1(x) = 2 sinx cosx => f^1(0) = 0

f^2(x) = -2 sin²x + 2 cos²x => f^2(0) = 2

f^3(x) = -8 sinx cosx => f^3(0) = 0

f^4(x) = 8 sin²x - 8 cos²x => f^4(0) = -8

f^5(x) = 32 sinx cosx => f^5(0) = 0

f(x) = 0(x^0) + 0(x^1) + (2/2!)(x^2) + (0/3!)(x^3) + (-8/4!)(x^4) + (0/5!)(x^5)

f(x)  = x^2 - (1/3)x^4

We can see that the coefficient of x² is 1.

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Answer:

30x+7

Step-by-step explanation:

3(10x+7)-15 = 30x+21-15 = 30x+7

Answer:

-130

Step-by-step explanation:

f(10) just means you plug in 10 for any X's in the equation

So it would be... f(10) = -10^2-3(10)

Hexadecimal and binary are two numbering systems that are commonly used in computing. Binary is a base-2 numbering system, which means it uses only two digits, 0 and 1, to represent all numbers. Hexadecimal, on the other hand, is a base-16 numbering system, which means it uses 16 digits, from 0 to 9 and A to F, to represent numbers.

One hexadecimal digit can represent 16 different values, while one binary digit can represent only two values (0 or 1). This means that one hexadecimal digit can represent 16 times as many values as one binary digit.

To understand this better, let's consider an example. The binary number 1111 is equivalent to the hexadecimal number F. In binary, 1111 can represent only one value, which is 15 in decimal. However, in hexadecimal, the digit F can represent 16 different values, from 0 to 15 in decimal.

Therefore, using hexadecimal notation can be more efficient and compact than using binary notation, especially when dealing with large numbers. In addition, hexadecimal is often used in computing to represent memory addresses, color codes, and other values that need to be represented in a compact and easily readable format.

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The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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In general, the energy levels of a system increase as the system gets closer. This is because when objects get closer, the force between them increases, which increases the potential energy of the system.

The potential energy of a system is related to the energy levels of the system, so increasing the potential energy leads to higher energy levels.

To see this mathematically, let's consider a system of two particles with masses m1 and m2, separated by a distance r, and interacting via a potential energy function U(r). The total energy of the system, E, is given by:

E = 1/2 m1 v1^2 + 1/2 m2 v2^2 + U(r)

where v1 and v2 are the velocities of the particles. We can simplify this expression by using the reduced mass μ, defined as:

1/μ = 1/m1 + 1/m2

and the relative distance vector r = r2 - r1. Then, we have:

E = 1/2 μ v^2 + U(r)

where v is the relative velocity of the particles.

If we assume that the particles are moving in a circular orbit with radius r, we can use the centripetal force to relate v to r:

v^2 = F_c/m = U'(r)/μr

where F_c is the centripetal force and U'(r) is the derivative of U with respect to r. Substituting this into the expression for E, we get:

E = U'(r)/2μ + U(r)

The first term on the right-hand side represents the kinetic energy of the system, while the second term represents the potential energy. The total energy E is conserved, so it must be a constant.

Now, suppose we decrease the distance r between the particles. This means that U'(r) is negative (since the force is attractive), so the first term on the right-hand side decreases, while the second term increases. Thus, the total energy E must increase to stay constant.

Therefore, we can conclude that when objects get closer, their energy levels get higher.

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Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

When a function is moved, it is said that the function is translated

The graph of f(x) is shifted 11 units up.

Given

\(f(x) = \frac 1x\)

\(g(x) = \frac 1x + 11\)

Substitute \(f(x) = \frac 1x\) in \(g(x) = \frac 1x + 11\)

\(g(x) = f(x) + 11\)

The rule of upward translation is:

\(g(x) = f(x) + h\)

Where h is the number of units moved upward.

By comparison:

\(h = 11\)

This means that: (b) The graph of f(x) is shifted 11 units up.

See attachment for the graph of f(x) and g(x)

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The probabilities are given as follows:

a) Even number: 5/9.

b) Number greater than five: 1/3.

A probability is the division of the number of desired outcomes by the number of total outcomes.

Given that each person draws one card from a set of three, hence the total number of outcomes is given as follows:

3² = 9.

Using the Fundamental Counting Principle,

The nine outcomes are given as follows:

1 x 1 = 1.

1 x 2 = 2.

1 x 3 = 3.

2 x 1 = 2.

2 x 2 = 4.

2 x 3 = 6.

3 x 1 = 3.

3 x 2 = 6.

3 x 3 = 9.

There are five outcomes that end with an even number, hence the probability is of:

p = 5/9.

There are three outcomes ending with a number greater than five, hence the probability is of:

p = 3/9 = 1/3.

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Answer: 5 degrees

Step-by-step explanation:

The difference between -7 and -12 is 5, I don't know what you are asking for though.

Step-by-step explanation:

and one of these day I must get straigh and drip all over you

The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.

What is synthetic division?

Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."

We are given the expression as (n^3+3n^2-15n+19)

The expression is to be divided by (n-2)

So, by using the synthetic division, we get

2 |  1     3     -15      19    

     -     2      10     -10        

     1     5      -5       9    

Quotient =  n^2+5n-5

Remainder = 9

Hence, the quotient is n^2+5n-5 and the remainder is 9.

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Answer:

$22.50....................

since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.

\(\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}\)

The required length of the side BM is 29.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

In the given question,

Point M is the midpoint of line AB.

AM = 4x + 13,

and BM = 3x + 17

To find the length of MB, use midpoint property.

Since, Point M is the midpoint of AB,

Therefore, AM = MB

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.

The length of MB, where M is midpoint of AB, is 29.

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