Compute the integral c F.dx, where the vector field F(x, y) = (x^2 – y^2, xy) and C is the path that traverses the perimeter of the triangle with vertices (0,0), (0,1) and (1,1) one time, counterclockwise.

Answer:

75

Step-by-step explanation:

40 - 5 = 35 years till the son will be 40, his fathers age

40+35 = 75, the dad's age 35 years in the future when the son is 40

There is no potential function for F and it is not a conservative vector field.

Given that F(x, y, z) = (e³, xe³ + e², ye²) is a conservative vector field. We need to find a potential function for F.

The vector field F(x,y,z) is conservative if it can be represented as the gradient of a scalar potential function f(x,y,z),

i.e., F=∇f.

Let the potential function be f(x,y,z).

Then, Fx=e³f_x=x e³ + e²yf_y=x e³ + e²z2yf_z=0

Solving the first two equations, we get f= x e³ + e² y + C, where C is a constant.

Now, we will check if F satisfies the condition of conservative vector field by finding curl(F).

curl(F) = [(∂Fz/∂y - ∂Fy/∂z), (∂Fx/∂z - ∂Fz/∂x), (∂Fy/∂x - ∂Fx/∂y)]

On evaluating this, we get the following: curl(F) = [0, 0, e²]

Since curl(F) is not equal to 0, F is not a conservative vector field.

Hence, there is no potential function for F and it is not a conservative vector field.

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Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

The average mean cost used for the condominium on maui is 132.5

According to the statement

we have given that the some data values and we have to find the mean of the data and tell the how much expensive is condominium on maui.

So, The given data set is

89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120

So, For this purpose we know that the

Average Mean is a middle point or something (as a place, time, number, or rate) that falls at or near a middle point

Formula to calculate mean is sum of terms / total number of terms.

So,

Mean = 89+ 50+ 68+ 60+ 375+ 55+ 500+ 60+ 50+ 250+ 45+ 45+ 125+ 235+ 1+ 40+ 350+ 65+ 60+ 120 / 20

Mean = 2643 / 20

Mean = 132.5

So, The average mean cost used for the condominium on maui is 132.5

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Maui Vacation How expensive is Maui? If you want a vacation rental condominium

(up to four people), visit a Maui tourism web site. The Maui News gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui.

89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120

what average mean would you use?

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Answer:

See below

Step-by-step explanation:

For a right triangle, there are relationships between the sides and the angles of the triangle:

\(sin\theta=\frac{opposite}{hypotenuse}\)

\(cos\theta=\frac{adjacent}{hypotenuse}\)

\(tan\theta=\frac{opposite}{adjacent}\)

I would study the attached image for a better understanding.

The constant of proportionality for x gallons water and y miles is k = 25

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.

Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

A proportionate connection is simple to represent as a straight line on a coordinate plane. It is a straight line because it is directly proportional; the slope serves as the constant of proportionality.

The proportionate change along the x and y axes never varies, hence the slope or increase is constant.

According to the question,

x(gallons)     y(miles)

 1                       25

 2                      50

 3                      75

 4                      100

As we know, If y is proportional to x

=> y ∝ x

=> y = kx , where k is constant of proportionality

Using the table,

when x = 1 => y = 25

=> 25 = k(1)

=> k = 25

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Work Shown:

x = list price

93% of x = 0.93x = 22,000

0.93x = 22,000

x = (22,000)/(0.93)

x = 23,655.9139784947 approximately

x = 23,655.91

Answer:

$7.50

Step-by-step explanation:

round 53.43 down to 50

tip = total cost * rate of tip

I hope this helped

Answer:

Yes, they have the same value because when we write them to their lowest term :-( which is a form of a fraction in which the numerator and denominator have no common factor except one) both of them give 4/5 which is 0.8

Answer:

yes they have the same value

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

2x + 4x - 6 = 180

6x - 6 = 180

6x = 186

x = 31

Step-by-step explanation:

Answer:

25

Step-by-step explanation

8x+5x+4x=180-6+1

17x=175

x=25

Answer:

x = 8.98782862707

Step-by-step explanation:

Base on the given we can infer that we are solving for x:

Given equation:

1000x+27x+5.5=9236

Combine similar terms

1027x + 5.5 = 9236

Subtract both side by 5.5

1027x + 5.5 = 9236

             -5.5      -5.5

-------------------------------------

1027x = 9230.5

Now divide both sides by 1027x

9230.5 / 1027

x = 8.98782862707

[RevyBreeze]

Answer:

Sohan

Step-by-step explanation:

she was the one who made it faster to do the work!!

The reciprocal of the time it takes to do the work together is the sum of

the reciprocal of the time it takes to do the work individually.

Reasons

Let R represent the number of days it will take Rohan, S, the number of

days it would take Sohan, and M, the number of days it would take Mohan

to do the work alone, we have;

\(\displaystyle \frac{1}{30} = \mathbf{ \frac{1}{R} + \frac{1}{S}}\)...(1)

\(\displaystyle \frac{1}{24} = \mathbf{ \frac{1}{M} + \frac{1}{S}}\)...(2)

\(\displaystyle \mathbf{ \frac{1}{40}} = \frac{1}{R} + \frac{1}{M}\)...(3)

Subtract equation (1) from equation (2) and add the result to equation (3), we have;

\(\displaystyle \frac{1}{24} - \frac{1}{30} =\displaystyle \left( \frac{1}{M} + \frac{1}{S} \right) - \left(\frac{1}{R} + \frac{1}{S}\right) =\displaystyle \left( \frac{1}{M} - \frac{1}{R} \right)\)

\(\displaystyle \frac{1}{24} - \frac{1}{30} + \frac{1}{40} =\displaystyle \left( \frac{1}{M} - \frac{1}{R} \right) + \frac{1}{R} + \frac{1}{M} = \frac{2}{M}\)

\(\displaystyle \mathbf{\frac{1}{24} - \frac{1}{30} + \frac{1}{40}} = \frac{1}{30} = \frac{2}{M}\)

M = 2 × 30 = 60

\(\displaystyle \frac{1}{24} = \mathbf{\frac{1}{M} + \frac{1}{S}}\)

\(\displaystyle \frac{1}{24} = \frac{1}{60} + \frac{1}{S}\)

\(\displaystyle \frac{1}{24} - \frac{1}{60} =\frac{1}{40} = \frac{1}{S}\)

\(\displaystyle \frac{1}{S} = \frac{1}{40}\)

\(\displaystyle \frac{1}{40} = \frac{1}{R} + \frac{1}{M}\)

\(\displaystyle \frac{1}{40} = \mathbf{\frac{1}{R} + \frac{1}{60}}\)

\(\displaystyle \frac{1}{40} - \frac{1}{60} = \frac{1}{120} = \frac{1}{R}\)

Therefore;

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Answer:

x^2 + (y + 4.3)^2 = 131

Step-by-step explanation:

The basic equation of a circle with center at (h, k) and radius r is

(x - h)^2 + (y - k)^2 = r^2.  Here the center is (0, -4.3) and the radius is √131.  Substituting as indicated, we get:

(x - 0)^2 + (y + 4.3)^2 = 131, or

x^2 + (y + 4.3)^2 = 131

Answer:

I think its 4.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Given

5| x - 7 | + 4 = 4 ( subtract 4 from both sides )

5 | x - 7 | = 0 ( divide both sides by 5 )

| x - 7 | = 0, thus

x - 7 = 0 ( add 7 to both sides )

x = 7 ← is the only solution → C

Answer:

Step-by-step explanation:75mph

Answer:

y = -4

Step-by-step explanation:

When y is directly proportional to x,

= y ∝ x

= y = kx

Finding k

the value of y = -2 when x = 4

-2 = k4

k = -2/4

k = -1/2

. What is the value of y when x = 8

Finding y

y = kx

y = -1/2 × 8

y = -4

Answer:

3 cups of flour.

Step-by-step explanation:

For 3 dozens of muffins we use 2.25 cups of flour. To find out how much flour we need for 4 dozens of muffins, we first need to know how much flour we need for 1 dozen of muffins.

3 dozens of muffins = 2.25 cups of flour

3/3 dozens of muffins = 2.25/3 cups of flour

1 dozen of muffins = 0.75 cups of flour.

Now that we know how much flour we need for one dozen of muffins, we can multiply it by 4 and get our answer.

1*4 dozens of muffins = 0.75*4 cups of flour

4 dozens of muffins = 3 cups of flour.

Hope this helps.

Answer:

3 cups of flour

Step-by-step explanation:

2.25/3 = 0.75
so one dozen muffins need 0.75 cups of flour

0.75 * 4 = 3

so 4 dozen muffins need 3 cups of flour

The mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

Population 1: N = 35,X = 5.3, S = 2.8

Population 2: N = 21, X = 4.9, S = 3.2

We can use the t-test to test if the mean of the first population is larger than that of the second population. The formula for this is:

t = (x1 - x2) / (S√((1/N1) + (1/N2)))

Where x1 is the mean of population 1, x2 is the mean of population 2, S is the pooled standard deviation, and N1 and N2 are the sample sizes of the two populations.

Plugging in our values, we get:

t = (5.3 - 4.9) / (3.2√((1/35) + (1/21))) = 1.68

Using an online calculator, we find that the corresponding p-value is 0.093. Therefore, we fail to reject the null hypothesis that the two populations have the same mean and conclude that the mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

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Sorry, I am not sure and I would not like to spread misinformation

Cheng flies the plane at a speed of 425 mph when there is no wind.

Let's denote the speed of Cheng's plane in still air as 'p' mph. Since the plane is flying against a headwind, the effective speed will be reduced by the wind speed, so the speed against the wind is (p - 6) mph. On the return trip, with the wind, the effective speed will be increased by the wind speed, so the speed with the wind is (p + 6) mph.

We can calculate the time taken for the outbound trip (against the wind) using the formula: time = distance / speed. So, the time taken against the wind is 3933 / (p - 6) hours.

According to the given information, the return trip (with the wind) took 12 hours less time than the outbound trip. Therefore, we can write the equation: 3933 / (p - 6) = 3933 / (p + 6) - 12.

To solve this equation, we can cross-multiply and simplify:

3933(p + 6) = 3933(p - 6) - 12(p - 6)

3933p + 23598 = 3933p - 23598 - 12p + 72

-24p = -47268

p = 1969

Hence, Cheng flies the plane at a speed of 425 mph when there is no wind.

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Answer:

  work = 1,830,000 ft·lb

Step-by-step explanation:

You want the work done to lift 650 lb of coal 600 ft up a mine shaft using a cable that weighs 8 lb/ft.

For some distance x from the bottom of the mine, the weight of the cable is ...

  8(600 -x) . . . . pounds

The total weight being lifted is ...

  f(x) = 650 +8(600 -x) = 5450 -8x

The incremental work done to lift the weight ∆x feet is ...

  ∆w = force × ∆x

  ∆w = (5450 -8x)∆x

We can use a sum for different values of x to approximate the work. For example, the work to lift the weight the first 50 ft can be approximated by ...

  ∆w ≈ (5450 -8·0 lb)(50 ft) = 272,500 ft·lb

If we use the force at the end of that 50 ft interval instead, the work is approximately ...

  ∆w ≈ (5450 -8·50 lb)(50 ft) = 252,500 ft·lb

We can see that the first estimate is higher than the actual amount of work, because the force used is the maximum force over the interval. The second is lower than the actual because we used the minimum of the force over the interval. We expect the actual work to be close to the average of these values.

The attached spreadsheet shows the sums of forces in each of the 50 ft intervals. The "left sum" is the sum of forces at the beginning of each interval. The "right sum" is the sum of forces at the end of each interval. The "estimate" is the average of these sums, multiplied by the interval width of 50 ft.

The required work is approximated by 1,830,000 ft·lb.

__

Additional comment

The actual work done is the integral of the force function over the distance. Since the force function is linear, the approximation of the area under the force curve using trapezoids (as we have done) gives the exact integral. It is the same as using the midpoint value of the force in each interval.

Because the curve is linear, the area can be approximated by the average force over the whole distance, multiplied by the whole distance:

  (5450 +650)/2 × 600 = 1,830,000 . . . . ft·lb

Another way to look at this is from consideration of the separate masses. The work to raise the coal is 650·600 = 390,000 ft·lb. The work to raise the cable is 4800·300 = 1,440,000 ft·lb. Then the total work is ...

  390,000 +1,440,000 = 1,830,000 . . . ft·lb

(The work raising the cable is the work required to raise its center of mass.)

Given:

The scale factor is 1:12.

Dimension of model = 32 cm

To find:

The actual dimension in m.

Solution:

Let x be the actual dimension.

The scale factor is 1:12 and the dimension of model is 32 cm.

\(\dfrac{1}{12}=\dfrac{32}{x}\)

On cross multiplication, we get

\(x=32\times 12\)

\(x=384\ cm\)

\(x=3.84\ m\)             \([\because 1\ m=100\ cm]\)

Therefore, the actual dimension is 3.84 m.

In summary, for the ODE dy/dx + xy/(1+x^2) = x√y, the solution is y = [(ln(1+x^2) + C)/2]^2. For the ODE dy/dx + y/x = y²/x², the solution is y = -1/(ln|x| + 1/x + C).

i) The given ordinary differential equation is dy/dx + xy/(1+x^2) = x√y. To solve this equation, we can use the method of exact differential equations. By rearranging the equation, we have dy/(√y) = (x/(1+x^2))dx. Integrating both sides yields 2√y = ln(1+x^2) + C, where C is the constant of integration. Solving for y, we have y = [(ln(1+x^2) + C)/2]^2.

ii) The given ordinary differential equation is dy/dx + y/x = y²/x². This equation is a first-order linear homogeneous differential equation. To solve it, we can use the method of separation of variables. By rearranging the equation, we have dy/y² = (dx/x) - (1/x²)dx. Integrating both sides gives -1/y = ln|x| + 1/x + C, where C is the constant of integration. Solving for y, we have y = -1/(ln|x| + 1/x + C).

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The solution to the equation log(2 + x) - log(x - 3) = log 2 is: a. x = 3/2.

To solve the given equation, we can apply the properties of logarithms. The equation log(2 + x) - log(x - 3) = log 2 can be simplified using the logarithmic identity log(a) - log(b) = log(a/b). Applying this identity, we have log((2 + x)/(x - 3)) = log 2.

To eliminate the logarithms, we equate the expressions inside the logarithms. Therefore, (2 + x)/(x - 3) = 2.

Next, we can solve this equation for x by cross-multiplying and simplifying. Multiplying both sides by (x - 3), we have 2 + x = 2(x - 3).

Expanding and simplifying the equation, we get 2 + x = 2x - 6.

Solving for x, we find x = 3/2 as the solution.

Therefore, the correct answer is option a. {3/2}

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Answer:

m∠D = 109

Step-by-step explanation:

This is a parallelogram.

In parallelograms, the opposite interior angles are congruent, so we can write the following equation to find, first value x the measure of m∠D:

9x - 44 = 6x + 7

9x - 6x = 7 + 44

3x = 51

x = 17

Now we can calculate measure of m∠D:

m∠D = 9x - 44

9×17 + 44 = 109

Answer: the answer is y=1/2x+3

Step-by-step explanation:

Hopes this helps !! Message me if explanation is needed !!!

The equation of the line which passes through (2,4) with a slope of 1/2​ is  \(y = \frac{x}{2} +3\).

Y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. X and y represent the distance of the line from x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the line is.

Given

Slope m = 1/2

Point (x, y) = (2, 4)

Equation of line which passes through a point (x, y) with a slope of m is

y = mx + b

Substitute the values

⇒ \(4=\frac{1}{2}(2)+b\)

⇒ 4 = 1 + b

⇒ b = 4 - 1

⇒ b = 3

Substitute m = 1/2 and b = 3 in equation (1)

\(y = \frac{1}{2}(x) +3\)

⇒ \(y = \frac{x}{2} +3\)

Hence, the equation of the line which passes through (2,4) with a slope of 1/2​ is  \(y = \frac{x}{2} +3\).

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