what is the y-intercept of the following equation:2x+y=5?

To find the value of the line integral ∮ (2xy - x^2)dx + (x + y^2)dy over the curve C enclosed by y = x^2 and y^2 = x, we need to evaluate the integral.

The given options are 77/30, 1/30, 7/30, and 11/30. We will determine the correct value using the properties of line integrals and the parametrization of the curve C.

We can parametrize the curve C as follows:

x = t^2

y = t

where t ranges from 0 to 1. Differentiating the parametric equations with respect to t, we get dx = 2t dt and dy = dt.

Substituting these expressions into the line integral, we have:

∮ (2xy - x^2)dx + (x + y^2)dy = ∫(0 to 1) [(2t^3)(2t dt) - (t^2)^2)(2t dt) + (t^2 + t^2)(dt)]

= ∫(0 to 1) [4t^4 - 4t^4 + 2t^2 dt]

= ∫(0 to 1) [2t^2 dt]

= [2(t^3)/3] evaluated from 0 to 1

= 2/3.

Therefore, the correct value of the line integral is 2/3, which is not among the given options.

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Answer:

x + (5 - 2x)

Step-by-step explanation:

The total revenue that will be maximized is 20 - 2a

From the question, we have the following parameters that can be used in our computation:

Qd = 20 - P

The revenue equation is calculated using

Revenue = Quantity * Price

So, we have

R = Qd * P

This gives

R = (20 - P) * P

Expand

R = 20P - P²

Differentiate

R' = 20 - 2P

Next, we have

Q = a

So, we have

R = 20 - 2a

Hence, the total revenue that will be maximized is 20 - 2a

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Answer:

5/9

Step-by-step explanation:

Solution

The gradient of the line ment when two segment given (X1, Y1) and (X2, Y1) is points

m =

\( \frac{y2 - y1}{x2 - x1 } \)

Here two points given, (-5,-2) and (4,3)

gradient (m):

\( \frac{3 - ( - 2)}{4 - ( - 5)} \)

Given :

Length of rink, L = 40 meters.

Width of rink , W = 20 meters.

To Find :

How many meters of handrail does Gus need to cover the perimeter of the rectangular skating rink.

Solution :

We know, perimeter is given by :

\(P=2(L+W)\)

Putting value of L = 40 meters and W = 20 meters, in above equation , we get:

\(P=2(40+20)\ meters\\\\P=120\ meters\)

Therefore, the perimeter of the rectangular skating rink is 120 meters.

Hence, this is the required solution.

Answer:

one side is 12 as the radius is 2 so x 2 for diameter which is 4. there are 3 circles so times it by 3 which = 12.

the other side is 4 as one circle daimeter is 4.

4 x 12 = 48.

Step-by-step explanation:

Answer:

A. ≈31.1

B. ≈19.7

Step-by-step explanation:

A. 245/798

B. 157/798

Answer:

Look at step-by-step explanation

Step-by-step explanation:

14a.

There are 798 students total and 245 freshman. To find the percent of freshman, divide 245 by 798:

245/789= 31.1%

Same process for part b. There are 798 students and 157 seniors:

157/789= 20.0%

Answer:

2367..58

Step-by-step explanation:

Answer:

$2368

Step-by-step explanation:

\(Interest=Value*((1+interest)^{years}-1) \\= 7000(1.06^{5}-1)=2368\)

Answer:

y- intercept --> Location on graph where input is zero

f(x) < 0         --> Intervals of the domain where the graph is below the x-axis

x- intercept --> Location on graph where output is zero

f(x) > 0         --> Intervals of the domain where the graph is above the x-axis

Step-by-step explanation:

Y-intercept: The y-intercept is equivalent to the point where x= 0. 'x' is the input variable in an equation, therefore the y-intercept is where the input, or x, is equal to 0.

f(x) <0: Notice the 'lesser than' sign. This means that the value of f(x), or 'y', is less than 0. This means that this area consists of intervals of the domain below the x-axis.

X-intercept: The x-intercept is the location of the graph where y= 0, or the output is equal to 0.

f(x) >0: In this, there is a 'greater than' sign. This means that f(x), or 'y', is greater than 0. Therefore, this consists of intervals of the domain above the x-axis.

Answer:

2k - 13

Step-by-step explanation:

1. Because this is an expression, we can only simplify it.

2. (Solving)

Step 1: Apply distributive property.

Step 2: Combine like terms.

Therefore, the answer is 2k - 13!

Answer:

The answer is D.

Step-by-step explanation:

Test each multiply choice to see if given the x-axis points.

(x+1)(x+2)(x-3)=0

(x+1) = 0 , (x+2) = 0 , (x-3) = 0

x = -1 , x = -2 , x = 3

(-1 , 0) , (-2 , 0) , (0 , 3)

The total number of 5- digit even palindromes present is 400 numbers.

For the stated question-

For example, 23432, 85658,

The number of 5- digit even palindromes are formed as;

4 * 10 * 10 = 400.

Thus, the total number of 5- digit even palindromes present is 400 numbers.

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The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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Answer:

3A+6B≤72

7A+5B≤84

Step-by-step explanation:

Just took the exam and got it right

Answer:

Approximately 15 minutes

Step-by-step explanation:

Let us use the idea of progression to solve the problem

Using arithmetic progression formula

Let the initial temperature be the first term i.e a = - 18°F

Since the fluid goes up by 5.4°F after 1 minutes, we can take our common difference to be 5.4°F

Looking for how long it take before the radiator fluid temperature reaches 60°F will be equivalent to looking for the number of terms 'n' when the nth term Tn is 60

Using the formula for finding the nth term of an Arithmetic sequence as shown:

Tn = a+(n-1)d

Substitute the given parameters

60 = -18+(n-1)(5.4)

Open the parentheses

60 = -18+(5.4n-5.4)

60 = -18+5.4n-5.4

60 = 5.4n-23.4

5.4n = 60+23.4

5.4n = 83.4

n = 83.4/5.4

n = 15.4

n ≈ 15

Hence it will take approximately 15minutes before the radiator fluid temperature reaches 60°F

Answer:

1/6

Step-by-step explanation:

Since you are rolling the die only one time there is only one way of you getting a 6 and that is rolling an actual 6. There are six sides to the die so you take the one 6 out of the the others and there is your probability.

Answer:

5/36

Step-by-step explanation:

I got it right

Answer: 2/3

Step-by-step explanation: use scratch work and compare the shaded amounts.

you do 479 x 2 = 958 there is your answer your welcome

Answer:

500 pts  :DDDD

Step-by-step explanation:

1 )   y = mx + b

hmmm 2 is wrong

2)  y = -a\(x^{2}\)+bx+c

I'm unsure about 3 also  hmm

3)  y = a\(x^{y}\)

Answer:

the answer is 80

Step-by-step explanation:

or, angleAFE =angleBFD [V.O.A]

or, 125=45+DFC

or, 125-45=DFC

or, 80 =DFC

Using the concepts of straight angle, ∠DFC = 80°.

A straight angle is an angle equal to 180 degrees. It is called straight because it appears as a straight line.

Since AD is a straight line.

∠AFE + ∠EFD = 180°

125° + ∠EFD = 180°

∠EFD = 180° - 125° = 55°

Now, EB is a straight line.

∠EFD + ∠DFC + ∠CFB = 180°

55° + ∠DFC + 45° = 180°

∠DFC = 180° - 100° = 80°

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The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

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The system of linear equation that represent this problem is

6x + 10y = 900

10x + 4y = 1220

Let's represent the number of CDs Roberto bought as x and the number of magazines as y

The problem states the following information:

Using the variables;  x and y as given;

1. Roberto bought 6 CDs and 10 magazines for $900.00 pesos. This can be represented as the equation:

  6x + 10y = 900

2. María bought 10 CDs and 4 magazines for $1,220.00 pesos. This can be represented as the equation:

  10x + 4y = 1220

So, the system of equations representing the problem is:

6x + 10y = 900

10x + 4y = 1220

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Translation: Roberto bought 6 cd's and 10 magazines for $900.00 pesos; In the same store, her friend María bought 10 CDs and 4

magazines at $1,220.00 pesos. What is the system of equations with two unknowns that represents the problem?

Answer: The answer is valid, because you survey 100 people and 80 of them support building a new stadium.

Step-by-step explanation:

80% agree. 80/100 = 80%

We utilize a two factors, independent measurements ANOVA, where, factor has 2 level and a factor likewise has 2 levels.

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

Factors and multiples are a part of our daily life. For example, they are employed in arranging objects in a box, handling money, recognizing patterns in numbers, solving ratios, and working with expanding

A number totally divides the provided number without leaving any residual is said to be the factor of that number.

The components of a number might be positive or negative. For example, let us find the factors of 8. Since 8 is divisible by 1, 2, 4, and 8, we may list the positive factors of 8 as, 1, 2, 4, and 8. Apart from this, 8 has negative elements as well, which might be stated as, -1, -2, -4,

According to our question-

Degrees of freedom for the F-test of the two way ANOVA

In this case, we utilize an ANOVA with two independent variables and two factors, each with two levels.

So, here,

= 2 for the number of layers of A

= B's level count is 2,

Moreover, n = sample size in each treatment condition is equal to 10.

So we have,

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of interaction effect (A x B) = ( - 1)( - 1) ( - 1)

= (2-1)(2-1) (2-1)

= 1

And = df of within variation (i.e. error variation) =

= 2 x 2 x (10 - 1) (10 - 1)

= 36

Consequently, the df value for the F-ratio measuring factors-primary A's impact is

= () ()

= (1, 36) (1, 36)

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Answer:

The order of ordered pairs of a function and its inverse reverse. The graph of the inverse of this function passes through the points (2,-1), (6,0), (-4,3).

Explanation:

I just took the test.

As per the graph, the non-invertible functions pass through the point of (-1, 2)), (0,6), and (3, - 4).  

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The bucket will be 30% full at 772 seconds

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this problem is:

v= x/t

Where:

Information about the problem:

Calculating how many ounces the bucket will be when it has 30% full:

Volume = 220.5 * 30%

Volume = 66.15oz

The bucket will lose:

x = 220.5oz - 66.15oz

x = 154.35 oz

The time that the bucket will have 66.15 oz (30%) is:

t = x/v

t = 154.35 oz / 0.2 oz/s

t = 771.75 s = 772 s

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Correctly written question:

A pail holds 220.5 ounces (oz.) of water when full. The bucket loses 0.2oz of water per second. In how many seconds will the bucket be 30% full? Round your answer to the nearest second.

Answer: the real answer for this will be p=3/2 and s=5

Step-by-step explanation: here

2p=3

2p/2=3b/2 divide both sides by 2

P=3/2

3/2 for p in s=5

S=5

S=5

Answer P=3/2 and s= 5

Got it

Hey there!

“Evaluate 2ps for p=3 and s=5”

• Side note: If p = 3 then SUBSTITUTE where “p” is at in the equation; if s = 5 then SUBSTITUTE where “s” is at in the equation!

• New equation: 2(3)(5)

2(3)(5)

2(3) = 6

6(5) = 30

Answer: A. 30 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

We found a particular solution to the nonhomogeneous differential equation y'' + 4y' + 5y = -10x + 3e^(-x) as y_p = -3/2 e^(-x).

To find a particular solution to the nonhomogeneous differential equation y'' + 4y' + 5y = -10x + 3e^(-x), we will use the method of undetermined coefficients.

Step 1: Homogeneous Solution

First, we need to find the solution to the corresponding homogeneous equation y'' + 4y' + 5y = 0. The characteristic equation is r^2 + 4r + 5 = 0, which has complex roots -2 + i and -2 - i. Therefore, the homogeneous solution is of the form y_h = e^(-2x)(c1cos(x) + c2sin(x)), where c1 and c2 are arbitrary constants.

Step 2: Particular Solution

We will look for a particular solution of the form y_p = ax + b + c e^(-x), where a, b, and c are constants to be determined.

Substituting y_p into the differential equation, we have:

y_p'' + 4y_p' + 5y_p = -10x + 3e^(-x)

Taking the derivatives and substituting back into the equation, we obtain:

(-c)e^(-x) + (-c)e^(-x) + 4(a - c)e^(-x) + 4a + 5(ax + b + c e^(-x)) = -10x + 3e^(-x)

Matching the coefficients of the terms on both sides, we get the following system of equations:

4a + 5b = 0 (for the x term)

4(a - c) = -10 (for the constant term)

-2c = 3 (for the e^(-x) term)

Solving this system of equations, we find a = 0, b = 0, and c = -3/2.

Therefore, a particular solution to the nonhomogeneous differential equation is y_p = -3/2 e^(-x).

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a) g(t) is increasing on the interval (-∞, 5/8) and decreasing on the interval (5/8, ∞).

b) The local minimum of g(t) is at t=5/8. The absolute minimum or maximum, are -∞ and ∞

c) The absolute maximum of f(x) on the interval [6,9] is 78, which occurs at x=6, and the absolute minimum is 27, which occurs at x=9.

A) To find the intervals where the function g(t)=4t^2−5t−1 is increasing and decreasing, we need to determine the sign of its first derivative g'(t). Taking the derivative of g(t), we get:

g'(t) = 8t - 5

To find where g'(t) is positive and negative, we can set it equal to zero and solve for t:

8t - 5 = 0

t = 5/8

This means that g(t) is increasing on the interval (-∞, 5/8) and decreasing on the interval (5/8, ∞).

B) To identify the local and absolute extreme values of g(t), we need to look at the critical points and endpoints of the interval. Since g'(t) is a linear function, it has only one critical point at t=5/8. This means that this is the location of the local minimum of g(t).

To find the absolute minimum or maximum, we need to compare the values of g(t) at the endpoints of the interval, which are -∞ and ∞. Since the function approaches positive infinity as t approaches infinity and negative infinity as t approaches negative infinity, it has no absolute maximum or minimum.

C) To find the absolute extrema of f(x)=(12+x)(12−x) on the interval [6,9], we first find the critical points of f(x) by setting its derivative equal to zero:

f'(x) = -2x + 24 = 0

x = 12

This critical point is inside the interval [6,9], so we also need to evaluate the function at the endpoints of the interval. We get:

f(6) = 78

f(9) = 27

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The average number of intersections the traffic engineer would need for each type of traffic signal to reject the null hypothesis at the 0.01 level of significance with a power of 0.90 is six

To test the effectiveness of these signals, the engineer must reject the null hypothesis, which states that there is no significant difference in the mean delays between the three types of signals. The engineer wants to reject the null hypothesis at the 0.01 level of significance with a power of 0.9. In other words, they want to be 90% sure that they can detect a significant difference if it exists.

Using the data provided in the study, the engineer can calculate the sample size needed for each type of signal. They need at least five intersections for pretimed signals, six intersections for semi-actuated signals, and four intersections for fully actuated signals to reject the null hypothesis at the desired level of significance with a power of 0.9.

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