simplify (2x+y)(3x²+2xy+5y²)​

The line integral over C alone is 60/3 - (-44) = 64.

What is integral?

Mathematicians define an integral as either a number equal to the area under the graph of a function for a certain interval or as a new function whose derivative is the original function.

solution:

It looks like the integral is

∫ xydx + x^2 y^3 dy

Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}

Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem

Compute the double integral:

From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by

C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}

The line integral over C' is

∫ xydx + x^2 y^3 dy = ∫ ( 1 - t) (  4 - 4t) ( -dt) + ( 1 - t)^2 (  4 - 4t)^3  ( -4dt)

so that the line integral over C alone is 60/3 - (-44) = 64.

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5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

Given that, the nth term of a series represented by \(a_n=\frac{4^n}{5^{n+1}.n}\).

A convergent series is a series whose partial sums tend to a specific number, also called a limit. A divergent series is a series whose partial sums, by contrast, don't approach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Next term in the series is \(a_{n+1}=\frac{4^{n+1}}{5^{n+2}.(n+1)}\)

Now, the ratio is \(|\frac{a_{n+1}}{a_n}| =|\frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|\)

⇒ \(\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} | \frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|\)

⇒ \(\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |\frac{4^{n+1}}{4^n}.\frac{5^{n+2}}{5^{n+1}} .\frac{(n+1)}{n} |\)

⇒ \(\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |4.\frac{1}{5}} .\frac{(n+1)}{n} |\)

⇒ \(\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |\frac{(n+1)}{n} |\)

⇒ \(\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+\frac{1}{n} |\)

⇒ \(\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+0|\)

⇒ \(\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= 0.8\)

Since 0.8 < 1 so the series converges.

The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

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Answer:

From the ratio test, r = 0.8. The series converges.

Step-by-step explanation:

TTT

Answer:

\(f^{-1}(x)=\frac{x-4}{5}\)

Step-by-step explanation:

1. replace f(x) with x, and x with y:  x=5y+4

2. solve for y: x=5y+4

                 ⇒  x-4=5y

                 ⇒  (x-4)/5=y

3. replace y with f⁻¹(x)

Answer:

x = y the answer is this...

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training

As an AI language model my understanding of subjects and skills is based on the information and data available to me up until my last training update in September 2021. I can provide accurate and comprehensive responses within the limits of my training, but please keep in mind that I may not have knowledge of events or developments that have occurred after that cutoff date.

With a wide range of general knowledge, I can understand and generate responses on various topics such as science, history, literature, mathematics, and more. I can also assist with specific skills like writing, editing, brainstorming ideas, offering explanations, and providing recommendations.

However, it's important to note that while I strive to be helpful, I am still an AI and may not always provide perfect answers. I do not possess personal experiences or opinions, and I am not able to perform physical actions. My responses are generated based on patterns and examples from my training data.

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.

Answer:

A

Step-by-step explanation:

reflection over x axis : (x , y) -> (x , -y)

(-1, -2), (-1, -5), and (-3, -5) - -> (-1, 2), (-1, 5), and (-3, 5)

The value of ∠N is 54.38 degrees.

Given that in ΔNOP, n = 56 inches, p = 61 inches and ∠P=80°.

We need to find the value of ∠N,

According to the cosine rule, the following equation is true for every triangle with sides a, b, and c and the corresponding opposite angles A, B, and C:

c² = 2ab cos(C) - a² + b²

In this instance, we have:

A = P and B = P

C = ∠P

When we enter the values, we obtain:

n² = p² + p² - 2p² cos(∠P)

Substituting the known values:

56² = 61² + 61² - 2(61²) cos(80°)

Simplifying:

3136 = 3721 + 3721 - 2(3721) cos(80°)

3136 = 3721 + 3721 - 7442 cos(80°)

Now we can solve for cos(80°):

3136 = 7442 - 7442 cos(80°)

7442 cos(80°) = 7442 - 3136

cos(80°) = (7442 - 3136) / 7442

cos(80°) ≈ 0.5798

∠N = arccos(0.5798)

∠N = 54.38 degrees.

Hence the value of ∠N is 54.38 degrees.

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The correct answer is: D) distance traveled since leaving Bay Town; x ≥ 0

The equation y = -x + 175 represents the distance left to travel to Oak Glen.

In this equation, x is the distance traveled since leaving Bay Town, and y is the distance left to reach Oak Glen.

The domain represents the possible values of x, which is the distance traveled since leaving Bay Town.

Since distance traveled cannot be negative, the domain is x ≥ 0. Therefore, the correct answer is:

D) distance traveled since leaving Bay Town; x ≥ 0

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The question in English is:

The distance between Bay Town and Oak Glen is 175 miles. If the equation y = -x +175 represents the distance to go to Oak Glen, what does the domain represent? What is the domain?

Answer:

65 packets and 4 stamps

Step-by-step explanation:

The first thing we see is that the stamps are mixed... which means they must be added.

208 + 186 = 394 stamps total

Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.

394/6= 65.66667

Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.

Now we find the number of stamps left over by multiplying the number of packets by 6.

65 x 6= 390

Now we take the total number of stamps minus the number of stamps in packets.

394 - 390 = 4

Therefore, there are four stamps left over.

Hope this helps!

The statement which best describes Gary’s error is; Gary did not use the greatest common factor in the equation.

This is the largest positive integer or polynomial that is a divisor of several different numbers. For instance, the greatest common divisor of 66, 30 and 18 is 6.

Gary's work:

66 + 36

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

66 + 36

= 3 (22 + 12)

Gary did not use the greatest common factor in the equation.

The correct answer:

66 + 36

= 6(11 + 6)

Therefore, Gary did not use the greatest common factor in the equation.

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Answer:

-131

Step-by-step explanation:

By dividing by 2, we find that x = 23

Plugging this into the equation we can find

7-6x=7-6(23)=-131

Answer:

-131

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

2x = 46

Step 2: Solve for x

Step 3: Define

7 - 6x

Step 4: Evaluate

Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 11 - 1 = 10 df, is t* = 1.796.

The parameters are given as follows:

\(\overline{x} = 8, s = 4, n = 11\)

Hence the margin of error is given as follows:

\(M = 1.796 \times \frac{4}{\sqrt{11}} = 2.166\)

Then the bounds of the interval are given as follows:

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I think you want 8/3 or 2.666666 or mabye 37%

The arrow after a 270° clockwise rotation will be pointing downward. Therefore, the correct answer is option C.

Thus, the correct answer is option c.

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P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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Answer:

50% decrease

Step-by-step explanation:

130-65 = 65

65/130 = 0.5

0.5 x 100 = 50

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.

However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.

This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.

As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.

It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.

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Answer:

Step-by-step explanation:

Find all real solutions of the equation. ( 2 b + 4 ) 2 − 12 = 0

( 2 b + 4 ) 2 − 12 = 0

4b + 8 - 12 = 0

4b - 4 = 0

4b = 4

b = 1

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

check

(2*1+4)*2-12=0

12 - 12 = 0

0 = 0

the answer is good

Answer:

i still get points

Step-by-step explanation:

^-^

Answer:

3.95cm

Step-by-step explanation:

This will help!

Answer:

\(x = \frac{15}{2} = 7 \frac{1}{2} \)

Step-by-step explanation:

\(5 \times 2 - 2x + 5 = 0\\ 10 - 2x + 5 = 0 \\ 15 - 2x = 0 \\ 15 - 2x - 15 = 0 - 15 \\ - 2x = 0 - 15 \\ - 2x = - 15 \\ x = 15 \div 2 \\ \)

\(\boxed{\green{\boxed{\bold{x = \frac{15}{2} = 7 \frac{1}{2} }}}}\)

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★ . ꜝꜞ ᳝ ࣪ hope that helped!  ʬʬ

No,  the form that Maria expanded is not correct.

What does it mean to "extend and simplify"?

We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression. We take out brackets by expanding them, often known as multiplying out.

Given:

(x+3)²

= x² + 2 . 3 . x + 3²

= x² + 6x + 9

Therefore the correct expansion is x² + 6x + 9.

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Question:

Maria expanded the following square (x+3)^2=x^2 Is the form she used correct?

Answer:

-1x+10

Step-by-step explanation:

The equation that shows how the number of fluid ounces of nectar remaining (y) depends on the number of days since Logan filled it (x) is:

y = 10 - x.

The relationship between the number of fluid ounces of nectar remaining (y) and the number of days since Logan filled the hummingbird feeder (x) can be represented using a linear equation.

Initially, when Logan fills the hummingbird feeder to its capacity of 10 fluid ounces, the nectar remaining is 10 fluid ounces.

As each day passes, 1 fluid ounce of nectar is released.

Therefore, the equation that shows how the number of fluid ounces of nectar remaining (y) depends on the number of days since Logan filled it (x) is:  y = 10 - x.

Here's an explanation of each component of the equation:

y: This represents the number of fluid ounces of nectar remaining.

As the days pass, this value will decrease as nectar is released.

10: This is the initial amount of nectar in the feeder when Logan fills it to its capacity of 10 fluid ounces.

x: This represents the number of days that have passed since Logan filled the feeder.

Each day, the amount of nectar decreases by 1 fluid ounce, hence the subtraction of "x."

This equation forms a linear relationship where the nectar remaining decreases by 1 fluid ounce for each day that passes.

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Answer:

75−4(4−2)^3

=43