Find the sum
please this is urgent ​

Using Newton's method with the initial approximation x₁ = 2, the second approximation x₂ is obtained by substituting x₁ into the formula x₂ = x₁ - f(x₁) / f'(x₁).

The initial approximation given is x₁ = 2. Using Newton's method, we can find the second approximation, x₂, by iteratively applying the formula:

x₂ = x₁ - f(x₁) / f'(x₁)

where f(x) represents the function and f'(x) represents its derivative.

In this case, the equation is f(x) = cos(x² + 4). To find the derivative, we differentiate f(x) with respect to x, giving us f'(x) = -2x sin(x² + 4).

Now, let's substitute the initial approximation x₁ = 2 into the formula to find x₂:

x₂ = x₁ - f(x₁) / f'(x₁)

   = 2 - cos((2)² + 4) / (-2(2) sin((2)² + 4))

Simplifying further:

x₂ = 2 - cos(8) / (-4sin(8))

Now we can evaluate x₂ using a calculator or computer software.

Newton's method is an iterative root-finding algorithm that approximates the roots of a function. It uses the tangent line to the graph of the function at a given point to find a better approximation of the root. By repeatedly applying the formula, we refine our estimate until we reach a desired level of accuracy.

In this case, we applied Newton's method to approximate a root of the equation cos(x² + 4). The initial approximation x₁ = 2 was used, and the formula was iteratively applied to find the second approximation x₂. This process can be continued to obtain even more accurate approximations if desired.

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Answer:

y=1/5x+7

Step-by-step explanation:

i hope this helps :)

Answer:

yes, the base is 4

Step-by-step explanation:

Answer:

A. -80

B. 60

C. 98

D. -54

Step-by-step explanation:

ez give brainliest pls

Step-by-step explanation:

For the number to be even, it needs to end in an even number ,,,,there are no even numbers that are primes ( because the number would be divisible by 2)

Answer:

\(d=4\sqrt{5}\approx8.94\)

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Let (-1, -2) be (x₁, y₁) and let (-9, 2) be (x₂, y₂).

Substitute appropriately:

\(d=\sqrt{(-9-(-1))^2+(2-(-2))^2\)

Evaluate:

\(d=\sqrt{(-8)^2+(4)^2\)

Square and evaluate:

\(d=\sqrt{64+16}=\sqrt{80}=4\sqrt{5}\approx8.94\)

Therefore, the distance between the two points is approximately 8.94 units.

Answer:

a² +3ab - 5ab - 15b² = (a+3b) (a-5b)

Step-by-step explanation:

We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,

\(a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)\)

Now taking a common from the first two terms and 3b from last two terms, then :

\((a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)\)

In the above expression, a factor (a-5b) is in both the terms. It would mean that,

\(a(a-5b)+3b(a-5b)=(a+3b)(a-5b)\)

So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).

Answer:

\(d \approx 2.8\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point A (-3, 1)

Point B (-1, -1)

Step 2: Find distance d

Answer:  d = 2.83

Step-by-step explanation: The distance between AB rounded to the nearest tenth is 2.83

The bushing shown in the figure weighs 0.2833 pounds per cubic inches.

The bushing shows is a hollow cylinder, the volume of a hollow cylinder is :

where Do is the outer diameter

Di is the inner diameter

h is the height of the cylinder

From the problem,

Di = 2 and 1/4 inches or 2.25 in

Do = 6 inches

h = 7 and 1/4 inches or 7.25 in

Using the formula above :

The volume is 176.16 cubic inches

Multiply this to the given weight per cubic inches.

The weight is 49.9 pounds

The answer is 49.9 pounds

The pοssible values οf angle J is 76 degrees.

It is a triangle in which οne οf the angles is 90 degrees and the οther twο are sharp angles. The sides οf a right-angled triangle are knοwn as the hypοtenuse, perpendicular, and base.

Given that,

Triangle = Triangle HIJ

j = 91 inches

i = 90 inches

Angle I = 106 degrees

The pοssible values οf angle J can be calculated using the fοllοwing law οf sines

sin(J)/j = sin(I)/i

By substituiοn, we have

sin(J)/91 = sin(106)/90

Sο, we have

sin(J) = 0.9719

Take the arc sin οf bοth sides

J = 76 and 104 degrees

The measure 104 degrees is nοt pοssible because a triangle cannοt have twο οbtuse angles

Hence, the measure οf J is 76 degrees

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Answer:

Income tax amount: $5047.50

Step-by-step explanation:

89172.5 is the total amount with income tax added.

The normal value is $84,125 so you can do this in your calculator in the future it's like this:

84,125 * .06 = 5047.5

Answer:

c

Step-by-step explanation:

a) It is not possible for everyone in a group of 5 friends to have exactly two friends.

b) It is possible for everyone in a group of 5 friends to have exactly three friends.

(a) It is not possible for everyone in a group of 5 friends to have exactly two friends. To see why, suppose that each person has exactly two friends. This means that each person is connected to two other people in the group. If we start at any person in the group, we can follow their connections to the other people in the group.

Since each person has only two friends, the connections will form a chain or loop. However, if we keep following the connections, we will eventually return to the original person, forming a loop. This means that the group must be connected in a loop or chain, but this is impossible with 5 people.

(b) It is possible for everyone in a group of 5 friends to have exactly three friends. One example is the complete graph on 5 vertices, denoted K5, where every vertex is connected to every other vertex. In this graph, every person has exactly 4 friends, since they are connected to all of the other people in the group.

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Answer: the answer is B

Step-by-step explanation:

The solutions of the equation X⁴-9x² + 8 = 0 is ±2√2 and ±1

X⁴-9x² + 8 = 0

Let x² = y

Then the equation becomes y² - 9y + 8 = 0

This is in the form ax² + bx + c = 0

We can solve by using quadratic formula for finding roots

x = {-b ± √(b² - 4ac)} / 2a

where,

= {-(-9) ± √((-9)2 - 4(1)(8))} / 2(1)

= {9 ± √(81 - 32)} / 2

= {9 ± √49} / 2

= {9 ± 7}/2

= 16/2, 2/2

= 8, 1

y = 8,1

x = ±2√2, ±1

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The penguin swims half the circumference of the circular island, which is equivalent to half the distance around the circle.

The circumference of a circle can be calculated using the formula:

C = πd,

where C is the circumference and d is the diameter of the circle.

Given that the diameter of the island is 20 meters, the radius (r) of the island is half the diameter, which is 10 meters.

Substituting the value of the radius into the formula, we have:

C = π * 10 meters = 10π meters.

To find half the circumference, we divide the total circumference by 2:

Half circumference = (10π meters) / 2 = 5π meters.

Therefore, the penguin swims a distance of 5π meters.

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Answer:

-4 < n ≤ 5

Step-by-step explanation:

_________________

Answer:

x>3  here is your answer

D it’s the base.

Shdnxnxhxb

The point where the tangent plane to the surface is horizontal will be (1.0899, 1.6595).

To determine the partial derivatives of the function f(x, y) with respect to x and y:

\(fx = 2xy^3 - 4y - 1\\fy = 2x^3y - 4x\)

Now, we can find the gradient of f:

\(grad(f) = < fx, fy > = < 2xy^3 - 4y - 1, 2x^3y - 4x >\)

To determine the point where the tangent plane to the surface is horizontal, the critical points of f where grad(f) = 0:

\(2xy^3 - 4y - 1 = 0\\2x^3y - 4x = 0\)

From the second equation,

\(2x(x^2y - 2) = 0\)

Therefore, either x = 0 or x^2y - 2 = 0 Substituting this into the first equation, we get:

\(2x(2/x^6) - 4(2/x^2) - 1 = 0\\4/x^5 - 8/x - 1 = 0\)

Therefore, the point where the tangent plane to the surface is horizontal  x ≈ 1.0899 and y ≈ 1.6595.

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The total number of times that the coin was flipped would be 10 times. Option D.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable." Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

In order to prove that the number of flips that was done by the families 10, we would have to solve for the probability of heads using total of 10 and 4 as the total for the Rodriguez.

4 / 10 * 100

= 40%

Hence the other family flipped the coin 60 percent of the time. Such that 10 - 4 = 6

6 + 4 = 10

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Answer:

Your answer would be C

Step-by-step explanation:

Hope I helped!! :)

Answer:

1 hour and 53 minutes

Step-by-step explanation:

Let's start at 7:10.

7:10 - 8:10 is 1 hour.

8:10 - 9:00 is 50 more minutes.

Total so far is 1 hour 50 minutes.

9:00 - 9:03 is 3 more minutes.

Total would be 1 hour and 53 minutes

Hope this answer helped! :)

Answer:

1 hour and 53 minutes

Step-by-step explanation:

You just need to subtract the times form each other.

There are two ways to do this.

Subtract the number of minutes and convert into total hours and remainder minutes.

Or you can just do the simple way shown by the answer above.

I will show the subtracting minutes one since it can be a base for all .

First we find how many minutes are in 7 hours and 10 minutes, and nine hours and three minutes.

7 hours and ten minutes is 430 minutes. 9 hours and 3 minutes is 543 minutes.

543 - 430 is 113.

Then you divide, we are using the remainder type division.

113/60(60 minutes in one hour)

60 goes into 113 one time and leaves 53.

Therefore, it takes 1 hour and 53 minutes.

Answer:

16m^2

Step-by-step explanation:

SA = 2bs + b^2

     = 2(2m)(3m) + (2m)^2

     = 16m^2

The crucial value (z) relies on the desired level of confidence and is predicated on a normal distribution when creating a confidence interval for a proportion (p) with a confidence level of 93%.

A 93% confidence level in this instance translates to an alpha level of 0.07 (1 - 0.93 = 0.07) that is split evenly between the two tails. In the usual normal distribution table, we search for the value that falls within the range of 0.07 to find the proper z-value. A 93% confidence level corresponds to a z-value of roughly 1.81. The confidence interval for the proportion p may be calculated using this number and provides a range where the genuine proportion is like to fall.

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Answer:

(4, -8) or x=4 y=-8

Step-by-step explanation:

Answer: x=4 and y=−8

Step-by-step explanation: 7x+2y=12, −3x−2y=4

7x+2y+−2y=12+−2y

7x /7 = −2y+12 /7

x= −2 /7 y+ 12 /7

−3( −2 /7 y+ 12 /7 )−2y=4

−8 /7 y+ −36 /7 + 36 /7 =4+ 36 /7

−8 /7 y / /−8/7 = 64 /7 /−8 /7

y=−8

x= −2 /7 y+ 12 /7

x= −2 /7 (−8)+ 12 /7

x=4

x=4 and y=−8

a.  If we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

b. Michael's substitution satisfies the requirement for u to be differentiable.

(a) i. Kayla's proposed substitution of u as (3 - 2x) will not work in this case. The reason is that when using the u-substitution method, it is necessary for the chosen u to be differentiable, meaning that its derivative du/dx should exist and be non-zero. However, if we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

ii. Kayla's idea of always picking the most inside factor as u does not work for all u-substitutions. There can be cases where choosing the most inside factor may not lead to a valid substitution that simplifies the problem or makes integration easier. It is important to consider the properties of the function and choose a suitable substitution accordingly.

(b) i. Michael's proposed substitution of u as 3√3 - 2x will work in this case. If we let u = 3√3 - 2x, then the derivative du/dx would be -2, which is non-zero. Therefore, Michael's substitution satisfies the requirement for u to be differentiable.

ii. Michael's idea of always picking the most complicated factor as u also does not hold true for all u-substitutions. The choice of u depends on various factors, including the structure of the function, simplification possibilities, and making the integration process more manageable. It is not necessarily the case that the most complex factor will always result in a successful substitution.

It is important to consider the specific characteristics of the function and apply appropriate judgment in choosing the substitution u to simplify the problem effectively.

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Answer: 40%

Step-by-step explanation:

It shows 4/10 which is 40%

The value of the 3rd term in the expansion of (x+6) ^6 will be as follows:

540x^4

What is expansion?

Expanding brackets, also known as multiplying out, seeks to eliminate the set of brackets by multiplying each phrase inside a bracket by the term on the outside and subsequently accumulating similar phrases. When solving equations, extending brackets, which is the opposite of factorization, is frequently an essential step.

Here in the question,

We have,

(x+6) ^6

Expanding it we get:

= x^6 + 36x^5 + 540x^4 +4320x³ + 19440x² + 46656x + 46656

So, the 3rd term of the expansion is 540x^4.

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The value of the 3rd term in the expansion of \((x+6) ^6\) will be as follows: \(540x^4\). The correct answer is option (c).  \((6\ \ 4)36x^4\)

By multiplying each phrase inside a bracket by the word on the outside and then accumulating similar phrases, expanding brackets, also known as multiplying out, aims to eliminate the set of brackets. Extending brackets, which is the opposite of factorization, is frequently a crucial stage in the solution of equations.

An affine transformation termed expansion, in which the scale is expanded, is also referred to as an enlargement or dilation. It is also sometimes referred to as an enlargement and is the polar opposite of a geometric constriction.

Here in the question,

We have,

\((x+6) ^6\)

Expanding it we get:

\(= x^6 + 36x^5 + 540x^4 +4320x^3 + 19440x^2 + 46656x + 46656\)

So, the 3rd term of the expansion is \(540x^4\).

The correct answer is option (c). \((6\ \ 4)36x^4\)

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