evaluate 4a+7b+3a-2b for a =5 and b=-3

We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

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What the given experiment demonstrates is; The magnitude of acceleration according tp newton's second law of motion

Newton's second law of motion states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

This law basically establishes a relationship between the net force and the acceleration, which is expressed as;

∑ F = m a

where;

∑F is the sum of the external forces

m the mass of the body

a is the acceleration of the body

The initial situation in the question shows the block and a baking mass. This means that an acceleration is created towards the hanging mass expressed as;

W₁ = M₁ g

F = ma

Thus;

M₁g = m a

a = (M₁g/m)

where;

W₁ is the weight of the body  

M₁ is the mass of the body hanging under the acceleration of gravity.

For the second case, there are two masses, with one on each side, and so we have;

∑ F = W₁ - W₂

∑F = (M₁ - M₂) g

Using Newton's second law of motion gives us;

(M₁ - M₂ )g = ma

a = (M₁ - M₂ )mg

Thus, the acceleration depends on the difference of the hanging masses which proves Newton's second law of motion.

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Answer:

61 is the mode.

Step-by-step explanation:

Remember, the mode is the most repeated number in the list. 6|1 is repeated the most times (twice).

Answer:

61 is the correct answer

Step-by-step explanation:

I take gas consumption as example.

Consider the followings,

Let M be the gas meter reading per month

A be the fuel adjustment fee

B be monthly maintenance fee

Y be unit cost per Joule

Let X be monthly bill

( 1 meter reading unit = 48 unit of Joule )

Monthly bill payment :

X = Mx48xY + A + B

in function notation, the monthly bill is f(M, Y, A, C)

Answer:

answer

Step-by-step explanation:

step by step explanation

With 99% confidence that the true difference lies between 0.1316 and 0.2694.

A 99% confidence interval for the difference in average SAT scores between coached and uncoached students can be constructed using the data above.

The confidence interval is calculated as (mean of coached students - mean of uncoached students) +/- (2 * standard error of the difference in means).

The mean of coached students is (0.3098 + 0.3399 + 0.219 + 0.0798) / 4 = 0.2155, and the mean of uncoached students is (0.0046 + 0.0248) / 2 = 0.0147. The standard error of the difference in means can be calculated as the square root of ((0.2155(1-0.2155)/4) + (0.0147(1-0.0147)/2)).

The confidence interval is then (0.2155 - 0.0147) +/- (2 * 0.0347) = 0.201 +/- 0.0694, or (0.1316, 0.2694). This indicates that, on average, coached students gain 0.201 points more than uncoached students, with 99% confidence that the true difference lies between 0.1316 and 0.2694.

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The value of square root of x + y squared + z squared is 30

x = 2, y = 3 and z = -5

\(( \sqrt{x + y} )^{2} + z ^{2} \)

substitute the value of x, y and z

\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)

simplify the square root and square

\( = (2 + 3) + 25\)

\( = 5 + 25\)

\( = 30\)

Ultimately, x + y squared + z squared is 30

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The sample variance and standard deviation are given as follows:

Variance = 87.22 %.

Standard deviation = 9.34%.

To obtain the variance and the standard deviation first, we must obtain the mean, which is given by the sum of all observations divided by the number of observations, hence:

Mean = (77.1 + 82.9 + 90 + 91.3 + 81.9 + 83.3 + 84.9 + 82.5 + 84.6)/10

Mean = 75.85.

Then we must obtain the sum of the differences squared between each observation and the mean, as follows:

(77.1 - 75.85)² + (82.9 - 75.85)² + (90 - 75.85)² + (91.3 - 75.85)² + (81.9 - 75.85)² + (83.3 - 75.85)² + (84.9 - 75.85)² + (82.5 - 75.85)² + (84.6 - 75.85)² = 784.9825

The sample variance is given by the above sum divided by one less than the sample size, hence:

Variance = 784.9825/9

Variance = 87.22 %.

The standard deviation is the square root of the variance, hence:

Standard deviation = sqrt(87.22)

Standard deviation = 9.34%.

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The probability that a person will purchase no more than one costume is given as follows:

93%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes for this problem is given as follows:

187 + 228 + 29 = 444.

Only 29 people purchased more than one costume, hence the probability of at most one costume is calculated as follows:

(444 - 29)/444 = 0.93 = 93%.

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Answer:

- sinu

Step-by-step explanation:

using the difference identity for sine

sin(a - b) = sinacosb - cosasinb

then

sin(u - π )

= sinucosπ - cosusinπ

= sinu(- 1) - cosu(0)

= - sinu - 0

= - sinu

The graph that shows the line y = - 3 x + 1 would be B. Graph B.

To find the graph, you need to find the x and y values from the given equation of line y=-3x+1.

Then look at the graph that has these points.

For x = -2:

y = -3(-2) + 1

y = 6 + 1

y = 7

For x = -1:

y = -3(-1) + 1

y = 3 + 1

y = 4

For x = 0:

y = -3(0) + 1

y = 0 + 1

y = 1

For x = 1:

y = -3(1) + 1

y = -3 + 1

y = -2

For x = 2:

y = -3(2) + 1

y = -6 + 1

y = -5

For x = 3:

y = -3(3) + 1

y = -9 + 1

y = -8

So, the y values for x = -3 to x = 3 are:

x = -3: y = 10

x = -2: y = 7

x = -1: y = 4

x = 0: y = 1

x = 1: y = -2

x = 2: y = -5

x = 3: y = -8

The graph that has these points is therefore Graph B.

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Answer:

The answer is 11n

Step-by-step explanation:

Why? Because when there is a variable (n), you just do the operation and put the variable like I showed above.

Srry, if cant understand but, hopefully, it helped :)

Answer:

P(0 < z < 1.56)=0.4406

Step-by-step explanation:

The blue curve of the image attached below represents the graph of the function f(x) = 3 · x².

In this question we have a power function formed by the product of a primitive function g(x) = x² and vertical dilation h(x) = 3, then:

f(x) = h(x) · g(x)

f(x) = 3 · x²

Now we proceed to graph both the primitive function and the transformed function with a graphing tool. Please notice that the primitive function is the red curve.

The statement presents typing mistakes. Correct form is shown below:

Show a graph for the following: f(x) = 3 · x².

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∠4  angle is complementary to ∠5.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Two angles are called complementary if their measures add to 90 degrees,

∠5+∠4=90 degrees.

Angle 5 is added with angle 4 to make 90 degrees.

Hence, ∠4  angle is complementary to ∠5.

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Answer:

21

Step-by-step explanation:

x2 + 3.4y, when x = 2, y = 5

(2)2+3.4(5)

2×2+3.4×5

4+5×3.4

4+17

21

Hope it helps! :)

Answer:

30 Degrees for sure

Answer:

D. The statement is false. Double blinding is used to decrease the placebo effect.

Step-by-step explanation:

In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.

Therefore, a​ double-blind experiment is used to decrease the placebo effect.

The z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

The mean of the set of data is equal to the sum of all the quantities in the data, and divide by the no of quantities.

Given:

The standard deviation, d = 182.56,

The mean, m = 265.95,

The observation value, X = 235.90

Calculate the z score by the following formula given below,

Z = (X - m) / d,

Here, Z is the Z score,

Z = 235.90 -  265.95 / 182.56

Z =  -0.165

Therefore, the z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

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The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

The length of an arc with a central angle Ф with circle radius (r) is given by:

Length of arc = (Ф/360) * 2πr

Given the length of arc as 115π/6 in and angle of 138°, hence:

Length of arc = (Ф/360) * 2πr

Substituting:

115π/6 = (138/360) * 2πr

r = 25 inches

The radius of the circle is 25 inches.

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Answer:

kok

Step-by-step explanation:

Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

Answer:

12000 rad/min

Step-by-step explanation:

One formula we can use here is that the linear speed is the same, and the linear speed is equal to the angular speed multiplied by the radius.

Therefore, 2400π rad/min* 35 cm = 7 cm* x, with x representing the angular speed of the smaller wheel in radians per minutes. Dividing both sides by 7 cm, we get

2400π rad/min * 35 cm / 7 cm = x

2400 π rad/min * 5 = 12000 rad/min = x as our answer

Based on the figures given in the table, the rate of change of the function is b. 5.

This can be found as:

= (Y₂ - Y₁) / (X₂ - X₁)

Use points:

(0, 1/2) and (1, 5/2)

Solving gives:

= (5/2 - 1/2) / (1 - 0)

= 5

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Answer:

Solve the equation for y by finding a, b, and c

of the quadratic then applying the quadratic formula.

Exact Form:

y = 3,−9/2

Decimal Form:

y = 3,−4.5

Mixed Number Form:

y = 3,− 4 1/2

Step-by-step explanation:

branliest pls

Answer:

It's is 3/2

Step-by-step explanation:

since the line is going up, the rise/run is going to be positive

Answer:

1.5/2

Step-by-step explanation:

slope formula = y2-y1/ x2 - x1

point one (2,0)

point 2 (0, 1.5)

you dont really need to subtract anything because the intercepts, so the slope is 1.5/2

(slope or m = 1.5 - 0 / 2 - 0 )

x intercept = value of x when y is 0

y intercept = value of y when x is 0

Answer:

Second and third answer

Step-by-step explanation:

Correct :

Second : 30,31,32

this is because it makes it GREATER than 10 and we are looking for equal or greater than 10.

Third : 30 , 29 , 28

Again same reason

Wrong :

First : 0

This is wrong because it would plug in as (0)(6) + 5 ≥10

solve it :

0*6 = 0 so

0+5 ≥10 , so i tis wrong

Last option : -30,-29,-28

This is because multiplying negative with positive number woulf get a negative number. And the adding 5 would make it greater but wont be enough to change it to a positive number equal to or greater than 10.