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Write the formula for Newton's method and use the given initial approximation to compute the approximations x_1 and x_2. f(x) = x^2 + 21, x_0 = -21 x_n + 1 = x_n - (x_n)^2 + 21/2(x_n) x_n + 1 = x_n - (x_n)^2 + 21 x_n + 1 = x_n - 2(x_n)/(x_n)^2 + 21 Use the given initial approximation to compute the approximations x_1 and x_2. x_1 = (Do not round until the final answer. Then round to six decimal places as needed.)

Answers

Answer 1

Answer:

Answer:

$x_(n+1) = x_(n) - (f(x_(n) ))/(f^(')(x_(n)))$

$x_(1) = -10$

$x_(2) = -3.95$

Step-by-step explanation:

Generally, the Newton-Raphson method can be used to find the solutions to polynomial equations of different orders. The formula for the solution is:

$x_(n+1) = x_(n) - (f(x_(n) ))/(f^(')(x_(n)))$

We are given that:

f(x) = $x^(2) + 21$ ; $x_(0) = -21$

$f^(') (x)$ = df(x)/dx = 2x

Therefore, using the formula for Newton-Raphson method to determine $x_(1)$ and $x_(2)$

$x_(1) = x_(0) - (f(x_(0) ))/(f^(')(x_(0)))$

$f(x_(0)) = x_(0) ^(2) + 21 = (-21)^(2) + 21 = 462$

$f^(')(x_(0)) = 2*(-21) = -42$

Therefore:

$x_(1) = -21 - (462)/(-42) = -21 + 11 = -10$

Similarly,

$x_(2) = x_(1) - (f(x_(1) ))/(f^(')(x_(1)))$

$f(x_(1)) = (-10)^(2) + 21 = 100+21 = 121$

$f^(')(x_(1)) = 2*(-10) = -20$

Therefore:

$x_(2) = -10 - (121)/(20) = -10+6.05 = -3.95$

Related Questions

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A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
This is so easy but i can find this in the internet but what i wanna know is what goes in the Missing blank 50 take away ? equals 20

Seventy percent of light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have an emergency locator. Suppose that a light aircraft has disappeared.a) If it has an emergency locator, what is the probability that it will not be discovered?b) If it does not have an emergency locator, what is the probability that it will be discovered?c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

Answers

Answer:

Figure out the various probabilities first, that will make the rest of the questions easier:

P(discovered) = .7

P(not discovered) = 1 - .7 = .3

P(locator|discovered) = .6

P(no locator|discovered) = 1 - .6 = .4

P(locator|not discovered) = 1 - .9 = .1

P(no locator|not discovered) = .9

P(discovered and locator) = .7 * .6 = .42

P(discovered and no locator) = .7 * .4 = .28

P(not discovered and locator) = .3 * .1 = .03

P(not discovered and no locator) = .3 * .9 = .27

a) The total probability that an aircraft has a locator is .42 + .03 = .45. So the probability it will not be discovered, given it has a locator, is .03/.45 = .067

b) The total probability that an aircraft does not have a locator is .28 + .27 = .55. So the probability it will be discovered, given it does not have a locator, is .28/.55 = .509

c) Probability that 7 are discovered = C(10,7) * P(discovered|locator)^7 * P(not discovered|locator)^3

We already figured out P(not discovered|locator) = .067, so P(discovered|locator) = 1-.067 = .933. C(10,7) = 10*9*8, so we can compute total probability: 10*9*8 * .933^7 * .067^3 = .133

Step-by-step explanation:

Please solve for x. Show the process (steps).
4x = 40

Answers

Answer:

x = 10

Step-by-step explanation:

4x = 40

you divide both sides by 4

and it gets you

x = 10

hope this helps

Answer:

x=10

Step-by-step explanation:

lets reverse engineer this. 4x=40. What is known in this? We know 40 is the unit amount of 4x. So we need to find out what x is, than multiply it by 4. We can do this by doing the opposite of multiplying, which is dividing! So we divide 4 by 40, which we get the answer 10! We know this is the correct answer because we can factor it into the equation. So 4*10=40!!! hope this helped!!!

6.2.Find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it that passes through the origin

Answers

First.

We need to find the triangle bounded by the y-axis the line $f(x)=9-(6)/(7)x$ and the line perpendicular to it that passes through the origin.

This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:

The y-axis has been identified by the green line.
The line $f(x)=9-(6)/(7)x$ has been identified by the red line.
To plot the line perpendicular to the previous one that passes through the origin, we need to know that the product of the slopes of two perpendicular lines is $m_(1)m_(2)=-1 \therefore Since \ m_(1)=-(6)/(7) \ then \ m_(2)=(7)/(6)$

Therefore, this line is the blue one and is written as:

$f(x)=(7)/(6)x$

Second.

a.

To find $y(t)$ we need to find the slope and y-intercept. So, taking two points:

$P_(1)(15,150) \ and \ P_(2)(25,450) \n \nm=(450-150)/(25-15)=30$

So:

$Using \ P_(1)(15,150) \n\ny=30t+b\n\n150=30(15)+b \therefore b=-300 \n\n\boxed{y(t)=30t-300}$

Third.

b.

The y-intercept is $b=-300$ and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.

Fourth.

c.

The x-intercept can be found when y=0 (year 1980), that is:

$y(t)=30t-300 \n\n0=30t-300 \therefore t=10$

This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.

Fifth.

d.

The slope of this function is $m=30$

This value tells you that the profit increases $30.000 each year.

Hello,

Please, see the attached files.

Thanks.

4 in.7 in18 in.4 in.The surface area of the rectangular prism issquare inches.The volume of the rectangular prism isy cubic inches.

Answers

We have been given a rectangular prism and we are required to find its surface area and volume.

We shall solve this question by first stating the formula of the parameter we want to find, then, we apply the respective formulas to find the values of these parameters.

Surface area:

The surface area is the sum total of all the areas of all the faces of the prism.

To solve this question, we need to note that there are 6 faces whose area we must calculate but out of the 6, there are two faces

each that are equal in area.

From the above figure, we have that:

FACE 1 = FACE 2

FACE 3 = FACE 4

FACE 5 = FACE 6.

Thus, once we find the area of FACE 1, we already have the area of FACE 2 and so on.

Also, since each face is a rectangle, the area of a rectangle is given by:

$\begin{gathered} A=l* b \n l=\text{length} \n b=\text{breadth or width} \end{gathered}$

Now, let us calculate the area of FACE 1, 3 and 5.

$\begin{gathered} \text{FACE 1:} \n A_1=18*4=72in^2 \n \text{FACE 3:} \n A_3=4*7=28in^2 \n \text{FACE 5:} \n A_5=18*7=126in^2 \end{gathered}$

Now we just sum up all the areas and multiply them by two to account for FACES 2, 4 and 6

$\begin{gathered} A_S=2*(72+28+126) \n \therefore A_S=452in^2\text{ } \end{gathered}$

Therefore, the Surface area of the rectangular prism is:

452 square inches

Volume:

The formula for the volume of a rectangular prism is given as:

$\begin{gathered} V=l* w* h \n l=\text{length} \n w=\text{width or breadth} \n h=\text{height or depth} \end{gathered}$

The length, width, and height are shown in the figure below:

Thus, we can easily calculate our volume as shown below:

$\begin{gathered} V=7*18*4in^3 \n \therefore V=504in^3 \end{gathered}$

Therefore, the Volume of the rectangular prism is:

V = 504 cubic inches

To recap, the final answers are:

Surface Area = 452 square inches

Volume = 504 cubic inches

The radius of a circle is 2.6 in. Find the circumference
to the nearest tenth.

Answers

Answer:

16.

Step-by-step explanation:

since given the radius and the formula of the circumference of a circle is 2pie*r

4x+10y=-20 into slope-intercept

Answers

y = -2/5x - 2

Hope this helps (:

10y=-20-4x
y=-20/10 -4x/10
y=-2-2x/5
y=-2x/5-2

ANSWER:
y=-2x/5-2

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NEED HELP ASAP OR I WILL FAIL