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


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Write 8×8×8×8×8 as power ​

Answers

Answer:

\boxed{\sf \ \ \ 8^5 \ \ \ }

Step-by-step explanation:

Hello,

8*8*8*8*8 =8^5

because we use five time 8 in the multiplication

hope this helps

Your answer would be 8^5, (8 to the power of 5) the reason behind the five is because we see the 8 being multiplied about 5 times

Heres a list of numbers 3 6 9 7 4 6 7 0 7 Find median,mean,range and mode

Answers

The median, mean, range and mode will be 6, 5.4, 9 and 7.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

Read related link on:

brainly.com/question/9426296

Answer:

median=order them and find the middle=6

mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4

range= the difference between the smallest and largest number=9-3=6

mode= the one that appears the most= 7

Jenny wants to share some stickers with her friends. If she gives each of her friends three stickers, she will have eight stickers left. If she gives each of her friends four stickers, she will need two stickers more. How many stickers does Jenny have?

Answers

how many friends does she have

Answer:

It depends how many friends there are

Step-by-step explanation:

HELP PLEZ TRIGONOMETRY!

Answers

(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha

Solution:

Given that we have to simplify:

(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) ---- eqn 1

We know that,

sin^2 x = 1 - cos^2 x

Substitute the above identity in eqn 1

(2\left(1-\cos ^(2) \alpha\right)-1)/(\sin \alpha+\cos \alpha)

Simplify the above expression

(2-2 \cos ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)

(1-2 \cos ^(2) \alpha)/(\sin \alpha+\cos \alpha) ------- eqn 2

By the trignometric identity,

(sin x + cos x)(sin x - cos x) = 1-2cos^2 x

Substitute the above identity in eqn 2

((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)

Cancel the common factors in numerator and denominator

((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)=\sin \alpha-\cos \alpha

Thus the simplified expression is:

(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha

6 X 9 =
6 X (5 + 4)
6 X 9 = (6 X 5) + (6 X 4)
6 X 9 =
6 X 9 =
54

Answers

You gave us the answer it will be 54.

Answer:

54

Step-by-step explanation:

9(6)=54

6(9)=54

54=(30)+(24)  54=54 so it is true

9x6=54

16+10/5-3*2=12 true or false.

Answers

We need to follow the order of operations to get this one right. 
16 + (10/5) - (3*2)
16 + (2) - (6)
16 + 2 - 6
18 - 6
12Your answer is true!