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3 years ago

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Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your ans

wers to four decimal places.) f(x) = cos x, x1 = 0.7

1 answer:

VikaD [51]3 years ago

4 0

Answer:

The two iterations of f(x) = 1.5598

Step-by-step explanation:

If we apply Newton's iterations method, we get a new guess of a zero of a function, f(x), xₙ₊₁, using a previous guess of, xₙ.

xₙ₊₁ = xₙ - f(xₙ) / f'(xₙ)

Given;

f(xₙ) = cos x, then f'(xₙ) = - sin x

cos x / - sin x = -cot x

substitute in "-cot x" into the equation

xₙ₊₁ = xₙ - (- cot x)

xₙ₊₁ = xₙ + cot x

x₁ = 0.7

first iteration

x₂ = 0.7 + cot (0.7)

x₂ = 0.7 + 1.18724

x₂ = 1.88724

second iteration

x₃ = 1.88724 + cot (1.88724)

x₃ = 1.88724 - 0.32744

x₃ = 1.5598

To four decimal places = 1.5598

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aev [14]

We are given:

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Now, we can add x to both sides, and subtract 8 from both sides to isolate the variable.

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We end up with:

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By dividing both sides by 9, we get x = $-\frac{1}{3}$ .

If you want to check your answer, just plug x in!

2( $-\frac{1}{3}$ ) + 5 - 3( $-\frac{1}{3}$ ) = 8( $-\frac{1}{3}$ + 1)

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$-\frac{2}{3}$ + $\frac{18}{3}$ = $-\frac{8}{3}$ + $\frac{24}{3}$

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3 years ago

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The U.S- based motorcycle manufacturer says that it expects to build 146,000 motorcycles this year , up from 128,000 last year .

beks73 [17]

Answer:

14.06%

Step-by-step explanation:

Here we are asked to find the percent increase in the production of the motorcycle for US based manufacturer.

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Total increased production = 146,000-128,000

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Hence percentage calculation = $\frac{\ increase \ in \ sale}{\ last \ year \ sale} \times 100$ %

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3 years ago

Paige and Natalie have the same ratio of green marbles in their bags of marbles. Paige has 4 green marbles and 16 total marbles.

laiz [17]

<h2><u>Answer:</u></h2>

Natalie has a total of <u>40 marbles.</u>

<u />

<h2><u>Step-by-step explanation:</u></h2>

If 4 of Paiges' marbles are green, then we would write this as the ratio

<u>4:16</u>, or <u>1:4</u>

This means that for every green marble she has, she has 4 total marbles

Therefore, if Natalie has 10 green marbles, we would multiply this by 4 to get a total of <u>40 marbles.</u>

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3 years ago

What is 0.25% of K2 000?

goldfiish [28.3K]

$\huge\text{Hey there!}$

$\large\text{When you hear/see the word of in mathematics, it usually means }\\\large\text{\bf multiplication. }$

$\large\text{So, when you think of think of the word \underline{of} think of its asking you to}\\\large\text{\bf multiply }$

$\large\text{Now that we got that run down out of the way lets answer your given}\\\large\text{question}$

$\large\textsf{0.25\% of 2,000}$

$\large\textsf{= 0.25\%} \times \large\textsf{2,000}$

$\large\textsf{0.25\%} = \mathsf{\bf \dfrac{25}{100}}$

$\mathsf{= \dfrac{25}{100} \times 2,000}$

$\mathsf{\dfrac{25}{100}= \bf 0.0025}$

$\large\textsf{= 0.0025} \times \large\textsf{2,000}$

$\large\text{= \bf 5}$

$\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf 5}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

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3 years ago

80% of _____ games is 32 games AND 75% of ____ peaches is 15 peaches

RoseWind [281]

Hi there!

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