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amorosoavap5cejz

12.07.2019 •

Mathematics

Explain how to write 20 miles/4hours as a unit rate

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Ответ:

andrew763

30.05.2020

To write this as a unit rate simply have the denominator equal 1. Or simply divide the 2 numbers together to find the unit rate.

Here it would be 5 miles/hour.

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Ответ:

jakeyywashere

13.12.2022

Iteration 1: $x_{2}=1.446$

Iteration 2: $x_{3}=1.337$

Step-by-step explanation:

Formula for Newton's method is,

$x_{n+1}=x_n-\dfrac{f\left(x_n\right)}{f'\left(x_n\right)}$

Given the initial guess as $x_{1}=1.6$ , therefore value of n = 1.

Also, $f\left(x\right)=x^{9}-9$ .

Differentiating with respect to x,

$\dfrac{d}{dx}\left(f\left(x\right)\right)=\frac{d}{dx}\left(x^9-9\right)$

Applying difference rule of derivative,

$\dfrac{d}{dx}\left(f\left(x\right)\right)=\dfrac{d}{dx}\left(x^9\right)-\dfrac{d}{dx}\left(9\right)$

Applying power rule and constant rule of derivative,

$\dfrac{d}{dx}\left(f\left(x\right)\right)=\left(9x^{9-1}\right)-0$

$\dfrac{d}{dx}\left(f\left(x\right)\right)=9x^{8}$

Substituting the value,

$x_{1+1}=x_1-\dfrac{f\left(x_1\right)}{f'\left(x_1\right)}$

$x_{2}=1.6-\dfrac{f\left(1.6\right)}{f'\left(1.6\right)}$

Calculating the value of $f\left(1.6\right)$ and $f'\left(1.6\right)$

Calculating $f\left(1.6\right)$

$f\left(1.6\right)=\left(1.6\right)^{9}-9$

$f\left(1.6\right)=59.71947674$

Calculating $f'\left(1.6\right)$ ,

$f'\left(1.6\right)=9\left(1.6\right)^{8}$

$f'\left(1.6\right)=386.5470566$

Substituting the value,

$x_{2}=1.6-\dfrac{59.71947674}{386.5470566}$

$x_{2}=1.446$

Therefore value after second iteration is $x_{2}=1.446$

Now use $x_{2}=1.446$ as the next value to calculate second iteration. Here n = 2

Therefore,

$x_{2+1}=x_2-\dfrac{f\left(x_2\right)}{f'\left(x_2\right)}$

$x_{3}=1.446-\dfrac{f\left(1.446\right)}{f'\left(1.446\right)}$

Calculating the value of $f\left(1.446\right)$ and $f'\left(1.446\right)$

Calculating $f\left(1.446\right)$

$f\left(1.446\right)=\left(1.446\right)^{9}-9$

$f\left(1.446\right)=18.63851065$

Calculating $f'\left(1.446\right)$ ,

$f\left(1.446\right)=9\left(1.446\right)^{8}$

$f\left(1.446\right)=172.0239252$

Substituting the value,

$x_{3}=1.446-\dfrac{18.63851065}{172.0239252}$

$x_{3}=1.337$

Therefore value after second iteration is $x_{3}=1.337$

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