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3 years ago

What’s 1/100000 as a fraction

Mathematics

2 answers:

Ket [755]3 years ago

8 0

That is a fraction... Do you mean as a decimal?<span />

Rzqust [24]3 years ago

4 0

It is 1/100000 you can not simply this so it’s 1/100000

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Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=

luda_lava [24]

Let $f(x) = x^3 - 2x - 2$ . Then differentiating, we get

$f'(x) = 3x^2 - 2$

We approximate $f(x)$ at $x_1=2$ with the tangent line,

$f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18$

The $x$ -intercept for this approximation will be our next approximation for the root,

$10x - 18 = 0 \implies x_2 = \dfrac95$

Repeat this process. Approximate $f(x)$ at $x_2 = \frac95$ .

$f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}$

Then

$\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}$

Once more. Approximate $f(x)$ at $x_3$ .

$f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}$

Then

$\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}$

Compare this to the actual root of $f(x)$ , which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

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2 years ago

Toni can carry up to 16 lb in her backpack. Her lunch weighs 1 lb, her gym clothes weigh 3 lb, and her books (b) weigh 3 lb each

Romashka-Z-Leto [24]

Answer:

4 Books

Step-by-step explanation:

3+1 = 4

16 - 4 = 12

3x4 = 12

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3 years ago

The quotient of 6 times a number and 16

alexandr1967 [171]

6x=16
÷6 both sides
x=16/6 or 8/3

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