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nordsb [41]
3 years ago
5

Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two successive approximations diff

er by less than 0.001. Then find the zero(s) to three decimal places using a graphing utility and compare the results. f(x) = x5 + x − 6
Mathematics
1 answer:
liubo4ka [24]3 years ago
5 0

Answer:

There is only one real zero and it is located at x = 1.359

Step-by-step explanation:

After the 4th iteration the solution was repeating the first 3 decimal places.  The formula for Newton's Method is

x_{n}-\frac{f(x_{n}) }{f'(x_{n}) }

If our function is

f(x)=x^5+x-6

then the first derivative is

f'(x)=5x^4+1

I graphed this on my calculator to see where the zero(s) looked like they might be, and saw there was only one real one, somewhere between 1 and 2.  I started with my first guess being x = 1.

When I plugged in a 1 for x, I got a zero of 5/3.  

Plugging in 5/3 and completing the process again gave me 997/687

Plugging in 997/687 and completing the process again gave me 1.36976

Plugging in 1.36976 and completing the process again gave me 1.359454

Plugging in 1.359454 and completing the process again gave me 1.359304

Since we are looking for accuracy to 3 decimal places, there was no need to go further.

Checking the zeros on the calculator graphing program gave me a zero of 1.3593041 which is exactly the same as my 5th iteration!

Newton's Method is absolutely amazing!!!

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Geometry Help I can't figure this out and it's stressing me out
stiv31 [10]

Answer:

Reason 3: Definition of sine.

Reason 4: Multiplication property of equality

Reason 6: Division property of equality

5 0
3 years ago
Find the equation of a line that is perpendicular to line g that contains (P, Q). coordinate plane with line g that passes throu
maw [93]

Answer:

y - Q =  -  \frac{1}{4}(x - P)

Step-by-step explanation:

Line g passes through (-2,6) and (-3,2).

The slope of line g is given by:

\frac{ y_2-y_1}{x_2-x_1}

Let's substitute the values to get:

\frac{2 - 6}{ - 3 -  - 2}= \frac{ - 4}{ - 1}  = 4

The equation that is perpendicular to line g will have a slope that is the negative reciprocal of 4.

i.e -1/4

If this line passes through (P,Q), then the equation is:

y - Q =  - \frac{1}{4} (x - P)

7 0
2 years ago
Select all sets of lengths that would form a right triangle.
VARVARA [1.3K]

Answer:

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Step-by-step explanation:

3 0
2 years ago
HELP THIS IS DUE TODAY!!!!!! AHHHHHH
belka [17]

Answer:

260 / 5 = 52

Step-by-step explanation:

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8 0
3 years ago
. Ralph’s Fill Dirt and Croissant Shop in Spencer makes both grand and petit croissants. Each grand requires 1 ounce of flour an
Gwar [14]

Answer:

1

Step-by-step explanation:

let G be the number of grand croisssants, and P the number of petit croissants :

we have that 1 ounce of flour and 2 ounces of butter result in one G.

additionally, we have that 1/4 ounce of flour and 1/3 ounce of butter result in one P.

Ralph has 4 ounces of flour and 6 ounces of butter, If he bakes more than 1 G then he will never use all of his ingredients!, let's see:

1 G:

he now has 3 ounces of flour, and 4 ounces of butter,

now we need to figure out how many P's we would obtain with such amounts:

let x be the number of P's

1/4*x = 3=>x=12\\ 1/3*x=4=>x=12

which is reasonable, Ralph can bake 12 P's,

now with more than 1 G:

2G:

Ralph has now 2 ounces of flour and 2 ounces of butter, now we have to figure out that x is the same using the remaining ingredients

1/4*x = 2=>x=8\\ 1/3*x=2=>x=6

This is impossible.

3G:

he runs out of butter.

There is the answer, he is able to bake 1 grand croissant and 12 petit croissants

7 0
3 years ago
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