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BaLLatris [955]
2 years ago
15

Graph the inequality on the axes below. y < - 2/3 x - 1

Mathematics
1 answer:
Colt1911 [192]2 years ago
5 0
You would start graphing with the y intercept which is -1 you then graph the slope -2/3x you want to start from -1 and then count 2 squares down and three across the get the next point. To get point the other direction you count two up and three left. It should look something like this when your done
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In the derivation of Newton’s method, to determine the formula for xi+1, the function f(x) is approximated using a first-order T
dimaraw [331]

Answer:

Part A.

Let f(x) = 0;

suppose x= a+h

such that f(x) =f(a+h) = 0

By second order Taylor approximation, we get

f(a) + hf'±(a) + \frac{h^{2} }{2!}f''(a) = 0

h = \frac{-f'(a) }{f''(a)} ± \frac{\sqrt[]{(f'(a))^{2}-2f(a)f''(a) } }{f''(a)}

So, we get the succeeding equation for Newton's method as

x_{i+1} = x_{i} + \frac{1}{f''x_{i}}  [-f'(x_{i}) ± \sqrt{f(x_{i})^{2}-2fx_{i}f''x_{i} } ]

Part B.

It is evident that Newton's method fails in two cases, as:

1.  if f''(x) = 0

2. if f'(x)² is less than 2f(x)f''(x)    

Part C.

In case  x_{i+1} is close to x_{i}, the choice that shouldbe made instead of ± in part A is:

f'(x) = \sqrt{f'(x)^{2} - 2f(x)f''(x)}  ⇔ x_{i+1} = x_{i}

Part D.

As given x_{i+1} = x_{i} = h

or                 h = x_{i+1} - x_{i}

We get,

f(a) + hf'(a) +(h²/2)f''(a) = 0

or h² = -hf(a)/f'(a)

Also,             (x_{i+1}-x_{i})² = -(x_{i+1}-x_{i})(f(x_{i})/f'(x_{i}))

So,                f(a) + hf'(a) - (f''(a)/2)(hf(a)/f'(a)) = 0

It becomes   h = -f(a)/f'(a) + (h/2)[f''(a)f(a)/(f(a))²]

Also,             x_{i+1} = x_{i} -f(x_{i})/f'(x_{i}) + [(x_{i+1} - x_{i})f''(x_{i})f(x_{i})]/[2(f'(x_{i}))²]

6 0
3 years ago
Find the total surface area of the rectangular prism 7.1 2.8 3.2
krek1111 [17]

lol

Step-by-step explanation:

5 0
2 years ago
A triangle has side lengths of x, x+11, and 3x+5.
horrorfan [7]

Answer:

The answer is 5X+16

Step-by-step explanation:

The formula for perimeter of a triangle is a+b+c.

meaning we are adding up everything.

That is

(x)+(x+11)+(3x+5).

collect like terms.

and u end up getting

5x+16

3 0
3 years ago
What is 19/5 as mixed number
icang [17]
3 4/5 because if 5 only goes into 19 3 times and then there is 4/5 left
6 0
3 years ago
Read 2 more answers
How do you collect like terms
pentagon [3]
Add them together 
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= 11a+13

6 0
3 years ago
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