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3 years ago

The following points for a function are graphed in the coordinate plane: (1, 2), (3, 8), (4, 11), and (6, 17).

Mathematics

1 answer:

aleksley [76]3 years ago

4 0

Answer: y=2x
I upload I picture of showing my work. Hope this help you.

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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

Can someone help me answer questions

ANEK [815]

Add 6 to both sides
2m2+7m+6=0

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3 years ago

Write exponent and bases of (-5)raise to power7 and (-9/7)raise to power6

AleksAgata [21]

Answer:

The base of -5 raise to 7 is -5 and its exponent is 7. The base-9/7 raise to the power of 6 is -9/7 and it's exponent is 6.

Step-by-step explanation:

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3 years ago

How many solutions does the equation below have?

Elina [12.6K]

Answer:

1.one solution is the answer

Step-by-step explanation:

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2 years ago

Pls help me i dont get it :(

ValentinkaMS [17]

Answer:

7.alternate interior

x=64

8. same side interior

x=12

same side exterior

x=12

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3 years ago

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