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3 years ago

Write the equation of a line in slope intercept form using the given information.

Mathematics

1 answer:

Hitman42 [59]3 years ago

5 0

Answer:

y=2x+4

Step-by-step explanation:

Slope intercept form:

y=mx+b where m is the slope of the line and b the y-coordinate of the y-intercept

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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 1.769292354, matching up to the first 5 digits after the decimal place.

4 0

1 year ago

Which is the graph of F(x)= (x+3)(x-2)

KonstantinChe [14]

Answer:

Vertex: (-1/2, -25/4)

Focus: (-1/2, -6)

Axis of Symmetry: x=-1/2

Directrix: y=-13/2

Step-by-step explanation:

x = -2, -1, -1/2, 1, 2

y = -4, -6, -25/4, -4, 0

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2 years ago

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Matematyka. Zad.7 str.24 ćw 5kl Proszę szybko o odp. Na zadanie 7 ze strony 27 w ćwiczeniach dla 5 klasy

marishachu [46]

Answer:

Iikij

Step-by-step explanation:

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2 years ago

Ble. 6 co 10 square units

Vlada [557]

Answer:

1/2×10×6=30

Step-by-step explanation:

H=6

L=10

therefore;

1/2×6×10=30

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2 years ago

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GenaCL600 [577]

Answer:

What is the question? there is only statement.

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2 years ago