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tatiyna
3 years ago
5

Find the missing length indicated?

Mathematics
1 answer:
kondor19780726 [428]3 years ago
6 0

Answer:

D. 15

Step-by-step explanation:

Let the missing length be represented as x.

Thus:

(24 - x)/12 = x/20 => angle bisector theorem

Cross multiply

20(24 - x) = x(12)

480 - 20x = 12x

480 - 20x + 20x = 12x + 20x

480 = 32x

480/32 = 32x/32

15 = x

Missing length = x = 15

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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=
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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}

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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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