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BigorU [14]
2 years ago
7

The diameter of a circle is 19 inches. If the diameter is extended 5 inches beyond the circle to point C, how long is the tangen

t segment from point C to the circle? Use the figure below to help guide your response. Explain your answer and show all work.

Mathematics
2 answers:
Anna [14]2 years ago
6 0
The tangent segment from point C is 5 inches from the circle
zysi [14]2 years ago
6 0

Answer:

Exact Length = 2*sqrt(30)

Approximate Length = 10.95445

======================================================

Work Shown:

(tangent)^2 = (external secant)*(whole secant)

(CD)^2 = (CB)*(CA)

(CD)^2 = (CB)*(CB+BA)

x^2 = 5*(5+19)

x^2 = 120

x = sqrt(120)

x = sqrt(4*30)

x = sqrt(4)*sqrt(30)

x = 2*sqrt(30)  .......... exact length

x = 10.95445 ............. approximate length

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y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence
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Let

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Substitute these into the given differential equation:

\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0

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a_{n=2k} = \dfrac{a_0}{(2k)!}

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

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\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}

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