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3 years ago

Find the measure of the missing angle.

Mathematics

1 answer:

Darina [25.2K]3 years ago

5 0

Answer:

The answer is

Step-by-step explanation:

Let the angle be x

Since the triangle is a right angled triangle we can use trigonometric ratios to find the value of x

To find the value of x we use cosine

$\cos( \theta) = \frac{adjacent}{hypotenuse}$

From the question

the adjacent is 13

the hypotenuse is 20

The angle is

$\cos(x) = \frac{13}{20} \\ x = \cos^{ - 1} ( \frac{13}{20} ) \\ x = 49.4583$

We have the final answer as

Hope this helps you

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4 years ago

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The Maclaurin series for ln(1+x) is given by

crimeas [40]

(a)

Replacing x with x/3 and then multiplying both sides by x

$\begin{aligned}
\ln(1+x) &= x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots + (-1)^{n+1} \frac{x^n}{n} + \cdots \\ \\
\ln\left(1 + \tfrac{x}{3}\right) &= \frac{x}{3} - \frac{x^2}{3^2 \cdot 2} + \frac{x^3}{3^3 \cdot 3} - \frac{x^4}{3^4 \cdot 4} + \cdots + (-1)^{n+1} \frac{x^n}{3^n \cdot n} \\ \\ 
x\ln\left(1 + \tfrac{x}{3}\right) &= \frac{x^2}{3} - \frac{x^3}{3^2 \cdot 2} + \frac{x^4}{3^3 \cdot 3} - \frac{x^5}{3^4 \cdot 4} + \cdots + (-1)^{n+1} \frac{x^{n+1}}{3^n \cdot n}
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The general term is

$\displaystyle(-1)^{n+1} \frac{x^{n+1}}{3^n \cdot n}$

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(b)

Due to the powers present in the general term, use the ratio test

$\displaystyle\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n}\right| = \lim_{n \to \infty} \left| \frac{ \frac{x^{n+2}}{3^{n+1}(n+1) } }{\frac{x^{n+1}}{3^n n} } \right| = \lim_{n\to\infty}\left|\frac{xn}{3n+3} \right| = \left|\frac{x}{n} \right| \ \textless \ 1$

The series converges on x ∈ (-3,3)
Determining the interval of convergence, test the endpoints

For x = -3, general term becomes

$\displaystyle \frac{(-1)^{n+1}(-3)^{n+1}}{3^n \cdot n} \\ \\
= \frac{(-1)^{n+1}(-1)^{n+1}(3)^{n+1}}{3^n \cdot n} \\ \\
= (-1)^{2n+2} \cdot \frac{3}{n}$

$(-1)^{2n+2} \implies 1 \text{ because $2n+2$ is all even}$

$\sum_{n=1}^{\infty} \frac{3}{n} \text{ diverges via harmonic series}$

Diverges at x = -3.

For x = -3, general term becomes

$\displaystyle \frac{(-1)^{n+1}3^{n+1}}{3^n \cdot n} = (-1)^{n+1} \frac{3}{n} \\ \\
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This is an alternate harmonic series, so it converges as the terms are decreasing in size (approaching zero as n approaches infinity)

The interval of convergence is

-3 < x ≤ 3

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(c)

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4 years ago

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miv72 [106K]

Answer:

B. 8:45

Step-by-step explanation:

One quarter of an hour is 15 minutes, meaning a quarter till nine is 15 minutes before nine, or 8:45.

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3 years ago

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Lapatulllka [165]

I believe the numbers are 19 and 38

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