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Mathematics

1 answer:

IrinaK [193]3 years ago

6 0

The volume is 32.4
get the circumference and divide by pi which is 3.1415926535897932384626

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Is the square root of 19 rational

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The local library has a childern section with pictures books and chapter books the ratio is 2:3 id thete are a total of 500 book

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Katherine has 4 red pens, 6 blue pens, and 11 black pens in her book bag. If she randomly pulls out one pen, what is the probabi

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Answer: 52.38%

Step-by-step explanation:

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What are the period and phase shift for f(x) = 3 tan(4x + π)?

Y_Kistochka [10]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\
% function transformations for trigonometric functions
\begin{array}{rllll}
% left side templates
f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\

\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks}\\
\quad \textit{horizontally by amplitude } |{{ A}}|\\\\
\bullet \textit{ horizontal or "phase" shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{function period}\\
\qquad \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\
\qquad \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)
\end{array}$

now.. with that template above in mind, let's see yours

$\bf \begin{array}{lllllll}
f(x)=&3tan(&4x+&\pi )\\
f(x)=&3tan(&4x+&1\pi )&+0\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

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3 years ago