Why is a mixed number a rational number

2 answers:

5 0

Any number that can be rewritten as a simple fraction is arational number. This means that natural numbers, wholenumbers and integers, like 5, are all part of the set ofrational numbers as well because they can be written as fractions, as are mixed numbers like 1 ½.

NeX [460]3 years ago

5 0

A mixed number is a rational number because you still say it the same way as every other rational number and because it can be written like a fraction and with :.

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

\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks}\\
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\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
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\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\
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\end{array}$

now.. hmmm let's see, keeping in mind the template above

so, amplitude of 2, A=2, thus |A| = ±2, so, you can use either

and period of 4π, well, that simply means that

$\bf \cfrac{2\pi }{B}=4\pi \implies \cfrac{2\pi }{4\pi }=B\implies \cfrac{1}{2}=B\\\\
-----------------------------\\\\

\begin{array}{llll}
f(\theta)=&\pm 2cos&\left(\frac{1}{2}\theta \right)\\
&\ \uparrow &\ \uparrow \\
&A&B
\end{array}$

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