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2 years ago

During which phase were no faults introduced?

Mathematics

1 answer:

dybincka [34]2 years ago

4 0

Step-by-step explanation:

phase 4 had no faults introduced

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Bobby decides to sell lemonade on a hot summer day. If Bobby sells 20 glasses of lemonade for $0.20 per cup, and his average tot

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Answer:

Bobby's economic profits for the day is $0.60.

Step-by-step explanation:

Bobby sells 20 glasses of lemonade for $0.20 per cup.

Amount earned = $20\times0.20=4$ dollars

The average total cost is $0.17.

So, difference in selling amount and average = $0.20-0.17=0.03$ dollars

Therefore, Bobby's economic profits for the day is = $20\times0.03=0.60$ dollars

Hence, the answer is $0.60.

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3 years ago

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NemiM [27]

Answer:

16x/5

Step-by-step explanation:

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Step-by-step explanation:

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2 years ago

Given cos(4x)+2<br><br> Find: Period, Shift, & Range

Yuki888 [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}}
\\\\
f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\
f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}}

\end{array}\qquad$

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

$\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 or frequency}\\
\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 in mind, let's see

$\bf \begin{array}{llccll}
cos(&4x&+0)&+2\\
&\uparrow &\uparrow &\uparrow \\
&B&C&D
\end{array} 
\\\\\\
period\qquad \cfrac{2\pi }{B}\implies \cfrac{2\pi }{4}\implies \cfrac{\pi }{2}
\\\\\\
\textit{horizontal/phase shift}\qquad \cfrac{C}{B}\implies \cfrac{0}{4}\implies 0\impliedby none
\\\\\\
\textit{vertical shift}\qquad D=+2\impliedby \textit{2 units up}$

now the range, how far up and down it goes on the y-axis

well, for the graph of cos(x), the range is, goes up to 1, down to -1, is all,

the midline is at 0

now, with a vertical shift of 2 upwards, it moves the midline by 2 units, used to be at 0, now is at y = 2, but the amplitude never changed, is goes up and down still one unit,

but with the midline at 2, goes up to 3 and down to 1, so the range is 3 ⩽ y ⩽ 1

4 0

3 years ago