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4 years ago

How to write a square root as an exponent?

Mathematics

2 answers:

Doss [256]4 years ago

8 0

$\sqrt{x} = x^{\frac{1}{2}}$

A more general form is:
$\sqrt[a]{x^{b}} = x^{\frac{b}{a}}$

Nikolay [14]4 years ago

6 0

Hello :
a square root is : √a a ≥ 0
as an exponent : a ^(0.5)

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Next four multiple of the fraction 3/5

OleMash [197]

6/10, 9/15, 12/20, 15/25

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3 years ago

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A store offers a 30% discount on a coat that originally sold for $120. The coat still does not sell, so the store offers another

Romashka [77]

Answer:

Step-by-step explanation:

120 *.3 = 36

120-36 = 84

84*.3 = 25.2

84-25.2= 59.8

120*.6 = 72

120-72 = 48

59.8-48 = 10.8 C

7 0

3 years ago

Six times a certain number increased by 10 is four times the same number

drek231 [11]

Answer:

x = -5

Step-by-step explanation:

6x + 10 = 4x

2x = -10

x = -5

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3 years ago

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Pleaseeeeee help with this question and explain it out pleaseeeee

marissa [1.9K]

Answer:

I don't have an image to show you, but I can explain where to put it

Step-by-step explanation:

A) Draw PQR Upside down, but in the top right corner.

B) Draw PQR in the bottom right corner.

It's a bit confusing, but it's the best I can do, ask questions if you need more explanation please :)

3 0

3 years ago

Given cos(4x)+2 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

4 years ago