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castortr0y [4]
1 year ago
13

Simplify each expression by writing the expression without absolute value bars.

Mathematics
1 answer:
sertanlavr [38]1 year ago
6 0

The expression of absolute value |m-11| id m is greater than equal 11 will be equivalent to (m-11).

The general function of absolute value is given as,

                  |a| = { a  ,  if  a≥0     and    -a    , if a<0 }

That is the absolute value will be positive if value of is greater than or equal to 0 and the absolute value will be negative if the value of a is less than 0.

As we have been given the absolute value which is | m – 11|. It can be formed as

             |m-11| = {   (m-11)   ,  if m≥11     and      -(m-11)    ,  if m<11}

So according to the question given the value of m is greater than equal to 11 that is m≥11.

Therefore,  when m≥11 then

                           |m-11| =  (m-11).

Hence if m is greater than equal to 11 then the expression |m-11| will be equivalent to (m-11).

Learn more about absolute value here : brainly.com/question/12928519

#SPJ9

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<h3>1)</h3>

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<h3>2)</h3>

\text{Given that,}~\\\\f(x) = \dfrac{1}{3x-2}\\\\\textbf{Power rule:}\\\\\dfrac{d}{dx}(x^n) = nx^{n-1}\\\\\textbf{Chain rule:}\\\\\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}\\\\\text{Now,}\\\\f'(x) = \dfrac{d}{dx} f(x)\\\\\\~~~~~~~~=\dfrac{d}{dx} \left( \dfrac 1{3x-2} \right)\\\\\\~~~~~~~~=\dfrac{d}{dx} (3x-2)^{-1}\\\\\\~~~~~~~~=-(3x-2)^{-1-1} \cdot \dfrac{d}{dx}(3x-2)\\\\\\~~~~~~~~=-(3x-2)^{-2} \cdot 3\\\\\\~~~~~~~~=-\dfrac{3}{(3x-2)^2}

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