3 - 6 = -3
Plug -3 in: $-\frac{12}{-3} + (-1)^{3}$
Simplify the fraction. Two negatives equal a positive. It should now look like this: $\frac{12}{3} + (-1)^{3}$
Simplify even more. Divide 12 by 3, and change -1 to a positive by removing the plug sign: $4 - 1^{3}$
$1^{3} = 1$
Plug 1 in: 4 - 1
4 - 1 = 3

I hope this helps!

6 0

3 years ago

A function is given. Determine the average rate of change of the function between the given values of the variable: f(x)= 4x^2;

nevsk [136]

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------$

$\bf f(x)= 4x^2 \qquad 
\begin{cases}
x_1=3\\
x_2=3+h
\end{cases}\implies \cfrac{f(3+h)-f(3)}{(3+h)~-~(3)}
\\\\\\
\cfrac{[4(3+h)^2]~~-~~[4(3)^2]}{\underline{3}+h-\underline{3}}\implies \cfrac{4(3^2+6h+h^2)~~-~~4(9)}{h}
\\\\\\
\cfrac{4(9+6h+h^2)~~-~~36}{h}\implies \cfrac{\underline{36}+24h+4h^2~~\underline{-~~36}}{h}
\\\\\\
\cfrac{24h+4h^2}{h}\implies \cfrac{\underline{h}(24+4h)}{\underline{h}}\implies 24+4h$

8 0

4 years ago

Henry rented a truck for one day. There was a base fee of $14.95, and an additional charge of 73 cents for each mile driven. Hen

Art [367]

$(145.62 - 14.95) \div 0.73 = miles \: driven \\ n$
I haven't done many of these, but I hope this helps.

7 0

4 years ago

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