$\bf ~\hspace{7em}\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
~\hspace{4.5em}
a^n\implies \cfrac{1}{a^{-n}}
~\hspace{4.5em}
\cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
(6^3)^{-3}\implies 6^{-3\cdot 3}\implies 6^{-9}\implies \cfrac{1}{6^9}\implies \cfrac{1}{10077696}$

3 0

3 years ago

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The times for three swimmers are 101.85 seconds, 101.6 seconds, and 59.625 seconds. Which is the winning time? how many seconds

bija089 [108]

Hello there! the winning time is 59.625 seconds.

This is the person who completed the lowest amount of time, meaning they finished first. The others too longer so they finished later, meaning they didn't win.

I hope this was helpful and have a great day! :)

3 0

3 years ago

f(x) = 500(1.05)x What was the average rate of change of the value of Sophia's investment from the second year to the fourth yea

hjlf

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\
f(x)=500(1.05)^x \qquad 
\begin{cases}
x_1=2\\
x_2=4
\end{cases}\implies \cfrac{f(4)-f(2)}{4-2}
\\\\\\
\cfrac{[500(1.05)^4]~-~[500(1.05)^2]}{4-2}\implies \cfrac{56.503125}{2}\implies 28.2515625$

6 0

4 years ago