Convert 6.1212 into a rarional number

1 answer:

3 0

in short, we will start off by making the left-side of the dot and the recurring numbers a variable, say "x", then multiplying it by some power of 10 that moves the recurring numbers over to the left, let's do so

$\bf x = 6.\overline{12}~\hspace{10em} \begin{array}{llll} 100\cdot x&=&612.\overline{12}\\\\ &&606+6.\overline{12}\\\\ &&606+x \end{array} \\\\\\ 100x=606+x\implies 99x=606\implies x = \cfrac{606}{99}\implies x = \cfrac{202}{33}\implies x = 6\frac{4}{33}$

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(see attached)

A. We can see from the graph that the possible x-values are -∞ ≤ x ≤ +∞ . Hence limiting to domain to x≤ -2 this is obviously not true.

B. We can see from the graph that the vertex is y = 6 and that the entirety of the graph is under this point, hence range y<6 is true

C. We can see that the vertex is located at x=-2. Every part of the graph to the left of this point has a positive slope, hence the function is increasing for negative infinity to this point x=-2 is true

D) We can see that for the interval -4<x<∞, the graph actually increases between -4<x<-2, and then decreases after that. Hence this statement is not true.

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