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-BARSIC- [3]
3 years ago
15

between 1995 and 2006, the population of samburg, usa(in thousands) can be modeled by f(x) = 0.35x(squared) - 2.1x+15.8 where x=

0 represents 1995. Based on this model, in what year did the population of samburg reached it's minimum?
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
5 0
\bf f(x)=0.35x^2-2.1x+15.8\qquad 
\begin{cases}
x=\textit{year since 1995}\\
f(x)=\textit{population amount}
\end{cases}

the equation is a quadratic one, and it has a positive coefficient on the leading term, meaning, is opening upwards, so it has a "burrow" for the vertex.

the minimum or lowest point for a quadratic opening upwards is, well, the vertex point :),   the "x" value is the year, the "y" or f(x) value is the population, we're asked for the year, or the x-coordinate of the vertex

well   \bf \begin{array}{llll}
f(x)=&0.35x^2&-2.1x&+15.8\\
&\quad \uparrow &\quad \uparrow&\uparrow \\
&\quad  a&\quad  b &c
\end{array}
\\\\

\\\\
\qquad  \textit{vertex of a parabola}\\ \quad \\
\qquad 

\left(\boxed{-\cfrac{{{ b}}}{2{{ a}}}}\quad ,\quad  {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
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Step-by-step explanation:

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3 years ago
Sylvia worked 3 hours and 45 minutes, while Paul worked 4 hours and 35 minutes. What’s the ratio of Sylvia’s work time to Paul’s
alexira [117]
Answer: 9 / 11

That is approximately 0.82


Explanation:

The ratio of two quantities x and y is x divided by y, i.e. the quotient x / y.

So, the ratio of Sylia's work time to Paul's work time is:

Sylvia's work time
---------------------------
Paul's work time

Given that you have the times in mixed units, hours and minutes, you must convert to one of the, either hours or minutes.

If you choose to work with hours, this is the work:

1) Silvia's time: 3 hours and 45 minutes = 3 hours + 45 / 60 hours = 3hours + 0.75 hours = 3.75 hours

2) Paul's work time: 4 hours and 35 minutes = 4 hours + 35/60 hours = 4 hours + 7/12 hours = (48+7)/12 = 55/12 hours ≈ 4.58 hours

3) Ratio:

Sylvia's work time             3.75 hours            3.75*12         45          9
------------------------- =      --------------------- = ---------------- =  -------- =   -----
Paul's work time               (55/12) hours            55              55         11

≈ 0.82

You can calculate the ratio using minutes and shall obtain the same result. Look:

1) 3 hours + 45 minutes = 3 * 60  minutes + 45 minutes = 180 minutes + 45 minutes = 225 minutes

2) 4 hours + 35 minutes = 4*60 minutes + 35 minutes = 240 minutes + 35 minutes = 275 minutes

3)

225 minutes          9
----------------- =     ------, which is the same result obtained above.
275 minutes         11
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3 years ago
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