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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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A drop of oil makes a circular ring in a water puddle. The radius of the oil ring expands at 1.5 cm per second. If r(t)=1.5t and
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Answer:

a(t) =n(0.25t^2)

Step-by-step explanation:

Given

r(t) = 0.5t

a(r) = nr^2

Required

Determine the area in terms of time

From the question, we have:

r(t) = 0.5t -> radius per time

and

a(r) = nr^2 --> area from radius

The interpretation of the question is to find the composite function: a(t)

If a(r) = nr^2, and r(t) = 0.5t, the

Substitute 0.5t for r

a(t) =n(0.5t)^2

a(t) =n*0.25t^2

a(t) =n(0.25t^2)

5 0
2 years ago
10 - 9 x 5 + 6 x (-2)
olya-2409 [2.1K]

Answer:

The answer to your equation is -47.

Step-by-step explanation:

Follow the order of operations. First do 9*5=45, and 6*-2 to get -12. Next, just finish the equation from left to right to get -47.

5 0
3 years ago
Read 2 more answers
Last Sunday a certain store sold copies of 256 Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the stor
Marat540 [252]

Answer:

D. \frac{400p}{500-p}

Step-by-step explanation:

let's call A the number of copies sold of newspaper A and B the number of copies sold of newspaper B.

So, we can formulate the following equations from the sentence: a certain store sold copies of 256 Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each as:

A + B = 256                               (1)

1A + 1.25 B = Total Revenue    (2)

Then, r and p are equal to:

r=\frac{A}{Total Revenue}*100=\frac{100A}{A+1.25B}     (3)

p=\frac{A}{256} *100=\frac{100A}{256}                            (4)

Isolating A from (4) and B from (1), we get:

A=\frac{256p}{100} =2.56p                (5)

B=256-A=256-2.56p                         (6)

Finally, replacing (5) and (6) in (3), we get:

r=\frac{100A}{A+1.25B}=\frac{100(2.56p)}{2.56p+1.25(256-2.56p)}\\\\r=\frac{256p}{2.56p+320-3.2p}=\frac{256p}{320-0.64p}\\\\r=\frac{256p/0.64}{(320-0.64p)/0.64}=\frac{400p}{500-p}

7 0
3 years ago
1.
iogann1982 [59]
  1. Answer:  Step-by-step explanation: It is 9 1/2– 7 1/3=2 1/3 if that helped give a thumbs up thank you bye.
6 0
3 years ago
Help I was absent when she taught this
DedPeter [7]

Answer:

b

Step-by-step explanation:

4 0
2 years ago
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