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dangina [55]
3 years ago
7

If f(x) = -4x^2 - 6x - 1 and g(x) = -x^2 - 5x + 3, find (f + g)(x).

Mathematics
1 answer:
Flauer [41]3 years ago
7 0

Answer:

-5x^{2}-11x+2

Step-by-step explanation:

-4x^{2} \\-6x-1-x^{2}-5x+3=-5x^{2}-11x+2

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A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is checked 60 minutes later, it is
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Answer:

P(t) = 100e^{0.0251t}

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

P(t) = P(0)e^{kt}

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that P(0) = 100. So

P(t) = 100e^{kt}

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that P(60) = 450, and we use this to find k. So

450 = 100e^{60k}

e^{60k} = 4.5

\ln{e^{60k}} = \ln{4.5}

60k = \ln{4.5}

k = \frac{\ln{4.5}}{60}

k = 0.0251

So

P(t) = 100e^{0.0251t}

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

200 = 100e^{0.0251t}

e^{0.0251t} = 2

\ln{e^{0.0251t}} = \ln{2}

0.0251t = \ln{2}

t = \frac{\ln{2}}{0.0251}

t = 27.65

The doubling time is of 27.65 minutes.

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Answer:

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