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Pepsi [2]
3 years ago
7

A temperature recorded in antarctica was -116 degrees fahrenheit. The teMPTURE rECORED iN tHE sHArA dESERT iS 131 dEGREES fAHREN

HEIT. HOW maNY dEGREES wARMER iS 131 dEGREES fAHRENHEIT tHAN -116 dEGREES fAhRENHEIT
Mathematics
1 answer:
Natalka [10]3 years ago
7 0

Step-by-step explanation:

Go from the negetive number to 0 to the positive number. -116 to 0 is 116. Then, 0 to 131 is 131. Do 116+131 then you will find your answer.

Hope this helps.  

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A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria
Kaylis [27]

Answer:

A) The expression for the number of bacteria is P(t) = 400e^{0.7783t}.

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

P' = kP

where P stands for the population of bacteria.

Writing P' as \frac{dP}{dt}, we get

\frac{dP}{dt} = kP.

Notice that this is a separable equation, so

\frac{dP}{P} = kdt.

Then, integrating in both sides of the equality:

\int\frac{dP}{P} = \int kdt.

We have,

\ln P = kt+C.

Now, taking exponential

P(t) = Ce^{kt}.

The next step is to find the value for the constant C. We do this using the initial condition P(0)=400. Recall that this is the initial population of bacteria. So,

400 = P(0) = Ce^{k0}=C.

Hence, the expression becomes

P(t) = 400e^{kt}.

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9000 = 400e^{k4}.

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\frac{90}{4} = e^{4k}.

Taking logarithm

\ln\frac{90}{4} = 4k, so \frac{1}{4}\ln\frac{90}{4} = k.

So, k=0.7783788273, and approximating to the fourth decimal place we can take k=0.7783. Hence,

P(t) = 400e^{0.7783t}.

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

P(5) =400e^{0.7783*5} = 19593.723 \approx 19593.  

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30000 = 400e^{0.7783t}.

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75 = e^{0.7783t}.

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\ln 75 = 0.7783t.

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t = \frac{\ln 75}{0.7783} \approx 5.55.

So, after 5.55 hours the population of bacteria will reach 30000.

6 0
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ElenaW [278]

Answer:

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no matter if u oppose the root

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(ii)((\frac{\sqrt{10} }{2})^{2} - 3 (\frac{\sqrt{10} }{2})(-\frac{\sqrt{10} }{2}) + ((-\frac{\sqrt{10} }{2})^{2}) = \frac{25}{2}

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4 0
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