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3 years ago

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What is the length of ? Round to the nearest tenth.

2 answers:

nalin [4]3 years ago

8 0

C. 14.5cm

hope this helps!

Ivenika [448]3 years ago

3 0

The answer is C:14.5

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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

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

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

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

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:

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

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

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

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

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3 years ago

The values of sine and cosine are always between 0 and 1. True or False

o-na [289]

Answer: True

Step-by-step explanation:

The length of the sides of a right triangle are always less than the length of the hypotenuse.

Also, the ratio of any side of a triangle and the hypotenuse is always less than 1.

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3 years ago

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Five of the quotient of a number

ipn [44]

Answer:

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3 years ago

draw a line representing the rise and a line repenting the run of the line. state the slope of the line in simplest

nexus9112 [7]

You need to select two points on the line:

The rise is the vertical distance, and the run is the horizontal distance:

Rise: Use the coordinates in y to find the rise:

$rise=-5.5-(-1)=-5.5+1=-4.5$

Run: Use the coordinates in x to find the run:

$\text{run}=0-9=-9$ The slope (m) is: 1/2 or 0.5 $\begin{gathered} m=\frac{rise}{\text{run}} \\ \\ m=\frac{-4.5}{-9}=\frac{1}{2} \end{gathered}$

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1 year ago

Write an equation of the line passing through the points (3,7) and (-1,-13)

kykrilka [37]

Answer:

Step-by-step explanation:

(-13 - 7)/(-1 + 3) = -20/2 = -10

y - 7 = -10(x - 3)

y - 7 = -10x + 30

y = - 10x + 37

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3 years ago