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3 years ago

Are these fractions equivalent or nonequivalent?xy/4y x/4

Mathematics

1 answer:

Nina [5.8K]3 years ago

8 0

Answer:

They are equivalent

Step-by-step explanation:

x/4 multiplied by y/y equals to xy/4y. Therefore, they are equivalent

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Tell whether the following relation is a function or not<br><br>3<br>. 2

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3 years ago

What is the sum of the interior angles of the polygon shown below?

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Answer:A quadrilateral always has a sum of 360o in total.

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3 years ago

Read 2 more answers

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.

6 0

3 years ago

If a complementary angle measures 24 more than the other what is that angle

Lelu [443]

The definition of a complementary angle is one angle who can be added to another complementary angle to sum to 90 degrees. More simply, just an angle is complementary to another angle if they add up to 90 degrees. In this case, to find the other angle, you subtract 24 from 90 which equals 66 degrees.

5 0

3 years ago

PLEASE HHELP!!! Bring the fraction:

Anna35 [415]

Answer:

$\frac{b}{7a^2c} = \frac{5abc^2}{35a^3c^3}$